Wiedemann-Franz Ratio Research Articles

Thermoelectric properties of topological chains coupled to a quantum dot

Topological one-dimensional superconductors can sustain zero energy modes protected by different kinds of symmetries in their extremities. Observing these excitations in the form of Majorana fermions is one of the most intensive quests in condensed matter physics. We are interested in another class of one-dimensional topological systems in this work, namely topological insulators. Which present symmetry-protected end modes with robust properties and do not require the low temperatures necessary for topological superconductivity. We consider a device in the form of a single electron transistor coupled to the simplest kind of topological insulators, namely chains of atoms with hybridized sp orbitals. We study the thermoelectric properties of the device in the trivial, non-trivial topological phases and at the quantum topological transition of the chains. We show that the device’s electrical conductance and the Wiedemann–Franz ratio at the topological transition have universal values at very low temperatures. The conductance and thermopower of the device with diatomic sp-chains, at their topological transition, give direct evidence of fractional charges in the system. The former has an anomalous low-temperature behavior, attaining a universal value that is a consequence of the double degeneracy of the system due to the presence of zero energy modes. On the other hand, the system can be tuned to exhibit high values of the thermoelectric figure of merit and the power factor at high temperatures.

Near-equilibrium approach to transport in complex Sachdev-Ye-Kitaev models

We study the non-equilibrium dynamics of a one-dimensional complex Sachdev-Ye-Kitaev chain by directly solving for the steady state Green's functions in terms of small perturbations around their equilibrium values. The model exhibits strange metal behavior without quasiparticles and features diffusive propagation of both energy and charge. We explore the thermoelectric transport properties of this system by imposing uniform temperature and chemical potential gradients. We then expand the conserved charges and their associated currents to leading order in these gradients, which we can compute numerically and analytically for different parameter regimes. This allows us to extract the full temperature and chemical potential dependence of the transport coefficients. In particular, we uncover that the diffusivity matrix takes on a simple form in various limits and leads to simplified Einstein relations. At low temperatures, we also recover a previously known result for the Wiedemann-Franz ratio. Furthermore, we establish a relationship between diffusion and quantum chaos by showing that the diffusivity eigenvalues are upper bounded by the chaos propagation rate at all temperatures. Our work showcases an important example of an analytically tractable calculation of transport properties in a strongly interacting quantum system and reveals a more general purpose method for addressing strongly coupled transport.

Heat-bath approach to anomalous thermal transport: Effects of inelastic scattering

We present results for the entire set of anomalous charge and heat transport coefficients for metallic systems in the presence of a finite-temperature heat bath. In realistic physical systems this necessitates the inclusion of inelastic dissipation mechanisms; relatively little is known theoretically about their effects on anomalous transport. Here we demonstrate how these dissipative processes are strongly intertwined with Berry-curvature physics. Our calculations are made possible by the introduction of a Caldeira-Leggett reservoir which allows us to avoid the sometimes-problematic device of the pseudogravitational potential. Using our formulas, we focus on the finite-temperature behavior of the important anomalous Wiedemann-Franz ratio. Despite previous expectations, this ratio is found to be non-universal as it can exhibit either an upturn or a downturn as temperature increases away from zero. We emphasize that this derives from a \textit{competition} between Berry curvatures having different signs in different regions of the Brillouin zone. We point to experimental support for these observations and for the behavior of an alternative ratio involving a thermoelectric response which, by contrast, appears to be more universal at low temperatures. Our work paves the way for future theory and experiment, demonstrating how inelastic scattering at non-zero temperature affects the behavior of all anomalous transport coefficients.

Electric field-induced electronic-thermoelectric-optical properties of typical isoelectronic HNC6 monolayers: A theoretical study

