A Voyage Intersecting Nano, Heat, and Energy: Professor Gang Chen’s Scientific Contributions

Professor Gang Chen turns 60 this year. He has made seminal contributions to nanoscale heat transfer and energy sciences in his career spanning over three decades. He has achieved both fundamental progresses and technological advancements with a profound impact on the scientific community and society at large. He is also a prolific educator, having mentored over 100 graduate students and postdocs, many of whom now occupy research and teaching positions in top institutions around the world. With this Special Issue in the Journal of Heat and Mass Transfer, we celebrate Professor Gang Chen’s multifaceted contribution to science and the scientific community by compiling research papers reporting recent progress by former members of his group, including one by Professor Chen himself.

Gang’s main research area is heat transfer and thermal science and their applications in energy systems. He often summarizes his broad research interest with three intersecting themes: Nano, Heat, and Energy. Taking a fundamental approach, Gang incorporates his deep knowledge in solid-state physics, statistical thermodynamics, and electromagnetism into heat transfer research, pushing its frontier into the smallest length and time scales. In this process, he pioneered many concepts in nanoscale heat transfer that have led to transformative advancements in renewable energy technologies. For example, Gang provided a solution of the phonon Boltzmann transport equation along the cross-plane direction of a superlattice [1], elucidating the role of interfaces in scattering phonons and reducing the thermal conductivity. This work laid the theoretical foundation for the nanostructuring approach of processing thermoelectric materials [2], a breakthrough in thermoelectric research. Gang’s other field-defining contributions include the experimental demonstration of enhanced radiative heat transfer at nanometer gaps [3], theoretical and experimental investigation of superior heat conduction in aligned polymer chains [4,5], coherent phonon transport and phonon localization [6,7], and his more recent works on applied energy systems, such as solar vapor generation [8,9]: the list goes on and on. For these original contributions, Gang is widely recognized as one of the pioneers establishing the field of nanoscale thermal transport. This Editorial briefly reviews Professor Gang Chen’s scientific contributions in five main areas: (1) nondiffusive phonon transport; (2) nanostructured thermoelectrics; (3) nanoscale thermal radiation; (4) thermal transport in polymers; and (5) solar-photovoltaic-thermal energy engineering. By no means do we attempt to cover the entire scope of research documented in Gang’s more than 400 journal publications. Instead, we discuss his representative works and summarize their scientific significance within a broader context, including a survey of the impact of these original results on defining new frontiers in each area.

Heat transfer is an old science, whose formal establishment is usually attributed to Fourier’s treatise on the theory of heat conduction in 1822 [10]. In the following two centuries, heat conduction was often referred to as heat diffusion, based on the common understanding that heat conduction is a “diffusive” process. Diffusive transport often implies two features of the underlying microscopic process: (1) the microscopic energy carriers can be modeled as particles, with insignificant wave nature and phase coherence; (2) the microscopic energy carriers experience significant intrinsic scattering events such that their mean free path (MFP) is much shorter than the extrinsic lengthscale associated with the driving temperature difference. In common solids, heat conduction is mediated by electrons and phonons (quantized lattice waves), and both conditions are often met in macroscopic samples. For example, a textbook estimation of the phonon MFP due to intrinsic phonon–phonon scattering in silicon at room temperature is roughly 50 nm [11]. Frequent intrinsic scattering events, such as phonon–phonon and electron–phonon scatterings, facilitate the thermalization of electrons and phonons, whose distribution functions only deviate slightly from local equilibrium distribution functions, a signature for diffusive transport. Therefore, heat conduction in a macroscopic sample can be accurately described using diffusive transport laws, such as Fourier’s law.

With the rapid advancement of nanotechnology over the past few decades, however, the notion of “heat diffusion” started to be challenged as the characteristic size of many devices, such as CMOS transistors, becomes comparable and even much smaller than the intrinsic MFP. In this new regime, novel behaviors of heat conduction emerge because of the breakdown of the assumptions underlying diffusive transport processes. Over his career, Gang has made systematic contributions to our fundamental understanding of these emerging nondiffusive heat conduction regimes, such as ballistic phonon transport, hydrodynamic phonon transport, and coherent phonon transport. In this section, we briefly review his seminal work in this direction.

When the characteristic device size becomes smaller than the intrinsic MFP of microscopic energy carriers such as electrons and phonons, these carriers experience more frequent scatterings with extrinsic sample boundaries and interfaces than intrinsic thermalizing scatterings, leading to the breakdown of local equilibrium and failure of diffusive transport laws. This scenario of ballistic or quasi-ballistic transport was first explored by Knudsen in rarefied gas flow and later studied by Fuchs and Sondheimer in electrical conduction in thin films. Early investigations of the ballistic transport of heat-carrying phonons in nanoscale recognized the similarity between ballistic phonons and photons as described in radiative heat transfer. For example, Majumdar showed that the governing phonon Boltzmann transport equation has a similar form as the radiative transport equation under certain approximations and, thus, analogies between ballistic phonon transport and radiative transfer can often be drawn [12]. In the early stage of his career, Gang conducted a series of theoretical and experimental studies on the thermal conductivity of thin films (quantum wells) and superlattices [13–17], motivated by the thermal management issues of III–V quantum well lasers and vertical-cavity surface-emitting lasers at the time. Based on the phonon Boltzmann transport equation and models of phonon–boundary scattering, Gang showed that the thermal conductivity in thin films and superlattices with nanoscale thickness (much shorter than intrinsic phonon MFP) is largely suppressed from its bulk value. In these structures, while phonons travel quasi-ballistically between collisions with the boundaries and interfaces, the small distance traveled between collisions effectively shortens the average MFP of heat-carrying phonons, reducing the effective thermal conductivity in the material. This quasi-ballistic phonon conduction bottleneck is now widely recognized as a fundamental challenge in the thermal management of micro-electronic and nano-electronic devices [18].

