Wiedemann-Franz Law Research Articles

Two-dimensional topological superconductivity candidate in a van der Waals layered material

Two-dimensional (2D) topological superconductors are highly desired because they not only offer opportunities for exploring novel exotic quantum physics, but also possesses potential applications in quantum computation. However, there are few reports on 2D superconductors, let alone topological superconductors. Here, we find a 2D monolayer W$_2$N$_3$, which can be exfoliated from its real van der Waals bulk material with much lower exfoliation energy than MoS$_2$, to be a topological metal with exotic topological states at different energy level. Due to the Van Hove singularities, the density of states near Fermi level are high, making the monolayer a compensate metal. Moreover, the monolayer W$_2$N$_3$ is unveiled to be a superconductor with the superconducting transition temperature Tc $\sim$ 22 K and a superconducting gap of about 5 meV based on the anisotropic Migdal-Eliashberg formalism, arising from the strong electron-phonon coupling around the $\Gamma$ point. Because of the strong electron and lattice coupling, the monolayer displays a non-Fermi liquid behavior in its normal states at temperatures lower than 80 K, where the specific heat exhibit T$^3$ behavior and the Wiedemann-Franz law dramatically violates. Our findings not only provide the platform to study the emergent phenomena in 2D topological superconductors, but also open a door to discover more 2D high-temperature topological superconductors in van der Waals materials.

Anomalous plasmon mode in strained Weyl semimetals

An exotic anomalous plasmon mode is found in strained Weyl semimetals utilizing the topological Landau Fermi liquid and chiral kinetic theories, in which quasiparticle interactions are modeled by long-range Coulomb and residual short-range interactions. The gapped collective mode is derived from the dynamical charge pumping between the bulk and the surface and behaves like $k_{\rm F}^{-1}$. The charge oscillations are accurately determined by the coupling between the induced electric field and the background pseudofields. This novel mode unidirectionally disperses along the pseudomagnetic field and manifests itself in an unusual thermal conductivity in apparent violation of the Wiedemann-Franz law. The excitation can be achieved experimentally by mechanical vibrations of the crystal lattice in the THz regime.

Thermal resistivity and hydrodynamics of the degenerate electron fluid in antimony

Detecting hydrodynamic fingerprints in the flow of electrons in solids constitutes a dynamic field of investigation in contemporary condensed matter physics. Most attention has been focused on the regime near the degeneracy temperature when the thermal velocity can present a spatially modulated profile. Here, we report on the observation of a hydrodynamic feature in the flow of quasi-ballistic degenerate electrons in bulk antimony. By scrutinizing the temperature dependence of thermal and electric resistivities, we detect a size-dependent departure from the Wiedemann-Franz law, unexpected in the momentum-relaxing picture of transport. This observation finds a natural explanation in the hydrodynamic picture, where upon warming, momentum-conserving collisions reduce quadratically in temperature both viscosity and thermal diffusivity. This effect has been established theoretically and experimentally in normal-state liquid 3He. The comparison of electrons in antimony and fermions in 3He paves the way to a quantification of momentum-conserving fermion-fermion collision rate in different Fermi liquids.

Analysis of Different Thermal Conductivity Measurements for Al-Si Casting Alloys

Three types of methods, including Laser flash, Hot-Disk, and Wiedemann-Franz law, have been applied for thermal conductivity measurements of Al-Si casting alloys. The first two methods can obtain the thermal parameter directly for specific samples, while the third one calculates the target value by formula containing the electrical conductivity. Thus, the latter is widely used in the foundries because of its convenient and rapid characteristics. The purpose of this paper was to make a polite comparison among them and optimize the key constant C in the Wiedemann-Franz law to improve the calculation accuracy for Al-Si alloys. Measurements were conducted on the same set of specimens of Al-Si-xCu alloys (x ranges from 0.1 wt.% to 2.0 wt.%) at room temperature. The results showed that the measured value of Laser Flash method was well consistent with Hot Disk. While that of the Wiedemann-Franz law was different with them, the average deviation percentages were 2.17% and 2.36% when using empirical constant C (12.6 W/m·K) in the formula. Then, the constant C was modified to 8.4 W/ m·K and the average deviation percentage were decreased to 0.4% and 0.2% respectively. The reason for the differences was analyzed and a thermal conductivity evaluation model was proposed.

Thermal and electrical transport at nanosized metallic contacts: In the diffusive-ballistic region at room temperature.