Using the combined first-principles, tight-binding, and machine-learning interatomic potential approaches, we explore the electric field effects on the electronic, thermoelectric, and optical properties of buckled hexagonal isoelectronic HNC6 monolayers, a member of HAC6 (A = N, P, As) family. These material(s) possess a Dirac cone in their band structure which can be attributed to the same electron count of every site (C/N) and the presence of a weak π bond between carbon and nitrogen atoms. We predict that a transverse electric field can induce a tunable bandgap, the gap is nearly proportional to the electric field strength, suitable for use in the electronics industry. The thermoelectric performance of HNC6 is better than graphene, which can be further improved by the application of an external electric field. The region of the chemical potential for the optimal thermoelectric performance can also be tuned by the electric field. The Wiedemann–Franz ratio deviates from that of ordinary metals and is nearly twice that of graphene and four times that of universal value. For parallel polarization, HNC6 shows pronounced optical response in the infrared and visible region. Plasma frequencies appear in the visible regions which are blue-shifted with electric field strength. The P and As counterpart of HNC6 shows similar electronic, thermoelectric, and optical properties on the application of electric field, with thermoelectric performance even superior to HNC6. These intriguing electronic, thermoelectric, and optical properties in presence of an electric field suggest great potential of HAC6 for novel electronic, energy harvesting, and optoelectronic devices.

Effect of BN dimers on the stability, electronic, and thermal properties of monolayer graphene

We theoretically investigate structural stability, electronic and thermal characteristic of boron and nitrogen codoped monolayer graphene using density functional theory and Boltzmann transport equation. Three types of BN dimers, ortho, meta, and para dimers, are identified at different concentration ratios of B and N atoms. Our DFT calculations suggest that the BN ortho dimers are structurally favorable configurations due to the lowest required formation energy. At low doping ratio, large bandgap for BN para dimer is predicted leading to high Seebeck coefficient and figure of merit. In addition, a large deviation in the Wiedemann–Franz ratio is also seen, and a maximum value of the Lorenz number is thus found. In contrast, at high doping ratio, high Seebeck coefficient and figure of merit are found for BN ortho dimer and a low Seebeck coefficient for BN para dimer is noticed. Furthermore, a small deviation in Lorenz number is found for high doping ratio where the distance between BN pair is large.

Electronic, thermal, and optical properties of graphene like SiCx structures: Significant effects of Si atom configurations

We investigate the electronic, thermal, and optical characteristics of graphene like SiCx structure using model calculations based on density functional theory. The change in the energy bandgap can be tuned by the Si atomic configuration, rather than the dopants ratio. The effects of the concentration of the Si atoms and the shape of supercell are kept constant, and only the interaction effects of two Si atoms are studied by varying their positions. If the Si atoms are at the same sublattice positions, a maximum bandgap is obtained leading to an increased Seebeck coefficient and figure of merit. A deviation in the Wiedemann-Franz ratio is also found, and a maximum value of the Lorenz number is thus discovered. Furthermore, a significant red shift of the first peak of the imaginary part of the dielectric function towards the visible range of the electromagnetic radiation is observed. On the other hand, if the Si atoms are located at different sublattice positions, a small bandgap is seen because the symmetry of sublattice remains almost unchanged. Consequently, the Seebeck coefficient and the dielectric function are only slightly changed compared to pristine graphene. In addition, the electron energy loss function is suppressed in Si-doped graphene. These unique variations of the thermal and the optical properties of Si-doped graphene are of importance to understand experiments relevant to optoelectronic applications.

Enhanced hydrodynamic transport in near magic angle twisted bilayer graphene

Using the semiclassical quantum Boltzmann theory and employing the Dirac model with twist angle-dependent Fermi velocity we obtain results for the electrical resistivity, the electronic thermal resistivity, the Seebeck coefficient, and the Wiedemann-Franz ratio in near magic angle twisted bilayer graphene, as functions of doping density (around the charge-neutrality-point) and modified Fermi velocity $\tilde v$. The $\tilde v$-dependence of the relevant scattering mechanisms, i.e. electron-hole Coulomb, long-ranged impurities, and acoustic gauge phonons, is considered in detail. We find a range of twist angles and temperatures, where the combined effect of momentum-non-conserving collisions (long-ranged impurities and phonons) is minimal, opening a window for the observation of strong hydrodynamic transport. Several experimental signatures are identified, such as a sharp dependence of the electric resistivity on doping density and a large enhancement of the Wiedemann-Franz ratio and the Seebeck coefficient.