Many of Gang’s early investigations of quasi-ballistic phonon transport laid the foundation for later important developments. For example, in a seminal study, Gang showed that heat conduction from a small heat source, whose size is much smaller than the phonon MFP of the surrounding medium, is significantly reduced from that predicted by using Fourier’s law [19]. This manifestation of ballistic phonon bottleneck was later confirmed using an optical measurement with small optical pump beam sizes [20] and served as the basis for the development of experimental techniques to map phonon MFP distribution in materials [21,22]. In another foundational work, Gang modeled the cross-plane heat conduction in a superlattice by solving the phonon Boltzmann transport equation coupled with elastic versus inelastic, and diffuse versus specular phonon–interface scatterings [1] (Fig. 1(a)). In this work, Gang systematically examined the role of quasi-ballistic phonon transport within each layer and interfacial phonon transport. He found that the thermal boundary resistance in these systems is no longer an intrinsic property of the interfaces but depends on the layer thickness and phonon MFP. Furthermore, this work suggested that, when the layer thickness is sufficiently small compared to the phonon MFP, the effective thermal conductivity of the superlattice is largely controlled by diffuse and inelastic scattering processes at interfaces. This observation provided the theoretical basis for the nanostructuring approach to reduce the thermal conductivity of bulk thermoelectrics [2], where the density of nanoscale grain boundaries was optimized to block phonon flow. Moreover, in this work, Gang also theoretically explored the roles of coherent phonon transport in superlattices, augmented by several subsequent papers [23,24], which was later experimentally observed in GaAs/AlAs superlattices [6] and will be discussed more in Sec. 2.2. Another important contribution by Gang in this period was the development of ballistic–diffusive heat conduction equations that bridge the complex phonon Boltzmann transport equation with the simple but inaccurate Fourier’s law in the quasi-ballistic transport regime [25,26].

Building upon these foundational understanding of quasi-ballistic phonon transport, Gang also made extensive contributions to developing simulation methods to reveal detailed phonon transport properties in realistic materials. Working with Sebastian Volz, Gang pioneered the application of equilibrium molecular dynamics (EMD) simulation together with the Green–Kubo formula to analyze phonon transport and thermal conductivity in Si bulk crystals [27] and Si/Ge superlattices [28]. They showed that EMD simulations with model potentials can accurately compute the thermal conductivity of high-thermal-conductivity materials like Si despite the small size of the simulation domain compared to the dominant phonon MFP. Asegun Henry and Gang further applied EMD simulation to quantify the MFP of individual phonon modes in Si and used an accumulated contribution to thermal conductivity by phonons with different MFPs to graphically show the distribution of phonon MFPs and their relative contribution to heat conduction [29]. This representation has now become a standard way to report phonon MFP distributions in materials. Their result showed that the phonon MFP in silicon has a wide distribution from tens of nanometers to tens of micrometers, with 50% of the thermal conductivity contributed from phonons with MFP shorter than 1 $μ$m, which was a significant refinement of the textbook estimation of a single MFP. This detailed mapping of phonon MFP distribution in real materials also provides important guidelines for designing nanostructures to engineer thermal transport in materials, such as nanostructure thermoelectrics [2].

Working with Keivan Esfarjani, David Broido, and others, Gang further advanced the prediction of phonon transport properties in real materials combining density functional theory (DFT) and lattice dynamics simulations [30]. Within this framework, interatomic forces when atoms are displaced from their equilibrium positions in real materials are calculated using DFT, from which second- and third-order force constants can be extracted. Based on the force constants, phonon dispersion relations and anharmonic phonon–phonon scattering rates can be computed, from which the thermal conductivity can be evaluated by solving the phonon Boltzmann transport equation. Compared to molecular dynamics, this method does not rely on model potentials for interatomic forces and can more directly provide mode-resolved phonon transport properties. Using this method, Gang’s group systematically evaluated phonon properties and MFP distributions in a wide range of materials, in particular thermoelectrics [31–35], with remarkable agreement with experimental measurements. In addition, Gang’s group also improved atomistic Green’s function method with force constants evaluated from DFT to provide more accurate and detailed understanding of phonon–interface interaction beyond conventional acoustic-mismatch and diffuse-mismatch models [36].

In parallel, Gang’s group and collaborators also pioneered experimental techniques to map the phonon MFP distribution in real materials. Austin Minnich and Gang first reported that the nominal thermal conductivity of Si measured by time-domain thermoreflectance (TDTR), an optical pump-probe technique that is routinely used to measure thermal conductivity in solids [37], was suppressed when the optical pump beam size was reduced, an effect that became particularly strong at lower temperatures [20] (Fig. 1(b)). This observation was reminiscent of Gang’s early theoretical investigation on the effect of small heat sources on quasi-ballistic phonon transport [19] and was thus attributed to the fact that the optical pump beam size was smaller than the MFP of certain long-wavelength heat-carrying acoustic phonons, which became much longer at lower temperatures. This explanation was confirmed by comparing the phonon MFP distribution extracted from the experiment to that computed using the DFT framework. Working with Keith Nelson group and others, Gang’s group utilized another optical spectroscopic method, transient grating spectroscopy (TGS), to detect quasi-ballistic phonon transport. In TGS, the periodicity of the optical excitation can be tuned to be comparable or smaller than the MFP of heat-carrying phonons, thus reducing the effective thermal conductivity [22]. However, optical diffraction limits the lengthscale that can be probed directly by TDTR and TGS. To overcome this limitation, Yongjie Hu, Lingping Zeng, and Gang used nanofabrication techniques to fabricate nanoscale transducers in TDTR to directly probe quasi-ballistic phonon transport down to 30 nm [21,38]. Collaborating with Keith Nelson and Alexei Maznev, Gang’s group also developed optical methods to directly probe phonon–electron scattering in Si membranes [39].

