Influence of dissipation on quantum Hall plateaus

Abstract

The influence of dissipative scattering on the integer quantum Hall effect is investigated numerically. Dissipation is implemented by connecting the sample to auxiliary phase-destroying electron reservoirs. Our calculations reveal a surprising stability of the Hall plateaus against dissipation, even in the regime of strong backscattering.

Generalized multi-terminal decoherent transport: recursive algorithms and applications to SASER and giant magnetoresistance

“…Thus, in spite of the growing need to include the effects of decoherent processes, [23,24] its applications remained mostly reduced to a few one-dimensional problems. [25][26][27][28][29][30][31] Besides, since the method deals with a great number of self-consistent local chemical potentials, it often involves a cumbersome matrix inversion. Thus, a general multiterminal formulation of the DP model for decoherent transport and an efficient computational strategy are still lacking.…”

Effect of incoherent scattering on shot noise correlations in the quantum Hall regime

“…We have to impose that the current through this probe is zero at any time. This approach, followed in a number of works [1,15,[17][18][19][20][21][22] (see [2] for a review), has the advantage to reduce the problem to the study of coherent scattering in a conductor with one additional contact. The method will be recalled in more detail in the following.…”

The quantum Hall effect in finite structures

“…As already mentioned above, we solve eqn (2) imposing current conservation at all sample sites [14], and thus electrons passing through a reservoir lose their phase memory. Expressed in the language of statistical mechanics, we search for the stationary solution of a stochastic process governed by a master equation.…”

“…In order to calculate the scattering matrix S from the Hamiltonian (eqn (1)), we add dephasing rates δ nm as imaginary self-energies to the on-site potentials in the Hamiltonian [14]. Practically, we solve the system of inhomogeneous equations…”