Disorder-enabled hydrodynamics of charge and heat transport in monolayer graphene

Hydrodynamic behavior in electronic systems is commonly accepted to be associated with extremely clean samples such that electron–electron collisions dominate and total momentum is conserved. Contrary to this, we show that in monolayer graphene the presence of disorder is essential to enable an unconventional hydrodynamic regime which exists near the charge neutrality point and is characterized by a large enhancement of the Wiedemann–Franz ratio. Although the enhancement becomes more pronounced with decreasing disorder, the very possibility of observing the effect depends crucially on the presence of disorder. We calculate the maximum extrinsic carrier density nc below which the effect becomes manifest, and show that nc vanishes in the limit of zero disorder. For n > nc we predict that the Wiedemann–Franz ratio actually decreases with decreasing disorder. We complete our analysis by presenting a transparent picture of the physical processes that are responsible for the crossover from conventional to disorder-enabled hydrodynamics. Recent experiments on monolayer graphene are discussed and shown to be consistent with this picture.

Breakdown of the Wiedemann-Franz law in AB -stacked bilayer graphene

We present a simple theory of thermoelectric transport in bilayer graphene and report our results for the electrical resistivity, the thermal resistivity, the Seebeck coefficient, and the Wiedemann-Franz ratio as functions of doping density and temperature. In the absence of disorder, the thermal resistivity tends to zero as the charge neutrality point is approached; the electric resistivity jumps from zero to an intrinsic finite value, and the Seebeck coefficient diverges in the same limit. Even though these results are similar to those obtained for single-layer graphene, their derivation is considerably more delicate. The singularities are removed by the inclusion of a small amount of disorder, which leads to the appearance of a "window" of doping densities $0<n<n_c$ (with $n_c$ tending to zero in the zero-disorder limit) in which the Wiedemann-Franz law is severely violated.

Thermoelectricity near Anderson localization transitions

The electronic thermoelectric coefficients are analyzed in the vicinity of one and two Anderson localization thresholds in three dimensions. For a single mobility edge, we correct and extend previous studies, and find universal approximants which allow to deduce the critical exponent for the zero-temperature conductivity from thermoelectric measurements. In particular, we find that at non-zero low temperatures the Seebeck coefficient and the thermoelectric efficiency can be very large on the "insulating" side, for chemical potentials below the (zero-temperature) localization threshold. Corrections to the leading power-law singularity in the zero-temperature conductivity are shown to introduce non-universal temperature-dependent corrections to the otherwise universal functions which describe the Seebeck coefficient, the figure of merit and the Wiedemann-Franz ratio. Next, the thermoelectric coefficients are shown to have interesting dependences on the system size. While the Seebeck coefficient decreases with decreasing size, the figure of merit first decreases but then increases, while the Wiedemann-Franz ratio first increases but then decreases as the size decreases. Small (but finite) samples may thus have larger thermoelectric efficiencies. In the last part we study thermoelectricity in systems with a pair of localization edges, the ubiquitous situation in random systems near the centers of electronic energy bands. As the disorder increases, the two thresholds approach each other, and then the Seebeck coefficient and the figure of merit increase significantly, as expected from the general arguments of Mahan and Sofo [J. D. Mahan and J. O. Sofo, Proc. Natl. Acad. Sci. U.S.A. 93, 7436 (1996)] for a narrow energy-range of the zero-temperature metallic behavior.

Violation of the Wiedemann-Franz Law in Hydrodynamic Electron Liquids.

The Wiedemann-Franz law, connecting the electronic thermal conductivity to the electrical conductivity of a disordered metal, is generally found to be well satisfied even when electron-electron (e-e) interactions are strong. In ultraclean conductors in the hydrodynamic regime, however, large deviations from the standard form of the law are expected, due to the fact that e-e interactions affect the two conductivities in radically different ways. Thus, the standard Wiedemann-Franz ratio between the thermal and the electric conductivity is reduced by a factor 1+τ/τ(th)(ee), where 1/τ is the momentum relaxation rate and τ(th)(ee) is the relaxation time of the thermal current due to e-e collisions. Here we study the density and temperature dependence of 1/τ(th)(ee) of two-dimensional electron liquids. We show that at low temperature 1/τ(th)(ee) is 8/5 of the quasiparticle decay rate; remarkably, the same result is found in doped graphene and in conventional electron liquids in parabolic bands.

