Combining linear-scaling quantum transport and machine-learning molecular dynamics to study thermal and electronic transports in complex materials.

We propose an efficient approach for simultaneous prediction of thermal and electronic transport properties in complex materials. Firstly, a highly efficient machine-learned neuroevolution potential (NEP) is trained using reference data from quantum-mechanical density-functional theory calculations. This trained potential is then applied in large-scale molecular dynamics simulations, enabling the generation of realistic structures and accurate characterization of thermal transport properties. In addition, molecular dynamics simulations of atoms and linear-scaling quantum transport calculations of electrons are coupled to account for the electron-phonon scattering and other disorders that affect the charge carriers governing the electronic transport properties. We demonstrate the usefulness of this unified approach by studying electronic transport in pristine graphene and thermoelectric transport properties of a graphene antidot lattice, with a general-purpose NEP developed for carbon systems based on an extensive dataset.

Curvature and van der Waals interface effects on thermal transport in carbon nanotube bundles.

A van der Waals (vdW) heterostructure, can be used in efficient heat management, due to its promising anisotropic thermal transport feature, with high heat conductance in one direction and low conductance in the rest. A carbon nanotube (CNT) bundle, can be used as one of the most feasible vdW heterostructures in a wide range of nanoscale devices. However, detailed investigations of heat transport in CNT bundles are still lacking. In this paper, we study heat transport in different CNT bundles-homogeneous bundles consisting of the one CNT radius (curvature) and inhomogeneous bundles constructed from different CNTs with different curvatures. We also investigate the comparison between two possible thermostatting configurations: the two ends connected (TEC) case in which there is at least a direct covalently connected path between the hot and cold heat baths, and the one end connected (OEC) case in which the system can be divided at least into two parts, by a vdW interacting interface. Nonequilibrium molecular dynamics simulations have been carried out for a wide range of configurations and curvature differences. We find that, in homogeneous bundles, by increasing the number of outer CNTs, the heat conductance increases. In inhomogeneous bundles, the total heat flux shows dependence on the difference between the curvature of the core and outer CNTs. The less the difference between the curvature of the core and the outer CNTs, the more the thermal conductance in the system. By investigating the spectral heat conductance (SHC) in the system, we found that a larger curvature difference between the core and outer CNTs leads to a considerable decrease in the contribution of 0-10 THz phonons in the bundled zone. These results provide an insightful understanding of the heat transport mechanism in vdW nano-heterostructures, more important for designing nanoelectronic devices as well as systems in which asymmetry plays a significant role.

Engineering Thermal Transport across Layered Graphene-MoS2 Superlattices.

Layering two-dimensional van der Waals materials provides a high degree of control over atomic placement, which could enable tailoring of vibrational spectra and heat flow at the sub-nanometer scale. Here, using spatially resolved ultrafast thermoreflectance and spectroscopy, we uncover the design rules governing cross-plane heat transport in superlattices assembled from monolayers of graphene (G) and MoS2 (M). Using a combinatorial experimental approach, we probe nine different stacking sequences, G, GG, MG, GGG, GMG, GGMG, GMGG, GMMG, and GMGMG, and identify the effects of vibrational mismatch, interlayer adhesion, and junction asymmetry on thermal transport. Pure G sequences display evidence of quasi-ballistic transport, whereas adding even a single M layer strongly disrupts heat conduction. The experimental data are described well by molecular dynamics simulations, which include thermal expansion, accounting for the effect of finite temperature on the interlayer spacing. The simulations show that an increase of ∼2.4% in the layer separation of GMGMG, relative to its value at 300 K, can lead to a doubling of the thermal resistance. Using these design rules, we experimentally demonstrate a five-layer GMGMG superlattice "thermal metamaterial" with an ultralow effective cross-plane thermal conductivity comparable to that of air.

Solid Solution Yb2-xCaxCdSb2: Structure, Thermoelectric Properties, and Quality Factor.

Solid solutions of Yb2-xAxCdSb2 (A = Ca, Sr, Eu; x ≤ 1) are of interest for their promising thermoelectric (TE) properties. Of these solid solutions, Yb2-xCaxCdSb2 has end members with different crystal structures. Yb2CdSb2 crystallizes in the polar space group Cmc21, whereas Ca2CdSb2 crystallizes in the centrosymmetric space group Pnma. Other solid solutions, Yb2-xAxCdSb2 (A = Sr, Eu), crystallize in the polar space group for x ≤ 1, and compositions with x ≥ 1 have not been reported. Both structure types are composed of corner-sharing CdSb4 tetrahedra condensed into sheets that differ by the stacking of the layers. Single crystals of the solid solution Yb2-xCaxCdSb2 (x = 0-1) were studied to elucidate the structural transition between the Yb2CdSb2 and Ca2CdSb2 structure types. For x ≤ 1, the structures remain in the polar space group Cmc21. As the Ca content is increased, a positional disorder arises in the intralayer cation sites (Yb2/Ca2) and the Cd site, resulting in inversion of the CdSb4 tetrahedral chain. This phenomenon could be indicative of an intergrowth of the opposing space group. The TE properties of polycrystalline samples of Yb2-xCaxCdSb2 (x ≤ 1) were measured from 300 to 525 K. The lattice thermal conductivity is extremely low (0.3-0.4 W/m·K) and the Seebeck coefficients are high (100-180 µV/K) across the temperature range. First-principles calculations show a minimum in the thermal conductivity for the x = 0.3 composition, in good agreement with experimental data. The low thermal conductivity stems from the acoustic branches being confined to low frequencies and a large number of phonon scattering channels provided by the localized optical branches. The TE quality factor of the Yb1.7A0.3CdSb2 (A = Ca, Sr, Eu) series has been calculated and predicts that the A = Ca and Sr solid solutions may not improve with carrier concentration optimization but that the Eu series is worthy of additional modifications. Overall, the x = 0.3 compositions provide the highest zT because they provide the best electronic properties with the lowest thermal conductivity.

