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arXiv:1609.02176 · Physical review. B./Physical review. B

Transverse thermoelectric response as a probe for existence of quasiparticles

Yoni Schattner, Vadim Oganesyan, Dror Orgad

Published Dec 13, 2016• 4 citations
arXivHTMLPDF

Abstract

The electrical Hall conductivities of any anisotropic interacting system with reflection symmetry obey ${\ensuremath{\sigma}}_{xy}=\ensuremath{-}{\ensuremath{\sigma}}_{yx}$. In contrast, we show that the analogous relation between the transverse thermoelectric Peltier coefficients, ${\ensuremath{\alpha}}_{xy}=\ensuremath{-}{\ensuremath{\alpha}}_{yx}$, does not generally hold in the same system. This fact may be traced to interaction contributions to the heat current operator and the mixed nature of the thermoelectric response functions. Remarkably, however, it appears that emergence of quasiparticles at low temperatures forces ${\ensuremath{\alpha}}_{xy}=\ensuremath{-}{\ensuremath{\alpha}}_{yx}$. This suggests that quasiparticle-free ground states (so-called non-Fermi liquids) may be detected by examining the relationship between ${\ensuremath{\alpha}}_{xy}$ and ${\ensuremath{\alpha}}_{yx}$ in the presence of reflection symmetry and microscopic anisotropy. These conclusions are based on the following results. (i) The relation between the Peltier coefficients is exact for elastically scattered noninteracting particles. (ii) It holds approximately within Boltzmann theory for interacting particles when elastic scattering dominates over inelastic processes. In a disordered Fermi liquid, the latter lead to deviations that vanish as ${T}^{3}$. (iii) We calculate the thermoelectric response in a model of weakly coupled spin-gapped Luttinger liquids and obtain strong breakdown of antisymmetry between the off-diagonal components of $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\alpha}}$. We also find that the Nernst signal in this model is enhanced by interactions and can change sign as function of magnetic field and temperature.

