Semiclassical transport with Berry curvature: Chambers formula and applications to systems with Fermi surface topological transitions

Abstract

Starting with general semiclassical equations of motion for electrons in the presence of electric and magnetic fields, we extend the Chambers formula to include in addition to a magnetic field, timedependent electric fields and bands with Berry curvature. We thereby compute the conductivity tensor σ αβ (B, ω) in the presence of magnetic field for bands in two (2D) and three (3D) dimensions with Berry curvature. We focus then on several applications to magnetotransport for metals with Fermi surface topological transitions in 2D. In particular, we consider a rectangular lattice and a model related to overdoped graphene, to investigate the signatures of different types of Fermi surface topological transitions in metals in the Hall coefficient, Hall conductivity σxy and longitudinal conductivity σxx. The behavior of those quantities as a function of frequency, when the electric field is time dependent, is also investigated. As an example of non-zero Berry curvature, we study the magnetotransport of the Haldane model within this context. In addition, we provide the linear and nonlinear electric current formula to order E 2 .

A Practical Method to Detect, Analyze, and Engineer Higher Order Van Hove Singularities in Multi‐band Hamiltonians

“…Low energy theories determined either by polynomial fits or purely symmetry considerations are often also a stepping stone for further analysis, such as diagrammatic many-body treatment of electronic correlations and transport studies. [7,29,30] But the full and correct Taylor expansion to a given order is needed for the unambiguous diagnosis of a HOVHS (see Ref. [3] for an illustration of how relying purely on symmetry considerations can lead to a misdiagnosis of the HOVHS, the DOS divergence exponent and the ratio of prefactors).…”

A practical method to detect, analyse and engineer higher order Van Hove singularities in multi-band Hamiltonians

“…The HOVHS can be diagnosed from the Taylor expansion of the band in question, at the chosen k point. Low energy theories determined either by polynomial fits or purely symmetry considerations are often also a stepping stone for further analysis, such as diagrammatic many-body treatment of electronic correlations and transport studies [7,29,30]. But the full and correct Taylor expansion to a given order is needed for the unambiguous diagnosis of a HOVHS (see Ref [3] for an illustration of how relying purely on symmetry considerations can lead to a misdiagnosis of the HOVHS, the DOS divergence exponent and the ratio of prefactors).…”