As micro to nanoscale devices containing dissimilar materials and interfaces became popular and interfaces were considered a common approach to manipulate thermal transport in solids, there was a growing interest in understanding thermal transport in heterostructures. The study of thermal transport mechanisms in heterostructures considered two extreme limits. In the first limit, interfaces cause complete diffuse phonon scattering, resulting in the loss of phase information of phonons. This scenario eliminates any wave interference effect, and interface scattering effectively reduces overall thermal conductivity. In the second limit, diffuse interface scattering is negligibly weak, allowing phonons to maintain their phase information. In this situation, wave interference occurs, and the entire system exhibits new phonon eigenmodes that differ from the eigenmodes of each constituent material. In such cases, the interface does not strongly suppress thermal transport. Superlattices were commonly used as model systems to study the nature of these extremes. Gang’s group has made significant contributions to this topic through simulations and experiments on superlattices. In an early work, Gang’s group developed a model that combines both coherent and incoherent pictures to explain the experimental thermal conductivity values of superlattices [24]. Their simulations demonstrated a transition from incoherent to coherent phonon transport as the period thickness decreases, highlighting the importance of considering both aspects to understand the experimental data. Although the coherent phonon transport was considered, its experimental evidence had remained inconclusive. Some previous studies observed coherent phonons, but they were limited to a single frequency and did not measure coherent thermal transport across a broad spectrum [40]. As the first-principles-based method and ultrafast pump-probe method became available, the group was able to report clear evidence for coherent phonon transport in superlattices [6] (Figs. 1(c) and 1(d)). In contrast to previous studies that varied interface roughness and period thickness, they measured thermal conductivity as a function of the number of periods. By using GaAs/AlAs superlattices with smooth interfaces and thus minimal diffuse boundary scattering, the group observed that thermal conductivity increased with the number of periods below 150 K as shown in Fig. 1(d), clearly indicating coherent phonon transport. Even at room temperature, the trend remained significant, though not as clear as in the low-temperature cases. These experimental observations were supported by first-principles-based calculations, which showed that low-frequency phonons have very long mean free paths, much longer than the periods, and contribute significantly to heat transport despite their relatively small density of states. Atomistic Green’s function simulations also demonstrated a similar trend to the experiments, where thermal conductivity increased with the number of periods. The presence of phonon coherence suggested that the interfaces are not effective in suppressing thermal transport by low-frequency phonons. To address this issue, the group investigated methods to effectively scatter low-frequency phonons and break the phonon coherence. They measured the thermal conductivity of GaAs/AlAs superlattices with randomly placed ErAs nanodots at the interfaces [7]. The inclusion of nanodots significantly suppressed thermal conductivity compared to superlattices without nanodots. Interestingly, they observed that the thermal conductivity of superlattices with nanodots at 30 K initially increased and then decreased with the number of periods, while superlattices without nanodots exhibited a monotonic increase followed by saturation of thermal conductivity. They attributed these results to the phenomenon of phonon localization, similar to the Anderson localization of electrons, using large-scale atomistic Green’s function calculations [41]. While the Anderson localization of electrons has been observed, the phonon localization, particularly in three-dimensional materials, had not been reported before.

The nanoscale thermal transport had mostly been discussed in the context of ballistic and diffusive regimes. Gang’s group has revealed that another regime, known as hydrodynamic phonon transport, must be considered for a better understanding of thermal transport in high-thermal-conductivity materials, particularly graphitic materials. The hydrodynamic phonon transport is distinctively different from the ballistic and diffusive regimes. It requires frequent scattering processes, unlike the ballistic regime. In the hydrodynamic regime, momentum-conserving scattering (N-scattering) is the dominant process, while in the diffusive regime, momentum-destroying scattering (U-scattering) needs to be the most dominant process. As a result, phonon transport in the hydrodynamic regime resembles fluid flow, where intermolecular scattering always conserves momentum. Indeed, hydrodynamic phonon transport features phonon Poiseuille flow and second sound, which are analogous to Poiseuille flow and acoustic sound in fluids. Although hydrodynamic phonon transport was extensively studied in the 1960s and 1970s, it was not considered highly relevant to practical engineering applications. The main reason for this is that hydrodynamic phonon transport has only been observed at very low and narrow temperature ranges, since N-scattering is usually much weaker than U-scattering in most solids. Motivated by strong N-scattering reported in graphene by another group [42], Gang’s group studied hydrodynamic phonon transport in graphitic materials. In 2015, Gang’s group predicted for the first time using first-principles-based calculations that hydrodynamic phonon transport can be the dominant regime of thermal transport in graphene up to 100 K [43], which is notably higher than the previously observed conditions (e.g., 15 K for second sound in NaF [44]). The simulation demonstrated the drift motion of phonons, the phonon Poiseuille flow, and the second sound, highlighting the strong features of hydrodynamic phonon transport in graphene. It also showed that the hydrodynamic regime can be as significant as, although not dominant over, the ballistic and diffusive regimes at room temperature. Subsequent numerical studies also showed that hydrodynamic phonon transport is significant in graphite, similar to graphene [45]. The study discovered that graphite exhibits a phonon Knudsen minimum, analogous to the Knudsen minimum in molecular flow, which strongly supports significant hydrodynamic phonon transport. Guided by the theoretical predictions using first-principles-based calculations, Gang’s group experimentally confirmed hydrodynamic phonon transport [46]. They successfully measured second sound at 100 K in commercially available graphite. They developed new experimental methods for detecting second sound based on the transient thermal grating setup, which is a substantial improvement from the conventional heat-pulse experiments conducted in the 1960s. The experiment showed wave-like fluctuations in the temperature field after a periodically applied heating pump beam, providing clear support for second sound in the graphite sample. Their efforts continued, and the group was able to reduce the grating period to 2 $μ$m from 5 $μ$m, enabling them to access smaller length and shorter temporal scales [47]. This could lead to the successful measurement of second sound in graphite at 200 K.

