High-frequency thermoelectric response in correlated electronic systems

Abstract

We derive a general formalism for evaluating the high-frequency limit of the thermoelectric power of strongly correlated materials, which can be straightforwardly implemented in available first principles LDA+DMFT programs. We explore this formalism using model Hamiltonians and we investigate the validity of approximating the static thermoelectric power S0, by its high-temperature limit, S * . We point out that the behaviors of S * and S0 are qualitatively different for a correlated Fermi liquid near the Mott transition, when the temperature is in the coherent regime. When the temperature is well above the coherent regime, e.g., when the transport is dominated by incoherent excitations, S * provides a good estimation of S0.

Maximum entropy analytic continuation for frequency-dependent transport coefficients with nonpositive spectral weight

“…For quantum Monte-Carlo data in particular, the most direct way to extract the real-frequency dependent response functions is then to perform maximum entropy analytic continuations (MEACs) [8,9]. However, as we explain in more details below, MEAC is not always trivial since it requires that the spectral weight of response functions is real and positive, which is not necessarily the case in general.Many approaches have been investigated to circumvent this major problem for the Seebeck coefficient [10][11][12][13][14][15][16][17][18][19], the Hall coefficient [20-24] and the Nernst coefficient [25] for instance, but all of them are either approximations or analytic methods that are exact only in a certain frequency limit [26]. The most common approach consists in neglecting vertex corrections, in which case it is possible to compute transport coefficients directly from the single-particle spectral weight.…”

“…Many approaches have been investigated to circumvent this major problem for the Seebeck coefficient [10][11][12][13][14][15][16][17][18][19], the Hall coefficient [20][21][22][23][24] and the Nernst coefficient [25] for instance, but all of them are either approximations or analytic methods that are exact only in a certain frequency limit [26]. The most common approach consists in neglecting vertex corrections, in which case it is possible to compute transport coefficients directly from the single-particle spectral weight.…”

“…where f is the Fermi-Dirac distribution and A( k, ω) is the spectral function containing the non-interacting square-lattice dispersion ε k and normalized so that dω A( k, ω) = 1. In this notation, χ ν=0 (ω) = χ ExEx (ω), χ ν=1 (ω) = χ ExTx (ω), and χ ν=2 (ω) = χ TxTx (ω) [19]. Here, the usual integral over wave-vectors has been replaced by an integral over the band energies ε weighted by the longitudinal transport function [36] (23) containing the non-interacting density of states N 0 , normalized so that N 0 (z) dz = 1.…”

“…We take U = 14, temperature T = 1, and set the chemical potential so that filling is n = 0.85, a case studied in Ref. [19]. It is at high-temperature that analytic continuation is most difficult and that the sign change in the frequency-dependent thermoelectric spectral weight is largest [19].…”

“…[19]. It is at high-temperature that analytic continuation is most difficult and that the sign change in the frequency-dependent thermoelectric spectral weight is largest [19]. A more thorough comparison and results at a lower temperature T = 1/10 are presented in the supplemental material Ref.…”