The Wiedemann-Franz law has been proved at the quantized metallic contacts but has never been verified at the nanosized contacts when the electrons travel in the diffusive-ballistic region. Herein, by developing a home-made inelastic tunneling spectroscope, the electrical and thermal resistances of the nanosized metallic contacts are investigated. The contact is established by pressing two wires crosswise against each other under the Lorentz force in the magnetic field. The nonmetallic surface layer is in situ removed by the resistive heating under high vacuum. The temperature dependence of the electrical contact resistance is used to separate the contributions from the diffusive and the ballistic transports. The thermal contact resistance is found to increase linearly with the electrical counterpart, indicating the validity of the Wiedemann-Franz law at the clean metallic contacts.

Electronic Transport of Uranium Mononitride

We investigated the electronic heat capacity, thermal conductivity, and resistivity of UN using Quantum Espresso and EPW code. GGA, PBEsol functional was used. The calculated electronic heat coefficient was found to be significantly reduced (0.0176 J⋅mol-1⋅K-2 versus 0.0006 J⋅mol-1⋅K-2) when the non-local hybrid functional (B3LYP) was used. Furthermore, we calculated electrical resistivity using a very transparent Ziman’s formula for metals with the Eliashberg transport coupling function as implemented in EPW code for non-spin-polarized calculations. The number of mobile electrons in UN, as a function of temperature, was derived from the ratio of the calculated resistivity and available experimental data. The electronic thermal conductivity was evaluated from the calculated electronic resistivity via Wiedemann-Franz law with the number of mobility electrons (nav) incorporated (averaged over the temperature range 300 K - 1000 K). Both the electronic thermal conductivity and resistivity, as calculated using newly evaluated nav, compare well with experimental data at ~700 K, but to reproduce the observed trend as a function of temperature, the number of mobile electrons must decrease with the temperature as evaluated.

Electronic and thermal transport in novel carbon-based bilayer with tetragonal rings: a combined study using first-principles and machine learning approach.

In this article, the structural, electronic and thermal transport characteristics of bilayer tetragonal graphene (TG) are systematically explored with a combination of first-principles calculations and machine-learning interatomic potential approaches. Optimized ground state geometry of the bilayer TG structure is predicted and examined by employing various stability criteria. Electronic bandstructure analysis confirmed that bilayer TG exhibits a metallic band structure similar to the monolayer T-graphene structure. Thermal transport characteristics of the bilayer TG structure are explored by analysing thermal conductivity, the Seebeck coefficient, and electrical conductivity. The electronic part of the thermal conductivity shows linearly increasing behaviour with temperature, however the lattice part exhibits the opposite character. The lattice thermal conductivity part is investigated in terms of the three phonon scattering rates and weighted phase space. On the other hand, the Seebeck coefficient goes through a transition from negative to positive values with increasing temperature. The Wiedemann-Franz law regarding electrical transport of the bilayer TG is verified and confirms the universal Lorentz number. Specific heat of the bilayer TG structure follows the Debye model at low temperature and constant behaviour at high temperature. Moreover, the Debye temperature of the bilayer TG structure is verified by ab initio calculations as well as fitting the specific heat data using the Debye model.

Research on the Influence of Temperature and Pressure on Volume, Enthalpy, Entropy, Debye Temperature, Electrical Resistivity, Thermal Conductivity and Thermal Diffusivity of AU with FCC Structure

The melting temperature, the jumps of volume, enthalpy and entropy at the melting point, the isothermal compressibility, the thermal expansion coefficient, the heat capacity at constant volume, the Gruneisen parameter, the Debye temperature, the electrical resistivity, the thermal conductivity and the thermal diffusivity for FCC defective and perfect metals are studied by combining the statistical moment method (SMM), the limiting condition of the absolute stability of the crystalline state, the Clapeyron-Clausius equation, the Debye model, the Gruneisen equation, the Wiedemann-Franz law and the Mott equation. Our numerical calculations of obtained theoretical results are carried out for Au under high temperature and pressure. The SMM calculated melting curve of Au is in good agreement with experiments and other calculations. Our calculations for the jumps of volume, enthalpy and entropy, the thermal conductivity and the thermal diffusivity of Au predict and orient experimental results in the future.