One prominent application of Gang’s systematic study of quasi-ballistic phonon transport was the development of nanostructured thermoelectrics [2], which initiated a rapid growth period in thermoelectric research for the past 20 years. Thermoelectric power generation first got its reputation in powering the Voyager spacecraft. After a near-30-year stagnation with a figure of merit (zT) limited to around 1, thermoelectrics research was revived in the early 1990s, when the pioneer works of M. S. Dresselhaus theoretically suggested that quantum-well structures could significantly change the transport behavior of charge carriers and hence have the potential to increase zT of thermoelectric materials [48]. Gang’s subsequent studies of suppressed thermal conduction in quantum wells and superlattices further boosted their promise for thermoelectric applications. Having collaborated closely with Dresselhaus and Zhifeng Ren, Gang and his group systematically explored the effect of nanostructures on the electrical and thermal transport properties in thermoelectrics with a series of seminal works that revolutionized thermoelectric research. Next, we highlight these contributions and summarize their impact on the recent progress in nanostructured thermoelectrics.

Good thermoelectric materials need to conduct electricity well but conduct heat poorly, often summarized as “electron crystal, phonon glass,” which is reflected by the figure of merit zT proposed by A. F. Ioffe, $zT=(S2σ/κ)T$⁠, where T, S, $σ$⁠, and $κ$ are temperature, Seebeck coefficient, electrical conductivity, and thermal conductivity, respectively. Conventionally, it is challenging to decouple the electrical and heat conduction properties of a single material. For example, the reduction of thermal conductivity can be achieved by the alloying effect to scatter phonons, resulting in the classic thermoelectric materials Si–Ge, Bi₂Te₃–Sb₂Te₃, and Bi₂Te₃–Bi₂Se₃. However, alloy scattering also significantly impacts electrical transport properties. Following the developments in understanding thermal and thermoelectric transport in quantum wells and superlattices in the 1990s, Dresselhaus, Gang, and others pointed out the possibility of using classical and quantum size effects in nanostructures to reduce the phonon thermal conductivity without causing much degradation of the power factor (⁠$S2σ$⁠) to pursue a higher zT [49,50]. The general idea is to boost the electronic density of states near band edges via a 3D to 2D (or 1D) transition of the electronic band structure to enhance the Seebeck coefficient [48], while using nanoscale interfaces to scatter and confine phonons and reduce the thermal conductivity [51–53]. While the interfaces can also scatter electrons, it was expected that electrons and phonons can have disparate MFP distributions, enabling the decoupling of electrical conduction and phonon conduction with rationally designed nanostructures. Later, first-principles simulations indeed confirmed that the electron MFP is usually much shorter than the phonon MFP in many semiconductors [54]. Following these general principles, Gang and collaborators conducted a series of measurements of thermal and thermoelectric properties of thermoelectric thin films and superlattices fabricated using pulsed laser deposition and molecular beam epitaxy [55–59]. The expected enhancements were observed in these experiments, especially the significant reduction of thermal conductivity. Parallel efforts by others during this period also demonstrated the promise of low-dimensional thermoelectric materials [60]. Despite the observed performance enhancements, the small volume and high manufacturing cost of these low-dimensional structures limited their practical applications. One important lesson from this exploratory period was that “…the periodicity of superlattices is not a necessary condition for thermal conductivity reduction. The reduced thermal conductivity in superlattices comes from the sequential interface scattering of phonons rather than the coherent superposition of phonon waves.” [61–63]. This realization led to the development of bulk thermoelectric nanocomposites with randomly distributed nanoscale interfaces that preserve the advantages of low-dimensional structures but overcome their associated volume and cost challenges.

Nanocomposites often refer to a host matrix containing nanoscale inclusions such as nanoparticles and nanowires. Nano-inclusions can be externally added or intrinsically precipitated due to phase separation. Nanocomposites can also be achieved through nonequilibrium synthesis processes, such as high-energy ball milling and melt spinning of precursors followed by hot pressing, or a direct self-propagating combustion synthesis. Among these synthesis routes, ball milling plus hot pressing is the most versatile and can be applied to almost all known thermoelectric material systems. Early adoption of ball milling and hot pressing for processing thermoelectric materials can be traced back to Rowe et al., who obtained fine-grained SiGe alloys in 1981 [64]. As the grain size was reduced to below 5 $μ$m, the corresponding lattice thermal conductivity was decreased by 28% as compared with that of a single crystal. Rowe et al. predicted that the thermal conductivity of SiGe alloys could be even lower if the grain size could be further reduced. However, grain growth during hot pressing remained a challenge in obtaining stable nanosized grains. Zhifeng Ren and Gang overcame this material processing challenge by using direct-current induced hot pressing, also known as spark plasma sintering. It is characterized with a rapid sintering process in a few minutes using a pulse current for heating, which were widely shown to be effective in preventing grain growth. In 2008, Ren, Dresselhaus, and Chen groups reported successful manufacturing of nanostructured SiGe and BiSbTe alloys with grain sizes down to a few nm [2,65,66], with significantly enhanced thermoelectric figure of merit zT mainly due to a reduced thermal conductivity. For example, in the case of BiSbTe alloy, the nanostructured sample showed a thermal conductivity reduction of around 30%, leading to an enhanced zT of 1.4 at 100 °C [2] (Fig. 2). This result represented a significant breakthrough in zT achieved in a bulk thermoelectric material in 50 years, initiating a new paradigm in thermoelectric research. The impact of this work is evidenced by its over 6000 citations since its publication in 2008.