Short-Range Order in GeSn Alloy.

Group IV alloys have been long viewed as homogeneous random solid solutions since perceiving them as Si-compatible, direct-band gap semiconductors 30 years ago. Such a perception underlies the understanding, interpretation, and prediction of alloys' properties. However, as the race to create scalable and tunable device materials enters a composition domain far beyond the alloys' equilibrium solubility, a fundamental question emerges as to how random these alloys truly are. Here, we show, by combining statistical sampling and large-scale ab initio calculations, that GeSn alloy, a promising group IV alloy for mid-infrared technology, exhibits a clear short-range order for solute atoms within its entire composition range. Such a short-range order is further found to substantially affect the electronic properties of GeSn. We demonstrate that the proper inclusion of this short-range order through canonical sampling can lead to a significant improvement over previous predictions on alloy's band gaps by showing an excellent agreement with experiments within the entire studied composition range. Our finding thus not only calls for an important revision of the current structural model for group IV alloy but also suggests that short-range order may generically exist in different types of alloys.

Mn-intercalated MoSe2 under pressure: Electronic structure and vibrational characterization of a dilute magnetic semiconductor.

Intercalation offers a promising way to alter the physical properties of two-dimensional (2D) layered materials. Here, we investigate the electronic and vibrational properties of 2D layered MoSe2 intercalated with atomic manganese at ambient and high pressure up to 7 GPa by Raman scattering and electronic structure calculations. The behavior of optical phonons is studied experimentally with a diamond anvil cell and computationally through density functional theory calculations. Experiment and theory show excellent agreement in optical phonon behavior. The previously Raman inactive A2u mode is activated and enhanced with intercalation and pressure, and a new Raman mode appears upon decompression, indicating a possible onset of a localized structural transition, involving the bonding or trapping of the intercalant in 2D layered materials. Density functional theory calculations reveal a shift of the Fermi level into the conduction band and spin polarization in MnxMoSe2 that increases at low Mn concentrations and low pressure. Our results suggest that intercalation and pressurization of van der Waals materials may allow one to obtain dilute magnetic semiconductors with controllable properties, providing a viable route for the development of new materials for spintronic applications.

Influence of thermostatting on nonequilibrium molecular dynamics simulations of heat conduction in solids.

Nonequilibrium molecular dynamics (NEMD) has been extensively used to study thermal transport at various length scales in many materials. In this method, two local thermostats at different temperatures are used to generate a nonequilibrium steady state with a constant heat flux. Conventionally, the thermal conductivity of a finite system is calculated as the ratio between the heat flux and the temperature gradient extracted from the linear part of the temperature profile away from the local thermostats. Here, we show that, with a proper choice of the thermostat, the nonlinear part of the temperature profile should actually not be excluded in thermal transport calculations. We compare NEMD results against those from the atomistic Green's function method in the ballistic regime and those from the homogeneous nonequilibrium molecular dynamics method in the ballistic-to-diffusive regime. These comparisons suggest that in all the transport regimes, one should directly calculate the thermal conductance from the temperature difference between the heat source and sink and, if needed, convert it into the thermal conductivity by multiplying it with the system length. Furthermore, we find that the Langevin thermostat outperforms the Nosé-Hoover (chain) thermostat in NEMD simulations because of its stochastic and local nature. We show that this is particularly important for studying asymmetric carbon-based nanostructures, for which the Nosé-Hoover thermostat can produce artifacts leading to unphysical thermal rectification.

Publisher Correction: An electrochemical thermal transistor.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Quasi-Ballistic Thermal Transport Across MoS2 Thin Films.

