A General Expression for Hall Coefficient Based on Fermi Liquid Theory

Kohno, Hiroshi; Yamada, Kōsaku

doi:10.1143/ptp.80.623

Cited by 68 publications

(18 citation statements)

References 5 publications

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“…The calculation of σ xy in the self-consistent Born approximation can be found in Refs [51][52][53]. At the level of approximation employed here, we find it easier to apply the method developed in Ref [54] to the conductivity diagrams shown in Fig 2 (c).…”

Section: Frequency-dependent Hall Conductivity In the Perturbatiomentioning

confidence: 97%

Optical and Hall conductivities of a thermally disordered two-dimensional spin-density wave: Two-particle response in the pseudogap regime of electron-doped high-Tcsuperconductors

Lin

Millis

2011

Phys. Rev. B

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We calculate the frequency-dependent longitudinal (σxx) and Hall (σxy) conductivities for twodimensional metals with thermally disordered antiferromagnetism using a generalization of a theoretical model, involving a one-loop quasistatic fluctuation approximation, which was previously used to calculate the electron self energy. The conductivities are calculated from the Kubo formula, with current vertex function treated in a conserving approximation satisfying the Ward identity. In order to obtain a finite DC limit, we introduce phenomenologically impurity scattering, characterized by a relaxation time τ . σxx(Ω) satisfies the f -sum rule. For the infinitely peaked spin correlation function, χ(q) ∝ δ(q − Q), we recover the expressions for the conductivities in the mean-field theory of the ordered state. When the spin correlation length ξ is large but finite, both σxx and σxy show behaviors characteristic of the state with long-range order. The calculation runs into difficulty for Ω 1/τ . The difficulties are traced to an inaccurate treatment of the very low energy density of states within the one-loop quasistatic approximation for the self energy. The results for σxx(Ω) and σxy(Ω) are qualitatively consistent with data on electron-doped cuprates when Ω > 1/τ .

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Section: Frequency-dependent Hall Conductivity In the Perturbatiomentioning

confidence: 97%

Optical and Hall conductivities of a thermally disordered two-dimensional spin-density wave: Two-particle response in the pseudogap regime of electron-doped high-Tcsuperconductors

Lin

Millis

2011

Phys. Rev. B

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“…The conductance is obtained from the Kubo formula [49] and by using the L‚Hôpital's rule and the Cauchy-Riemann equations. Within DMFT, the contribution from the vertex corrections of the CO to the Hall conductance is suppressed by the dimensionality of the system [43,50]. Thus, Π yx = 1 β ∑ n Tr[ j y G(iω n + iω n ) j x G(iω n )], where the trace is for both momentum and spin degree of freedom.…”

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confidence: 99%

Interaction-enhanced integer quantum Hall effect in disordered systems

2019

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We study transport properties and topological phase transition in two-dimensional interacting disordered systems. Within dynamical mean-field theory, we derive the Hall conductance, which is quantized and serves as a topological invariant for insulators, even when the energy gap is closed by localized states. In the spinful Harper-Hofstadter-Hatsugai model, in the trivial insulator regime, we find that the repulsive on-site interaction can assist weak disorder to induce the integer quantum Hall effect, while in the topologically non-trivial regime, it impedes Anderson localization. Generally, the interaction broadens the regime of the topological phase in the disordered system. PACS numbers: xxThe quantum Hall effect (QHE) in the presence of interaction and disorder has been of great interest for a long time.Interactions play an essential role in the fractional QHE [1] and disorder is responsible for the existence of the plateaux in the Hall conductance [2][3][4][5]. For different models, the perfect quantization of conductance can be violated [6][7][8][9][10][11][12][13][14][15][16] or conversely induced [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] by disorder and interaction, respectively. Topological invariants are constructed to classify the resulting transport properties [33][34][35] in systems with bulk energy gaps. General expressions for the invariants of interacting and disordered systems were developed from the perspective of the many-body wave functions (MBW) [36][37][38][39]. Nonetheless, the MBW can be captured numerically only for a rather small size of the interacting system. Equivalent expressions in terms of the single-particle Green's function were developed thereafter, based on the microscopic theory [40][41][42], which are numerically accessible even for infinite systems if translational symmetry (TS) is assumed [43]. arXiv:1805.10491v2 [cond-mat.dis-nn]

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“…As shown in [22] this formula leads to the constant Hall coefficient if the spectral function ρ p (ε) is delta-function-like and isotropic in momentum space. The Fermi-liquid theory for the Hall coefficient [2] also assumes the delta-function-like spectral function so that it also leads to almost temperature-independent Hall coefficient. While the Fermi-liquid theory exploits only the information on the Fermi surface, our scheme exploits the entire Brillouin zone.…”

Section: Remarksmentioning

confidence: 99%

“…One of the most striking and puzzling anomalies is the strong temperature dependence of the Hall coefficient [1]. In the Fermi-liquid theory for a single-band case the Hall coefficient is a measure for the carrier density of the metal and almost temperature-independent [2]. Thus many attempts have been made to explain the Hall coefficient from non-Fermi-liquid viewpoints [1,3,4].…”

Section: Introductionmentioning

confidence: 99%

Spectral function method for Hall conductivity of incoherent metals

Narikiyo

2017

Int. J. Mod. Phys. B

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Using a model spectral function of the electron the Hall conductivity in the normal metallic state of the Pr_{2-x}Ce_xCuO_4 (PCCO) superconductor is calculated neglecting the current vertex-correction. The result is qualitatively consistent with the experiment. Consequently the reason becomes clear why the Fermi-liquid theory fails to explain the anomaly of the Hall conductivity. The inconsistency of the fluctuation-exchange approximation also becomes clear.Comment: arXiv admin note: substantial text overlap with arXiv:1204.530

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A General Expression for Hall Coefficient Based on Fermi Liquid Theory

Cited by 68 publications

References 5 publications

Optical and Hall conductivities of a thermally disordered two-dimensional spin-density wave: Two-particle response in the pseudogap regime of electron-doped high-Tcsuperconductors

Optical and Hall conductivities of a thermally disordered two-dimensional spin-density wave: Two-particle response in the pseudogap regime of electron-doped high-Tcsuperconductors

Interaction-enhanced integer quantum Hall effect in disordered systems

Spectral function method for Hall conductivity of incoherent metals

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