In the following decade, this bulk nanostructuring approach was adopted by research groups worldwide and applied to a broad range of thermoelectric materials [67,68]. For example, Kanatzidis group designed nanocomposite PbTe with point defects and hierarchical nanostructures to scatter a wide spectrum of phonons to achieve a zT of 2.2 at 915 K [69]. In the same period, theoretical and experimental developments in understanding phonon MFP distribution in real materials, an effort led by Gang’s group, contributed to a detailed understanding of the impact of nanosized grains on phonon and electron transport, a manifestation of strong interactions between theory and experiment in Gang’s research. In addition to suppressed phonon transport in nanocomposites, Gang and his group also made fundamental contributions to other innovative concepts in thermoelectric research, such as modulation doping [70], electron cloaking [71,72], resonant doping [73], resonant bonding [74], and phonon drag [75], among others.

Gang and his group have made numerous contributions to radiative heat transfer. Gang’s work has sought to address how the laws of thermal radiation as presented in classic textbooks need to be modified when the fundamental assumptions underlying these classic laws are violated. For example, Gang’s work explored how thermal radiation is modified in nanoscale gaps to achieve heat fluxes that greatly exceed the blackbody limit. Specifically, theoretical and experimental work from Gang’s group in this near-field regime, i.e., the regime where the gap size between objects is comparable to or smaller than the Wien’s wavelength, explored how surface phonon polaritons (SPhPs) can result in dramatic enhancement in radiative heat transfer rates. Further, Gang’s group explored how phonon-polaritons can result in significant contributions to heat transfer in nanoscale films. Finally, more recent work from Gang’s group has explored how the Kirchhoff’s law of thermal radiation, which is central to all far-field radiative heat transfer theories, can be violated in nonreciprocal systems. Below, we provide a brief summary of Gang’s work on radiative heat transfer.

Theoretical exploration of near-field radiative heat transfer (NFRHT): Gang and co-workers employed the dyadic Green’s functions and fluctuational electrodynamics (FED) to calculate the NFRHT for planar or spherical geometries. These theoretical results were further applied to study the energy conversion mechanisms in both near-field thermophotovoltaic cells and thermoradiative cells [76–81]. In order to explore NFRHT, Gang’s group developed theoretical approaches to model NFRHT in the sphere–sphere geometry. Specifically, they modeled NFRHT between spheres of arbitrary diameters and gaps, using a theoretical framework based on dyadic Green’s function of the vector Helmholtz equation and fluctuation–dissipation theorem [77]. Results from this new theory converged with the dipole approximation for spheres of small diameters compared to the wavelength; however, it was found that the Derjaguin approximation [82], which is often used to model NFRHT, is not valid for spheres with diameters much larger than the gap. In addition to modeling NFRHT, Gang and co-workers also explored how near-field effects can be employed for energy conversion. Specifically, they explored near-field thermophotovoltaic configurations, in which the surface modes along polar dielectrics can be utilized to increase the power density and efficiency of thermophotovoltaic generators [76]. Similarly, Gang and co-workers showed that NFRHT enhanced by surface modes can also increase the efficiency and power density of thermoradiative cells [80].

Experimental exploration of near-field heat transfer: Gang and co-workers pioneered an experimental technique to measure the NFRHT between a microsphere and a plate using a bimaterial atomic force microscope (AFM) cantilever as a temperature sensor [3,83,84]. In this experimental platform (Fig. 3(a)), a smooth microsphere with a wide range of sizes and materials (or coatings) was attached to the tip of the AFM cantilever and placed in close proximity to a substrate. A laser beam was used to detect the deflection of the cantilever. The substrate was rigidly fixed to a piezoelectric moving stage which was used to continuously reduce the gap size. In contrast to the standard AFM measurements, the cantilever with the microsphere was oriented perpendicular to the substrate to reduce the bending caused by the Casimir and electrostatic forces. Based on this experimental technique, NFRHT between a sphere and a plate was measured for a variety of materials such as polar dielectrics, semiconductors, and metals. Particularly, due to the contributions from surface modes, NFRHT was demonstrated to exceed the blackbody radiation limit by about 3 orders of magnitude at a 30-nm gap. Furthermore, Gang and co-workers measured the NFRHT between two parallel planar glass surfaces, in which small polystyrene particles were used as spacers to maintain a micron-sized gap. The radiative heat flux across a 1.6-$μ$m gap was demonstrated to exceed the far-field upper limit given by Planck’s law of blackbody radiation for more than 35% [86]. Gang’s seminal work on near-field thermal radiation has inspired a number of investigations in near-field heat transfer in the last few decades, some of which can be found in these review articles [82,87,88]. Recently, Gang and co-workers developed a new scheme to electrically tune NFRHT via ferroelectric materials [81], which could be of significant interest for future studies. Gang’s group has also performed some of the most sophisticated calculations of extreme-NFRHT (that is, the regime in which the gap size between objects is in the nanometer to the subnanometer range). Specifically, in a seminal work [85], they investigated RHT between planar surfaces of two ionic crystals (NaCl) separated by nm to subnm gaps. These computations revealed (Fig. 3(b)) that NFRHT rates can differ significantly from theoretical predictions based on FED when the gap size between surfaces is <1 nm. While FED predicts a divergence in heat transfer at zero gap, these first-principles simulations predict that RHT in <1-nm gaps deviates from FED calculations and monotonically converges to the conduction limit. Experimental progress on extreme-NFRHT has been rather limited [89–93], and these computational predictions will likely motivate significant future work.