Thermoelectric effect enhanced by resonant states in graphene

Thermoelectric effects in graphene are considered theoretically with particular attention paid to the role of impurities. Using the T -matrix method we calculate the impurity resonant states and the momentum relaxation time due to scattering on impurities. The Boltzmann kinetic equation is used to determine the thermoelectric coefficients. It is shown that the resonant impurity states near the Fermi level give rise to a resonant enhancement of the Seebeck coefficient and of the figure of merit $ZT$ . The Wiedemann-Franz ratio deviates from that known for ordinary metals, where this ratio is constant and equal to the Lorentz number. This deviation appears for small chemical potentials and in the vicinity of the resonant states. In the limit of a constant relaxation time, this ratio has been calculated analytically for $\mu=0$.

Thermodynamic and transport signatures of a fractionalized Fermi liquid

Several heavy-fermion metals display a quantum phase transition from an antiferromagnetic metal to a heavy Fermi liquid. In some materials, however, recent experiments seem to find that the heavy Fermi liquid phase can be directly tuned into a non-Fermi liquid phase without apparent magnetic order. We analyze a candidate state for this scenario where the local moment system forms a spin liquid with gapless fermionic excitations. We discuss the thermal conductivity and spin susceptibility of this fractionalized state both in two and, in particular, three spatial dimensions for different temperature regimes. We derive a variational functional for the thermal conductivity and solve it with a variational ansatz dictated by Keldysh formalism. In sufficiently clean samples and for an appropriate temperature window, we find that thermal transport is dominated by the spinon contribution which can be detected by a characteristic maximum in the Wiedemann-Franz ratio. For the spin susceptibility, the conduction electron Pauli paramagnetism is much smaller than the spinon contribution whose temperature dependence in three dimensions is logarithmically enhanced as compared to the Fermi liquid result.

Violation of the Wiedemann-Franz Law at the Kondo Breakdown Quantum Critical Point

We study the electrical and thermal transport near the heavy-fermion quantum critical point, identified with the breakdown of the Kondo effect. We show that the electrical conductivity comes mainly from conduction electrons while the thermal conductivity is given by both conduction electrons and localized fermions (spinons), scattered with hybridization fluctuations of dynamical exponent z = 3. As a result, we reveal that not only electrical but also thermal resistivity displays quasilinear temperature dependence in the intermediate temperature range, the main prediction of our transport study. An important feature turns out to be emergence of additional entropy carriers, that is, spinon excitations. We find that the Wiedemann-Franz ratio should be larger than the standard value, differentiating the Kondo breakdown scenario from the Hertz-Moriya-Millis framework.

Universal thermal and electrical transport near the superconductor-metal quantum phase transition in nanowires

The Wiedemann-Franz law relates the low temperature (T) limit of the ratio W ≡ κ/(σT) of the thermal (κ) and electrical (σ) conductivities of metals to the universal Lorenz number L0 = (π 2 /3)(kB/e) 2 . This remarkable relationship is independent of the strength of the interactions between the electrons, relates macroscopic transport properties to fundamental constants of nature, and depends only upon the Fermi statistics and charge of the elementary quasiparticle excitations of the metal. It has been experimentally verified to high precision in a wide range of metals [1], and realizes a sensitive macroscopic test of the quantum statistics of the charge carriers. It is interesting to note the value of the WiedemannFranz ratio in some other important strongly interacting quantum systems. In superconductors, which have low energy bosonic quasiparticle excitations, σ is infinite for a range of T > 0, while κ is finite in the presence of impurities [2], and so W = 0. At quantum phase transitions described by relativistic field theories, such as the superfluid-insulator transition in the Bose Hubbard model, the low energy excitations are strongly coupled and quasiparticles are not well defined; in such theories the conservation of the relativistic stress-energy tensor implies that κ is infinite, and so W = ∞ [3]. Li and Orignac [4] computed W in disordered Luttinger liquids, and found deviations from L0, and found a non-zero universal value for W at the metal-insulator transition for spinless fermions. The present paper will focus on the quantum phase transition between a superconductor and a metal (a SMT). We will consider quasi-one dimensional nanowires with a large number of transverse channels (so that the electronic localization length is much larger than the mean free path (l)) which can model numerous recent experiments [5, 6, 7, 8, 9, 10, 11, 12, 13]. We will describe universal deviations in the value of W from L0, which can serve as sensitive tests of the theory in future experiments. The mean-field theory for the SMT goes back to the early work [14] of Abrikosov and Gorkov (AG): in one of the earliest discussions of a quantum phase transition, they showed that a large enough concentration of magnetic impurities could induce a SMT at T = 0. It has since been shown that such a theory applies in a large variety of situations with ‘pair-breaking’ perturbations: anisotropic superconductors with non-magnetic impurities [15], lower-dimensional superconductors with magnetic fields oriented in a direction parallel to the Cooper pair motion [16], and s-wave superconductors with inhomogeneity in the strength of the attractive BCS interaction [17]. Indeed, it is expected that pair-breaking is present in any experimentally realizable SMT at T = 0: in the nanowire experiments, explicit evidence for pairbreaking magnetic moments on the wire surface was presented recently by Rogachev et al. [13].