DOI
10.1103/physrevb.94.235130

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The electrical Hall conductivities of any anisotropic interacting system with reflection symmetry obey \ensuremathσxy=\ensuremath−\ensuremathσyx{\ensuremath{\sigma}}_{xy}=\ensuremath{-}{\ensuremath{\sigma}}_{yx}\ensuremathσxy​=\ensuremath−\ensuremathσyx​. In contrast, we show that the analogous relation between the transverse thermoelectric Peltier coefficients, \ensuremathαxy=\ensuremath−\ensuremathαyx{\ensuremath{\alpha}}_{xy}=\ensuremath{-}{\ensuremath{\alpha}}_{yx}\ensuremathαxy​=\ensuremath−\ensuremathαyx​, does not generally hold in the same system. This fact may be traced to interaction contributions to the heat current operator and the mixed nature of the thermoelectric response functions. Remarkably, however, it appears that emergence of quasiparticles at low temperatures forces \ensuremathαxy=\ensuremath−\ensuremathαyx{\ensuremath{\alpha}}_{xy}=\ensuremath{-}{\ensuremath{\alpha}}_{yx}\ensuremathαxy​=\ensuremath−\ensuremathαyx​. This suggests that quasiparticle-free ground states (so-called non-Fermi liquids) may be detected by examining the relationship between \ensuremathαxy{\ensuremath{\alpha}}_{xy}\ensuremathαxy​ and \ensuremathαyx{\ensuremath{\alpha}}_{yx}\ensuremathαyx​ in the presence of reflection symmetry and microscopic anisotropy. These conclusions are based on the following results. (i) The relation between the Peltier coefficients is exact for elastically scattered noninteracting particles. (ii) It holds approximately within Boltzmann theory for interacting particles when elastic scattering dominates over inelastic processes. In a disordered Fermi liquid, the latter lead to deviations that vanish as T3{T}^{3}T3. (iii) We calculate the thermoelectric response in a model of weakly coupled spin-gapped Luttinger liquids and obtain strong breakdown of antisymmetry between the off-diagonal components of \ensuremathα\ifmmode^\elseˆ\fi\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\alpha}}\ensuremathα\ifmmode^\elseˆ\fi​. We also find that the Nernst signal in this model is enhanced by interactions and can change sign as function of magnetic field and temperature.
We study the thermoelectric transport properties of fractional quantum Hall systems based on an exact diagonalization calculation. Based on the relation between the thermoelectric response and thermal entropy, we demonstrate that thermoelectric Hall conductivity ${\ensuremath{\alpha}}_{xy}$ has power-law scaling ${\ensuremath{\alpha}}_{xy}\ensuremath{\propto}{T}^{\ensuremath{\eta}}$ for gapless composite Fermi-liquid states at filling numbers $\ensuremath{\nu}=1/2$ and 1/41/41/4 at low temperatures (TTT), with an exponent $\ensuremath{\eta}\ensuremath{\sim}0.5$ distinctly different from Fermi liquids. The power-law scaling remains unchanged for different forms of interaction including Coulomb and short-range ones, demonstrating the robustness of non-Fermi-liquid behavior of these interacting systems at low TTT. In contrast, for the 1/31/31/3 fractional quantum Hall state, ${\ensuremath{\alpha}}_{xy}$ vanishes at low TTT with an activation gap associated with neutral collective modes rather than charged quasiparticles. Our results establish another manifestation of the non-Fermi-liquid nature of quantum Hall fluids at a finite temperature.
For pure fermionic systems, and in the absence of symmetry breaking (e.g. magnetism, superconductivity, …), two types of metallic phases are well established: (i) the “normal” Fermi liquid phase in d = 3 presented in Chapters 12 and 19 via the response and the Green functions techniques; and (ii) the “anomalous” Luttinger liquid phase in d = 1 originally formulated with the bosonization technique by which the fermionic operators are represented in terms of “bosonic” density operators (Luther and Peschel (1974); Haldane (1981)) with the exact solution (Mattis and Lieb (1965)) of the Tomonaga–Luttinger model (Tomonaga (1950); Luttinger (1963)) discussed inmany reviews and books (see for instance the book by Giamarchi (2004)). Here, to stress similarities and differences between the Fermi liquid and the Luttinger liquid, we will follow the alternative route of response and Green functions techniques (Dzyaloshinskii and Larkin (1973), Di Castro and Metzner (1991), Metzner et al. (1998)) and add a few comments on the renormalization group approach (Metzner and Di Castro (1993)). As we have seen in Chapters 12 and 19, the Fermi liquid is described asymptotically by the free low-lying single-particle excitations, i.e., the quasiparticles with a zero-kelvin discontinuous occupation number in momentum space n k (see Eq. (18.54)) at a well defined Fermi surface (k = k F ): where here k F> and k F< indicate the limit k → k F from above and below. This discontinuity still marks the Fermi surface in the interacting system. The finite reduction of the single-particle spectral weight z kF with respect to the Fermi gas (z kF = 1) is given by the finite (i.e. non-critical) “wavefunction renormalization” (see Eq. (18.94)). The presence of the discontinuity at the Fermi surface, together with the Pauli principle, compel the inverse quasiparticle lifetime to be τ −1 ≈ max( T 2 , ϵ 2 ), where _ is the deviation of the energy of the quasiparticle from the Fermi energy. The energy uncertainty ħτ −1 due to the finite lifetime of a quasiparticle near the Fermi surface is small compared to its energy ϵ , and the quasiparticle concept is well defined. All the momentum transferring scattering processes become asymptotically ineffective, as derived phenomenologically in Chapter 12 and confirmed microscopically in Chapter 19.