Unified ballistic transport relation for anisotropic dispersions and generalized dimensions

An analytical formula is derived for particle and energy densities of fermions and bosons, and their ballistic momentum and energy currents for anisotropic energy dispersions in generalized dimensions. The formulation considerably simplifies the comparison of the statistical properties and ballistic particle and energy transport currents of electrons, acoustic phonons, and photons in various dimensions in a unified manner. Assorted examples of its utility are discussed, ranging from blackbody radiation to Schottky diodes and ballistic transistors, quantized electrical and thermal conductance, generalized ballistic Seebeck and Peltier coefficients, their Onsager relations, the generalized Wiedemann-Franz law and the robustness of the Lorenz number, and ballistic thermoelectric power factors, all of which are obtained from the single formula. The new formulation predicts a thermoelectric power factor behaviour of 3D Dirac bands which has not been observed yet.

Heat capacities and thermal conductivities of palladium and titanium melts and correlation between thermal diffusivity and density of states for transition metals in a liquid state

The normal spectral emissivities at 807 and 940 nm, heat capacities at constant pressure and thermal conductivities of Pd and Ti melts were measured using an electromagnetic levitation technique in a static magnetic field. The static magnetic field suppresses the surface oscillation, translational motion, and convection flow on electromagnetically levitated samples. The convections in the levitated Pd and Ti melts were suppressed sufficiently for thermal conductivity measurement by the static magnetic field. The emissivities and heat capacities of Pd and Ti melts showed no temperature dependence within the experimental temperature region. The thermal conductivity of Pd melt was constant within experimental temperature region, on the other hand, the thermal conductivity of Ti melt increased with increasing temperature. The measured emissivity and thermal conductivity were compared with values evaluated by a free electron model such as Drude model and Wiedemann-Franz law. Based on the results, the correlation between density of states (DOS) at Fermi energy and thermal diffusivities for transition metals was discussed.

Thermal transport in compensated semimetals: Effect of electron-electron scattering on Lorenz ratio

It is well known that the electronic thermal conductivity of clean compensated semimetals can be greatly enhanced over the electric conductivity by the availability of an ambipolar mechanism of conduction, whereby electrons and holes flow in the same direction experiencing negligible Coulomb scattering as well as negligible impurity scattering. This enhancement -- resulting in a breakdown of the Wiedemann-Franz law with an anomalously large Lorenz ratio -- has been recently observed in two-dimensional monolayer and bilayer graphene near the charge neutrality point. In contrast to this, three-dimensional compensated semimetals such as WP$_2$ and Sb are typically found to show a reduced Lorenz ratio. This dramatic difference in behavior is generally attributed to different regimes of Fermi statistics in the two cases: degenerate electron-hole liquid in compensated semimetals versus non-degenerate electron-hole liquid in graphene. We show that this difference is not sufficient to explain the reduction of the Lorenz ratio in compensated semimetals. We argue that the solution of the puzzle lies in the ability of compensated semimetals to sustain sizeable regions of electron-hole accumulation near the contacts, which in turn is a consequence of the large separation of electron and hole pockets in momentum space. These accumulations suppress the ambipolar conduction mechanism and effectively split the system into two independent electron and hole conductors. We present a quantitative theory of the crossover from ambipolar to unipolar conduction as a function of the size of the electron-hole accumulation regions, and show that it naturally leads to a sample-size-dependent thermal conductivity.

Electron-phonon drag enhancement of transport properties from a fully coupled ab initio Boltzmann formalism

We present a combined treatment of the non-equilibrium dynamics and transport of electrons and phonons by carrying out \textit{ab initio} calculations of the fully coupled electron and phonon Boltzmann transport equations. We find that the presence of mutual drag between the two carriers causes the thermopower to be enhanced and dominated by the transport of phonons, rather than electrons as in the traditional semiconductor picture. Drag also strongly boosts the intrinsic electron mobility, thermal conductivity and the Lorenz number. Impurity scattering is seen to suppress the drag-enhancement of the thermal and electrical conductivities, while having weak effects on the enhancement of the Lorenz number and thermopower. We demonstrate these effects in \textit{n}-doped 3C-SiC at room temperature, and explain their origins. This work establishes the roles of microscopic scattering mechanisms in the emergence of strong drag effects in the transport of the interacting electron-phonon gas.

