Conductivity of 2D Lattice Electrons in an Incommensurate Magnetic Field

Abstract

We consider conductivities of two-dimensional lattice electrons in a magnetic field. We focus on systems where the flux per plaquette φ is irrational (incommensurate flux). To realize the system with the incommensurate flux, we consider a series of systems with commensurate fluxes which converge to the irrational value. We have calculated a real part of the longitudinal conductivity σ xx (ω). Using a scaling analysis, we have found ℜσ xx (ω) behaves as 1/ω γ (γ = 0.55) when φ = τ, (τ = √ 5−12 ) and the Fermi energy is near zero. This behavior is closely related to the known scaling behavior of the spectrum.Typeset using REVT E X

Topological aspects of the quantum Hall effect

“…Let us focus on the dc Hall conductance σ xy , since we can clearly demonstrate the topological origin via the adiabatic approximation [30]. (Also we can derive a general expression for the conductance via the Kubo formula [34,35]. It is, however, not topological in general as shown later.…”

“…General expressions for the conductance tensors can be obtained by using the Kubo formula. We simply cite the results here [35]. (Some of the results are also obtained in reference [34].)…”

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