Recently, the influence of electron-electron interactions on the thermoelectric transport in a two-channel charge Kondo circuit has been studied in [Phys. Rev. B 105, L121405 (2022)]. In this paper, we revisit the Luttinger-liquid-based model and discuss in details the limit where the spin field is noninteracting (gσ=1g_\sigma = 1gσ​=1) and the interaction in the charge sector is repulsive (0<gρ≤10< g_\rho \leq 10<gρ​≤1). The thermoelectric transport coefficients are computed nonperturbatively with respect to the reflection amplitude at the quantum point contact. At low temperatures the thermopower shows the non-Fermi liquid behavior in the vicinity of the Coulomb peaks. We also demonstrate that repulsive interaction results in the enhancement of the thermoelectrical power.
We have carried out a comprehensive investigation of the quasiparticle properties of a two-dimensional electron gas, interacting via the long-range Coulomb interaction in the presence of bare mass anisotropy (i.e., with an elliptic noninteracting Fermi surface) by calculating the self-energy, the spectral function, the scattering rate, and the effective mass within the leading-order dynamical self-energy approximation. Our theory is exact in the high-density limit. We find anisotropic features of quasiparticle properties that are not captured by the commonly used isotropic approximation where the anisotropic effective mass is replaced by the isotropic averaged density-of-states mass. Some of these interesting results are as follows: (1) The many-body renormalization of the quasiparticle spectrum becomes highly anisotropic as the quasiparticle energy increases away from the Fermi energy; (2) the interaction-induced inelastic-scattering rate features a strong anisotropy, exhibiting an abrupt jump at different injected energies depending on the momentum direction of the injected electron; (3) the effective-mass enhancement is larger (smaller) for the light (heavy) mass, showing that the anisotropy is reduced by interactions. Our results and analysis show that the unjustified neglect of the mass anisotropy can lead to an incorrect description of quasiparticle properties of the anisotropic system and inaccurate estimates of physical quantities of interest although the use of an equivalent isotropic approximation using the density-of-states effective mass as is commonly and uncritically performed in the literature, works as a reasonable approximation in many situations. In addition to the complete random phase approximation theory for the anisotropic quasiparticles, we also provide a theory using the simpler plasmon-pole approximation, commenting on its validity for anisotropic self-energy calculations. We comment also on the interaction effect on the Fermi-surface topology, finding that the elliptic shape of the bare Fermi surface is preserved with suppressed ellipticity in the interacting system to a high degree of accuracy except in the very strongly interacting limit (and for very high bare mass anisotropy). Our theory provides a complete generalization of the existing isotropic many-body theory of interacting electrons to the corresponding anisotropic systems.
Nonreciprocal control of thermoelectric responses offers a promising strategy for next-generation thermal-management and energy-conversion. While nonlinear electrical transport has recently emerged as an intrinsic property of low-symmetry quantum materials, their thermoelectric counterparts have not been demonstrated. Here, exploiting harmonic detection with gradient-reversal techniques, we report intrinsic nonlinear thermoelectric responses up to room temperature in the low-symmetry type-II Weyl semimetals TdT_\mathrm{d}Td​-WTe2_22​ and TaIrTe4_44​ in the absence of magnetic fields or magnetic materials. We resolve all symmetry-allowed components of the second-order thermoelectric tensor, including the nonlinear Seebeck, nonlinear Nernst, and nonlinear mixed-directional thermoelectric effects and demonstrate that both Berry-curvature-related and scattering-induced contributions govern the different nonlinear thermoelectric responses. Our results show that nonlinear thermoelectricity arises intrinsically from reduced crystal symmetry and that engineering effects related to scattering in these materials provides a versatile platform for exploring higher-order heat-to-charge current conversion beyond the linear response.
In this work we discuss extensions of the pioneering analysis by Dzyaloshinski ǐ and Larkin [Sov.Phys.JETP 38, 202 (1974)] of correlation functions for one-dimensional Fermi systems, focusing on the effects of quasiparticle relaxation enabled by a nonlinear dispersion.Throughout the work we employ both, the weakly interacting Fermi gas picture and nonlinear Luttinger liquid theory to describe attenuation of excitations and explore the fermion-boson duality between both approaches.Special attention is devoted to the role of spin-exchange processes, effects of interaction screening, and integrability.Thermalization rates for electron-and hole-like quasiparticles, as well as the decay rate of collective plasmon excitations and the momentum space mobility of spin excitations are calculated for various temperature regimes.The phenomenon of spin-charge drag is considered and the corresponding momentum transfer rate is determined.We further discuss how momentum relaxation due to several competing mechanisms, viz.triple electron collisions, electron-phonon scattering, and long-range inhomogeneities affect transport properties, and highlight energy transfer facilitated by plasmons from the perspective of the inhomogeneous Luttinger liquid model.Finally, we derive the full matrix of thermoelectric coefficients at the quantum critical point of the first conductance plateau transition, and address magnetoconductance in ballistic semiconductor nanowires with strong Rashba spin-orbit coupling.