Ultrahigh Power Factors in Ultrawide-Band-Gap GaB3N4 and AlB3N4 for High-Temperature Thermoelectric Applications

With recent thermoelectric studies concentrating too much on low- and mid-temperature applications, an interesting question is, “are there any materials suitable for high-temperature thermoelectric operations?” To answer this, we have demonstrated in this work the viability of the ternary ultrawide-band-gap materials GaB3N4 and AlB3N4 for high-temperature thermoelectric applications using the first-principles calculation method. Our accurate transport calculations, considering both elastic and inelastic scattering mechanisms, reveal the ultrahigh power factors as high as 1821 μW m–1 K–2 in GaB3N4 and 1876 μW m–1 K–2 in AlB3N4 at 2000 K. The power factors are calculated from the Seebeck coefficients and electrical conductivities for both electron and hole carrier concentrations between 1018 and 1021 cm–3. For the figure-of-merit (ZT) calculation, the obtained power factors along with the electronic thermal conductivities determined from the definite Lorenz numbers and the lattice thermal conductivities from the phonon vibrations were used. The calculated ZT values seem to be appreciable for high-temperature applications considering the materials’ stability factor and the temperature range within the optimum electron carrier concentration of 1021 cm–3. Although the lattice thermal conductivities are higher, which decrease the values of ZT, considering the ultrahigh power factors instead of the ZT factor could be the right choice for high-temperature thermoelectric applications.

Linear and nonlinear thermoelectric transport in a magnetic topological insulator nanoribbon with a domain wall

We theoretically investigate the thermoelectric transport in the nanoribbon of the magnetic topological insulator with a domain wall in the linear and nonlinear regimes. The Lorenz number $L$, the Seebeck coefficients ${S}_{c}$, and the thermoelectrical figure of merit $ZT$ in the linear response regime are obtained by the nonequilibrium Green's function method. These thermoelectric coefficients strongly depend on the configuration of the domain wall, that is, the configuration of the domain wall can regulate the thermoelectric transport performance. We also discuss the effect of the width of nanoribbon and the thickness of the domain wall on the thermoelectric coefficient. The results show that the N\'eel-type wall is more dependent on the size effect of the domain wall than the Bloch-type wall. For a device with a given width, we can always allow the setup to be in high performance thermoelectric transport by adjusting the configuration of the domain wall. Moreover, considering the disorder, the transmission coefficient is robust against disorder even if the disorder strength is very strong, and ${S}_{c}$ and $ZT$ are robust against moderate disorder. Finally, for a nonlinear situation, we calculate the maximum power-generation efficiency $\ensuremath{\eta}$ and the equivalent thermoelectric figure of merit $Z{T}_{M}$, indicating the potential application as an effective thermoelectric device.

Thermal transport properties of Ni–Co-based superalloy

We report systematic measurements of thermal transport properties of a Ni–Co-based superalloy at temperatures ranging from room temperature to around 800 K. In this temperature range, the thermal diffusivity and conductivity of the superalloy monotonically increase with an increase in the temperature, while the specific heat capacity is almost temperature-independent. We found that the observed thermal conductivity of the Ni–Co-based superalloy is higher than the electronic thermal conductivity expected from the Wiedemann–Franz law, indicating the substantial contribution of phonon thermal conductivity. The temperature dependence of the phonon thermal conductivity for the Ni–Co-based superalloy was observed to be weaker than that for other Ni-based alloys, which can be qualitatively explained by enhanced phonon scattering due to small γ′-phase precipitates in the superalloy. This result suggests possible tuning of the thermal conductivity of the superalloy based on phonon transport engineering.

High-throughput phase-field simulations and machine learning of resistive switching in resistive random-access memory

Metal oxide-based Resistive Random-Access Memory (RRAM) exhibits multiple resistance states, arising from the activation/deactivation of a conductive filament (CF) inside a switching layer. Understanding CF formation kinetics is critical to achieving optimal functionality of RRAM. Here a phase-field model is developed, based on materials properties determined by ab initio calculations, to investigate the role of electrical bias, heat transport and defect-induced Vegard strain in the resistive switching behavior, using MO2−x systems such as HfO2−x as a prototypical model system. It successfully captures the CF formation and resultant bipolar resistive switching characteristics. High-throughput simulations are performed for RRAMs with different material parameters to establish a dataset, based on which a compressed-sensing machine learning is conducted to derive interpretable analytical models for device performance (current on/off ratio and switching time) metrics in terms of key material parameters (electrical and thermal conductivities, Vegard strain coefficients). These analytical models reveal that optimal performance (i.e., high current on/off ratio and low switching time) can be achieved in materials with a low Lorenz number, a fundamental material constant. This work provides a fundamental understanding to the resistive switching in RRAM and demonstrates a computational data-driven methodology of materials selection for improved RRAM performance, which can also be applied to other electro-thermo-mechanical systems.