Theory by Gang’s group: Inspired by the exploration of near-field radiative heat transfer, Gang and co-workers also made notable contributions that enriched our understanding of heat conduction in solids. As is well known, the heat flow in metals and insulators is often predominantly mediated by electrons and phonons [11]. In contrast to this expectation, in 2005, Gang and co-workers [94] theoretically predicted that SPhPs can also contribute substantially to or even dominate thermal conductivity, especially in amorphous thin films made of polar dielectrics. For example, by including the contribution of SPhPs, the total thermal conductivity of a 40-nm-thick silicon dioxide (SiO₂) film was calculated to be about 4 W m⁻¹ K⁻¹ at 500 K, more than twice the conventional value considering only phonons. It was emphasized that central to such enhancement is the unusually long propagation lengths of the SPhPs, which can even reach a few centimeters. Therefore, comparatively large samples are desired to facilitate the experimental verification of the theoretical results, which presents a nontrivial challenge.

Experiments by others: Following the theoretical work, Gang and colleagues [95] also made an effort to measure the propagation lengths of SPhPs on amorphous SiO₂, obtaining results that agreed well with theoretical calculations (⁠$∼$11 $μ$m for the resonance at 9 $μ$m). In the last few years, several experimental observations of enhanced thermal conductivity in both nanofilms and nanowires have finally been reported, not only for polar dielectrics (e.g., silicon oxide, nitride, and carbide) but also for metals (e.g., titanium, gold, and silver), which benefit from surface plasmon polaritons instead [96–100]. These experimental breakthroughs have not only invigorated this field but also led to interesting new experimental results, which deviate vastly (by almost 2 orders of magnitude) from the predictions of well-accepted models. These deviations, attributed to novel nonequilibrium effects [97] by the authors, require additional work to clarify and can motivate significant future studies.

Gang’s group has also explored how the Kirchhoff’s law of thermal radiation, which states that the spectral directional emittance and the spectral directional absorptance are equal, can be violated. Specifically, past works [101–103] have argued that Kirchhoff’s law is only valid when Lorentz reciprocity [104] is satisfied and therefore can be violated under suitable conditions by breaking Lorentz reciprocity. Past theoretical work [105] has indeed identified that Lorentz reciprocity can be violated in devices featuring magneto-optic materials because the magnetic permeability of such materials can be tuned to be asymmetric by applying a magnetic field enabling breaking of Lorentz reciprocity. However, realization of such effects often requires application of relatively large magnetic fields. In 2020, the groups of Gang Chen and Shanhui Fan simultaneously reported [106–108] how the violation of Kirchhoff’s law can be accomplished in Weyl semimetals without the application of magnetic fields. Specifically, they argued that Lorentz reciprocity can be broken in Weyl semimetals due to internal magnetization even in the absence of an external magnetic field. This internal magnetization arises due to the large anomalous Hall effect associated with enhanced Berry curvature at the Weyl nodes, which act as sources and sinks of Berry curvature. We note that recent experiments [109,110] have indeed shown a violation of Kirchhoff’s law in magneto-optic materials but there are so far no demonstrations in Weyl semimetals, which may offer rich opportunities for future work.

Gang’s interest in thermal transport in polymer chains was extended from his earlier studies of low-dimensional systems. One example is a one-dimensional system with nonlinear interactions, exemplified by isolated polymer chains. For such a system, a classic result by Fermi, Pasta, and Ulam showed that a nonergodic behavior is expected, where microscopic configurations can reemerge periodically [111]. From a thermal transport point of view, this periodic recurrence of energy among a few normal modes suggests that there is no effective energy decay in this system and the thermal conductivity should diverge. Gang and Asegun Henry first used molecular dynamics simulations to study single chains of the simple polymer polyethylene and showed that thermal transport in straight and aligned polyethylene chains can exhibit significantly higher thermal conductivities compared to bulk materials [4,110] (Fig. 4(a)). Through normal mode analysis, they found the reason for the high thermal conductivity is due to the lack of ergodicity leading to nondecayed phonon energy [4]. This seminal result suggested that, contrary to common belief that polymers are poor thermal conductors, highly ordered and aligned polymer chains can give rise to exceptionally high thermal conductivity that is promising for thermal management applications.

