Conductivity of 2D lattice electrons in an incommensurate magnetic field

Details Conductivity of 2D lattice electrons in an incommensurate magnetic field Conductivity of 2D lattice electrons in an incommensurate magnetic field

1995-04-26

arxiv.org/abs/cond-mat/9504102v1

Physics

Condensed Matter

16 pages, postscript files are available on request

Scientific paper

10.1143/JPSJ.65.529

We consider conductivities of two-dimensional lattice electrons in a magnetic field. We focus on systems where the flux per plaquette $\phi$ 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 $\sigma_{xx}(\omega)$. Using a scaling analysis, we have found $\Re\sigma_{xx}(\omega)$ behaves as $1/\omega ^{\gamma}$ \,$(\gamma =0.55)$ when $\phi =\tau,(\tau =\frac{\sqrt{5}-1}{2})$ and the Fermi energy is near zero. This behavior is closely related to the known scaling behavior of the spectrum.

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