Thermal measurements of a one-dimensional wire in the quantum limit

The single-particle properties of a ballistic one-dimensional (1D) conductorare reviewed; the breakdown in these properties is used to characterize the0.7 structure, an anomalous but reproducible feature in the conductanceG that ismeasured at G = 0.7 × 2e2/h.We show how alternating current heating creates a temperature differenceΔT across a 1D wire, allowing thermopower measurements. The thermopower characteristicsS(Vg) show deviations from Cutler–Mott predictions (a single-particle theory) close tothe 0.7 structure. The magnitude of a thermovoltage peak is used to measurethe electron temperature, and we have incorporated a mesoscopic thermometerinto a simple thermal circuit that allows us to measure the thermal conductanceof a 1D wire. For the first four 1D subbands the heat carried by electronspassing through the 1D constriction is proportional to the electrical conductanceG(Vg); this is the first demonstration that the thermal conductance due to electronsis quantized. In the vicinity of the 0.7 structure the Wiedemann–Franzratio breaks down, and a plateau at the quantum of thermal conductanceπ2kB2T/3h is observed.

Flattening of single-particle spectra in strongly correlated electron systems and the violation of the Wiedemann-Franz law

The renormalization of the Wiedemann-Franz (WF) ratio in strongly correlated electron systems is analyzed within the Landau quasiparticle picture. We demonstrate that the WF law is violated: (i) at the quantum critical point, where the effective mass diverges, and (ii) beyond a point of fermion condensation, where the single-particle spectrum ∈(p) becomes flat. Results of the analysis are compared with available experimental data.

Thermal Hall conductivity and long-lived quasiparticles in CeCoIn5

In CeCoIn5, the thermal conductivity κxx and Hall conductivity κxy below Tc display large anomalies below Tc. The strong suppression of the anomalies in weak fields implies the existence of long-lived quasiparticles. We also discuss briefly the Wiedemann–Franz ratio and the existence of a strongly field-dependent spin-fluctuation heat current.

Fully self-consistent determination of transport properties inEu-richEuO

The magnetization, the Curie temperature, the resistivity, the electronic thermal conductivity, the Wiedemann-Franz ratio, the conduction-electron density and the scattering time of $\mathrm{Eu}$-rich $\mathrm{EuO}$ are calculated fully self-consistently within a microscopic model including the exchange of the conduction and the oxygen-vacancy electrons with and the exchange between the $\mathrm{Eu}$ spins. The spectacular metal--insulator transition near the Curie temperature is reproduced quantitatively. The Wiedemann-Franz law holds in the metallic phase, where the system is supposed to form a Fermi liquid, but it is invalid for the insulator. For higher oxygen-vacancy concentrations there is a jump in the scattering time (mobility) of the conduction electrons at the Curie temperature, which is also observed in the experiment.

Wiedemann-Franz ratio in plasmas in the mixtures of xenon, argon and cesium

In the present paper, the xenon plasmas containing argon and cesium as additive and pertaining to the above mentioned type (high-pressure low-temperature, LIE) are studied, and a theoretical evaluation of their basic transport parameters is presented. The numerical calculations were based on the assumption that the system is kept under constant pressure and temperature and that it attained local thermo dynamical equilibrium. Some results of a theoretical study which embraced numerical evaluations of the plasma composition, electron collision frequency, electrical and thermal conductivities and Wiedemann-Franz ratio, all regarded as functions of pressure and temperature, are given for high-pressure (from 0,1 MPa to 1,5 MPa) and low-temperature (from 2 000 K to 20 000 K). A previously derived modified expression for the Debye radius, offering the possibility to treat the plasmas considered as weakly non-ideal in the whole temperature range of interest, is used in the evaluations, in combination with the Saha equations for the relevant ionization stages of xenon, argon and cesium. .