Layered two-dimensional (2D) materials have highly anisotropic thermal properties between the in-plane and cross-plane directions. Conventionally, it is thought that cross-plane thermal conductivities (κ z) are low, and therefore c-axis phonon mean free paths (MFPs) are small. Here, we measure κ z across MoS2 films of varying thickness (20-240 nm) and uncover evidence of very long c-axis phonon MFPs at room temperature in these layered semiconductors. Experimental data obtained using time-domain thermoreflectance (TDTR) are in good agreement with first-principles density functional theory (DFT). These calculations suggest that ∼50% of the heat is carried by phonons with MFP > 200 nm, exceeding kinetic theory estimates by nearly 2 orders of magnitude. Because of quasi-ballistic effects, the κ z of nanometer-thin films of MoS2 scales with their thickness and the volumetric thermal resistance asymptotes to a nonzero value, ∼10 m2 K GW-1. This contributes as much as 30% to the total thermal resistance of a 20 nm thick film, the rest being limited by thermal interface resistance with the SiO2 substrate and top-side aluminum transducer. These findings are essential for understanding heat flow across nanometer-thin films of MoS2 for optoelectronic and thermoelectric applications.

An electrochemical thermal transistor.

The ability to actively regulate heat flow at the nanoscale could be a game changer for applications in thermal management and energy harvesting. Such a breakthrough could also enable the control of heat flow using thermal circuits, in a manner analogous to electronic circuits. Here we demonstrate switchable thermal transistors with an order of magnitude thermal on/off ratio, based on reversible electrochemical lithium intercalation in MoS2 thin films. We use spatially-resolved time-domain thermoreflectance to map the lithium ion distribution during device operation, and atomic force microscopy to show that the lithiated state correlates with increased thickness and surface roughness. First principles calculations reveal that the thermal conductance modulation is due to phonon scattering by lithium rattler modes, c-axis strain, and stacking disorder. This study lays the foundation for electrochemically-driven nanoscale thermal regulators, and establishes thermal metrology as a useful probe of spatio-temporal intercalant dynamics in nanomaterials.

Efficient thermal diode with ballistic spacer.

Thermal rectification is of importance not only for fundamental physics, but also for potential applications in thermal manipulations and thermal management. However, thermal rectification effect usually decays rapidly with system size. Here, we show that a mass-graded system, with two diffusive leads separated by a ballistic spacer, can exhibit large thermal rectification effect, with the rectification factor independent of system size. The underlying mechanism is explained in terms of the effective size-independent thermal gradient and the match or mismatch of the phonon bands. We also show the robustness of the thermal diode upon variation of the model's parameters. Our finding suggests a promising way for designing realistic efficient thermal diodes.

Anisotropy Enhancement of Thermal Energy Transport in Supported Black Phosphorene.

Thermal anisotropy along the basal plane of materials possesses both theoretical importance and application value in thermal transport and thermoelectricity. Though common two-dimensional materials may exhibit in-plane thermal anisotropy when suspended, thermal anisotropy would often disappear when supported on a substrate. In this Letter, we find a strong anisotropy enhancement of thermal energy transport in supported black phosphorene. The chiral preference of energy transport in the zigzag rather than the armchair direction is greatly enhanced by coupling to the substrate, up to a factor of approximately 2-fold compared to the suspended one. The enhancement originates from its puckered lattice structure, where the nonplanar armchair energy transport relies on the out-of-plane corrugation and thus would be hindered by the flexural suppression due to the substrate, while the planar zigzag energy transport is not. As a result, thermal conductivity of supported black phosphorene shows a consistent anisotropy enhancement under different temperatures and substrate coupling strengths.

Thermoelectricity of interacting particles: a numerical approach.

A method for computing the thermopower in interacting systems is proposed. This approach, which relies on Monte Carlo simulations, is illustrated first for a diatomic chain of hard-point elastically colliding particles and then in the case of a one-dimensional gas with (screened) Coulomb interparticle interaction. Numerical simulations up to N>10^{4} particles confirm the general theoretical arguments for momentum-conserving systems and show that the thermoelectric figure of merit increases linearly with the system size.

Finite-size effects on current correlation functions.

We study why the calculation of current correlation functions (CCFs) still suffers from finite-size effects even when the periodic boundary condition is taken. Two important one-dimensional, momentum-conserving systems are investigated as examples. Intriguingly, it is found that the state of a system recurs in the sense of microcanonical ensemble average, and such recurrence may result in oscillations in CCFs. Meanwhile, we find that the sound mode collisions induce an extra time decay in a current so that its correlation function decays faster (slower) in a smaller (larger) system. Based on these two unveiled mechanisms, a procedure for correctly evaluating the decay rate of a CCF is proposed, with which our analysis suggests that the global energy CCF decays as ∼ t(-2/3) in the diatomic hard-core gas model and in a manner close to ∼ t(-1/2) in the Fermi-Pasta-Ulam-ß model.

Nonintegrability and the Fourier heat conduction law.

We study in momentum-conserving systems, how nonintegrable dynamics may affect thermal transport properties. As illustrating examples, two one-dimensional (1D) diatomic chains, representing 1D fluids and lattices, respectively, are numerically investigated. In both models, the two species of atoms are assigned two different masses and are arranged alternatively. The systems are nonintegrable unless the mass ratio is one. We find that when the mass ratio is slightly different from one, the heat conductivity may keep significantly unchanged over a certain range of the system size and as the mass ratio tends to one, this range may expand rapidly. These results establish a new connection between the macroscopic thermal transport properties and the underlying dynamics.