Anomalous Lorenz number in massive and tilted Dirac systems

We analytically calculate the anomalous transverse electric and thermal currents in massive and tilted Dirac systems, using β-borophene as a representative material, and report on conditions under which the corresponding Lorenz number (Lan) deviates from its classically accepted value (L0). The deviations in the high-temperature regime are shown to be an outcome of the quantitative difference in the respective kinetic transport expressions for electric (σ) and thermal (κ) conductivity and are further weighted through a convolution integral with a non-linearly energy-dependent Berry curvature that naturally arises in a Dirac material. In addition, the tilt and anisotropy of the Dirac system that are amenable to change via an external stimulus are found to quantitatively influence Lan. The reported deviations from L0 hold practical utility inasmuch as they allow an independent tuning of σ and κ, useful in optimizing the output of thermoelectric devices.

Influence of nonstoichiometry point defects on electronic thermal conductivity

Electronic contribution to thermal conductivity (κe) is proportional to electrical conductivity (σ) as given by the Wiedemann–Franz law (κe=LσT). The Lorenz number (L) scales the thermal current associated with the electrical current and implies the electrons' capability of carrying heat. By experimental transport measurements and first-principles calculations, we show that electron transport overwhelmingly dominates thermal conductivity in β-Ag2Se, which has intrinsically low lattice thermal conductivity. The Lorenz number linearly decreases from Ag1.95Se to Ag2.03Se, as the point defect changes from a cation vacancy to a self-interstitial. This striking behavior reveals the inelastic electron scattering process due to nonstoichiometry point defects and suggests that the cation vacancies increase while self-interstitials reduce the amount of heat carried by electrons. Remarkably, the Lorenz number varies by 40% for such a narrow nonstoichiometry window, with the deviation as large as 36% from the Sommerfeld value. Finally, we predict the maximum Lorenz number that can be achieved in β-Ag2Se for various electron scattering mechanisms. This work provides insights into the physics of electronic heat conduction in solids containing point defects.

Thermoelectric Properties of InA Nanowires from Full-Band Atomistic Simulations.

In this work we theoretically explore the effect of dimensionality on the thermoelectric power factor of indium arsenide (InA) nanowires by coupling atomistic tight-binding calculations to the Linearized Boltzmann transport formalism. We consider nanowires with diameters from 40 nm (bulk-like) down to 3 nm close to one-dimensional (1D), which allows for the proper exploration of the power factor within a unified large-scale atomistic description across a large diameter range. We find that as the diameter of the nanowires is reduced below d < 10 nm, the Seebeck coefficient increases substantially, as a consequence of strong subband quantization. Under phonon-limited scattering conditions, a considerable improvement of ~6× in the power factor is observed around d = 10 nm. The introduction of surface roughness scattering in the calculation reduces this power factor improvement to ~2×. As the diameter is decreased to d = 3 nm, the power factor is diminished. Our results show that, although low effective mass materials such as InAs can reach low-dimensional behavior at larger diameters and demonstrate significant thermoelectric power factor improvements, surface roughness is also stronger at larger diameters, which takes most of the anticipated power factor advantages away. However, the power factor improvement that can be observed around d = 10 nm could prove to be beneficial as both the Lorenz number and the phonon thermal conductivity are reduced at that diameter. Thus, this work, by using large-scale full-band simulations that span the corresponding length scales, clarifies properly the reasons behind power factor improvements (or degradations) in low-dimensional materials. The elaborate computational method presented can serve as a platform to develop similar schemes for two-dimensional (2D) and three-dimensional (3D) material electronic structures.

Effective Lorenz Number of the Point Contact between Silver Nanowires.

Electrical and thermal transport through metal point contacts, a key issue in the design and operation of various engineering devices, is of great recent interest. The effective Lorenz number (L), which relates the thermal to electrical conductance of point contacts, could provide valuable information on the relative contribution of electrons and phonons to thermal transport. Through measuring electrical and thermal transport across point contacts between silver nanowires, we report that L significantly deviates from the Sommerfeld value by up to 5.2 times and exhibits nonmonotonic variation with temperature. Analyses show that these observations are due to the more important phonon contribution to the thermal conductance of the point contact as Sharvin resistance greatly hinders electron transport, which is further confirmed by the size dependence of L with a higher value for a smaller contact size. These results provide critical insights into engineering designs involving point contacts between metal nanostructures.