To experimentally test these findings, Gang and co-workers developed a novel technique to fabricate ultradrawn polyethylene nanofibers by combining tip-drawing and conventional gel-spun methods [5]. A polyethylene gel was prepared by quenching a decalin solution which contains ultrahigh molecular weight polyethylene. A microscale fiber was drawn from the heated polyethylene gel using a sharp tungsten or glass tip. A second heating procedure was used to heat the fiber close to the glass transition temperature of polyethylene. The fiber was then mechanically stretched (ultradrawn) at a controlled speed. The diameter of the fabricated fibers has a broad range of 50–500 nm, depending on the drawing speed and the heating temperature (Fig. 4(b)). Based on a thermal measurement technique using a sensitive bimaterial AFM cantilever, the thermal conductivities of these nanofibers were measured to be as high as 104 W/m K at room temperature, which is greater than many metals (Fig. 4(c)). Motivated by the seminal experimental work by Chen, subsequent experiments were conducted to investigate the unique thermal transport in polyethylene nanofibers and demonstrate high-performance nanofiber based thermal switches and thermal diodes [113–115].

Gang and co-workers’ research findings on ultrahigh thermal conductivity in polymers like polyethylene, demonstrated through molecular dynamics simulations [4] and experiments [5], have garnered significant industrial interest for thermal management applications [116]. However, the practical use of polyethylene nanofibers has been constrained by their small size and scalability issues, as well as incomplete understanding of the thermal transport mechanisms in polymers. To overcome these challenges, Gang and co-workers developed a new continuous fabrication platform for producing highly aligned polymer films. This platform, which involves a three-step process—sol–gel extrusion, structural freezing and drying, followed by mechanical drawing—scaled the high thermal conductivity of individual nanofibers to macroscale films [117,118]. Polyethylene films achieved a thermal conductivity of 62 W/m K, with structural studies and thermal modeling revealing a combination of crystalline and amorphous regions in the nanofibers, the amorphous region exhibiting a high thermal conductivity exceeding 16 W/m K [118].

Building on experimental advancements, it is noted that there is a limitation in current research: the historical focus on engineering either strong intramolecular interactions, which facilitate efficient thermal transport along polymer chains, or strong intermolecular interactions, which promote thermal transport between chains [119–121]. This traditional approach has overlooked the potential benefits of simultaneously optimizing both types of interactions, thereby limiting the full potential for enhancing thermal conductivity in polymers. Gang and co-workers addressed this limitation by achieving high thermal conductivity in a thin film of the conjugated polymer poly(3-hexylthiophene) using a bottom-up oxidative chemical vapor deposition method. This unique approach leverages both strong C=C covalent bonding along the extended polymer chain and strong $π$–$π$ stacking noncovalent interactions between chains. Systematic structural characterization confirmed the presence of both types of interactions, leading to a near-room temperature thermal conductivity of 2.2 W/m K, which is ten times higher than that of conventional polymers [122]. This achievement represents the first integration of both intramolecular and intermolecular interactions to enhance thermal transport in polymers.

In this section, we briefly review Professor Gang Chen’s contributions to applied energy and material sciences.

Solar thermoelectric generators (STEGs) are solid-state devices able to convert solar power into electricity by means of a two-step process [123]. The system first converts Sun’s light into heat, and then heat into electricity. A typical STEG cell is composed by a selective solar absorber coupled to the hot side of a pair of p-type and n-type thermoelectric elements that generate electricity as depicted in Fig. 1(a). At the cold side, a dissipator rejects the excess heat toward the environment keeping the thermoelectric elements’ cold side at nearly ambient temperature. The system typically has to work in an evacuated environment in order to setup a significant difference of temperature between the hot and cold sides and avoid heat losses. Gang started working on STEGs around 2007. Along with his students Daniel Kraemer, Kenneth McEnaney, and in collaboration with Professor Zhifeng Ren, he first developed a solid theoretical foundation on this matter [124], then moved on to the actual development of STEG systems [125]. It is important to highlight that until that time, several publications had already been published on STEGs for both terrestrial and space applications [123,126], but none of them had been able to reach efficiencies high enough to raise any practical interest.

The first paper from Gang on STEGs can be found in 2011, when he set the theoretical background for the estimation of the maximum efficiency achievable for these kinds of system [124]. This work also introduces the fundamental concept of thermal concentration, for which the thermoelectric element’s cross-sectional area is much smaller than the absorber. This design increases the hot side temperature for a given input from the solar spectrum. On the basis of this theoretical analysis, further supported by later modeling studies [127,128], Gang’s group was able to engineer their first generation of STEG systems, with efficiency reaching 4.6% without optical concentration and 5.2% with 2X optical concentration [125] (Figs. 5(a) and 5(b)). This study had a groundbreaking impact on the thermoelectric community as it sparked the possibility of a real-world application for thermoelectric materials. This was also supported by the fact that the authors estimated a competitive cost of around $0.17 per electrical watt generated. Within the next few years, Gang and his group further improved selective solar absorber materials [129–132] and found new strategies for optical concentration and heat loss prevention [133]. These efforts led to the development of the second generation of STEG systems able to reach an outstanding efficiency of 7.6% at 38X optical concentration and 9.6% at 211X optical concentration [134]. In the following years, Gang and co-workers also explored hybrid systems combining photovoltaic cells and thermoelectric generators to take full use of the entire solar spectrum [135–137].

Gang’s group involved in nanofluids topic from 2005 supported by the Ford-MIT alliance. The purpose of this industrial project was to understand the mechanisms underpinning the higher thermal conductivity of nanofluids than that of their corresponding base fluids which cannot be explained by existing theories [138,139]. However, different groups reported high thermal conductivity of nanofluids that sometimes cannot be reproduced by others even with the same ingredients and techniques. Theoretically, previous mechanisms leading to this enhancement were still under scrutiny. Gang’s group first demonstrated that nanoparticle clustering was the key contributor to the thermal conductivity enhancement in nanofluids [140]. Following this insight, graphite flakes, with micron-sized thin sheets, were used by Gang’s group as additives to prepare stable graphite suspensions, which showed outstanding thermal conductivity enhancement [141]. Gang’s group further observed a new thermal percolation phenomenon, where the thermal conductivity varied with phase changes in a nanofluid, which was analyzed by optical and AC impedance spectroscopy studies [142]. Finally, a temperature regulator/switch was demonstrated based on a nanofluid, with electrical and thermal properties of graphite suspensions changing through a solid–liquid phase change, which might be potentially useful in energy systems in the future [143].

