Wednesday, January 23, 2013

1301.5305 (Juntao Song et al.)

The plateau-insulator transition in the Integer Quantum Hall Effect:
When simulation meets experiment

Juntao Song, Emil Prodan
The transport coefficients for the Hofstadter model of non-interacting electrons in the presence of a magnetic field and strong on-site disorder are computed using an efficient numerical implementation of the non-commutative Kubo formula. The conductivity $\sigma$ and resistivity $\rho$ tensors are mapped as functions of Fermi energy $E_F$ and temperature $T$, and an asymptotic analysis in the limit of low temperatures is performed. In particular, the critical behaviors of the model at the plateau-insulator transition is simulated. The results reproduce all the key experimental findings on the plateau-insulator transition in the Integer Quantum Hall Effect: 1) The graphs of $\rho_{xx}$ as function of $E_F$ at different temperatures intersect each other at a single critical point; 2) All these graphs collapse into a single curve after a one-parameter re-scaling; 3) The scaling exponents are in good agreement with the existing theoretical predictions; 4) The flow of $\sigma$ with the temperature, plotted in the $(\sigma_{xy},\sigma_{xx})$ plane, obeys the semi-circle law; 5) At the critical point, $\sigma_{xx}=\sigma_{xy}=1/2\frac{e^2}{h}$; 6) The Quantized Hall Insulator phase, characterized by $\sigma_{xx}=\sigma_{xy}=0$ and $\rho_{xy}=h/e^2$, is observed at low temperatures.
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