Solar-driven evaporation has the potential for cost-effective steam sterilization and desalination. Improving the overall solar thermal efficiency for water evaporation at the system level has been a major focus of extensive research efforts. Gang’s group became interested in materials approaches for this challenge in approximately 2012. At the time, Gang and Hadi Ghasemi designed a carbon foam supporting a thin exfoliated graphite layer [8] (Fig. 5(c)). The extremely high solar thermal absorptance (⁠$∼$97%) of the graphite, combined with the extremely low conduction loss (⁠$∼$5%) of the carbon foam, enabled a temperature rise of 10 °C under a solar intensity of 1 kW/m². This temperature increase enhances the evaporation rate by a factor of 6 compared to a dark environment, due to the ability of the sandwich structure to localize the heat at the interface where evaporation is taking place (Fig. 5(d)).

This seminal work on solar-driven interfacial evaporation gave rise to a range of works within Gang’s group, while simultaneously sparking a flourishing new research field. Facilitated by this work, over the next few years, the research within this field would grow exponentially. Gang’s group would continue to innovate in this field. For example, steam generation under one-sun illumination was demonstrated by thermal concentration design [9]. Desalination was also identified as a promising application for the solar-driven evaporation concept. Gang’s group developed low-cost floating solar stills capable of passively producing clean drinking water with innovative antifouling designs that prevent the accumulation of salt left behind [144,145].

Parallel to the interfacial system design, volumetric system designs based on photothermal nanomaterials suspended in water (nanofluids) have emerged as an alternative solar-thermal receiver. Previous volumetric approaches have been limited by the comparatively narrow solar absorbance spectrum and the comparatively large convection loss. To address previous limitations due to the comparatively narrow solar absorbance spectrum and large convection loss, Gang’s group designed a volumetric system consisting of nanofluids containing carbon-based nanoparticles suspended in water [146]. This formulation benefits from full spectrum solar absorbance, while the low-thermal-conductivity aerogel insulation helps to mitigate convection loss. Collectively, this delicate design achieved a vapor generation efficiency of 69% at solar concentrations of ten suns.

In addition to its role in reducing thermal convection in the volumetric system, aerogel can also minimize both convective and radiative heat loss in the isolation system, owing to its high transparency, solar spectral selectivity, and low thermal conductivity [147]. Coupling the aerogel with an underlying photothermal absorber enables the system to harness a significant amount of thermal energy, positioning it as a promising solar thermal receiver. Building upon this design principle, Gang’s group collaborated with Evelyn Wang group to design an aerogel-assisted system. In their design, the low-scattering silica aerogel with the tailored nanostructures serves as a transparent window, allowing near-complete passage of sunlight to the underlying blackbody absorber. Simultaneously, the aerogel functions as an insulator, suppressing convection and radiation loss to the environment. This design induces a greenhouse effect for solar energy conversion, resulting in temperatures as high as over 265 °C [148]. The ability to harness diffuse solar energy at intermediate temperatures without relying on expensive mechanical systems paves the way for the use of solar energy for a variety of potential applications.

In recent years, Gang has focused on developing a fundamental understanding of solar-driven water evaporation processes, in particular to explain the experimental observation of evaporation rates exceeding the theoretical thermal evaporation rate limit in some photothermal evaporation processes [149]. Gang has proposed a novel mechanism: direct cleavage of water clusters from the water surface upon interactions with photons in the visible spectrum, which is termed the photomolecular effect. Gang and co-workers have conducted careful experimental investigations of this effect in hydrogels [150] and at a single water/air interface [151], showing strong evidence of absorption of visible light at the water surface. This effect can stem from the discontinuity of the dielectric constant across the water/air interface that leads to a local sharp change of electric field. Gang also developed a phenomenological theory for this effect based on generalized electromagnetic boundary conditions [152]. This is a groundbreaking concept in water–light interaction but more theoretical and experimental studies are needed to elucidate the underlying microscopic process.

Professor Gang Chen has made transformative contributions to nanoscale heat transfer and energy science, profoundly impacting both fundamental research and technological applications. His work has redefined understanding in areas such as nondiffusive phonon transport, nanostructured thermoelectrics, nanoscale thermal radiation, thermal transport in polymers, and solar-photovoltaic-thermal energy systems. Gang’s groundbreaking studies, such as solving the phonon Boltzmann transport equation and exploring coherent phonon transport, have laid the theoretical foundations for advanced thermoelectric materials and nanoscale energy systems. His experimental innovations include techniques to map phonon mean free path distributions and develop high thermal conductivity materials like polyethylene nanofibers. These contributions have enabled breakthroughs in efficient energy harvesting, thermal management, and sustainable water desalination through solar-driven evaporation systems.

Looking forward, Gang’s work points to exciting frontiers in nanoscale energy, heat, and water research. As the challenges of energy efficiency and sustainability grow, Gang’s research continues to inspire future directions in nanotechnology and energy science, fostering a deeper understanding of heat transfer mechanisms and their application to critical global issues. Happy Birthday, Professor Gang Chen!