Transition from coherent to ohmic conductance explained by a statistical model for the effects of decoherence
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1260-T12-02
Transition from coherent to ohmic conductance explained by a statistical model for the effects of decoherence
Matías Zilly1,*, Orsolya Ujsághy2, and Dietrich E. Wolf1 1
Department of Physics, University Duisburg-Essen and CeNIDE, 47048 Duisburg, Germany
2
Department of Theoretical Physics and Condensed Matter Research Group of the Hungarian Academy of Sciences, Budapest University of Technology and Economics, Budafoki út 8., 1521 Budapest, Hungary ABSTRACT
Using a statistical model for the effects of decoherence [1], we show that in linear tightbinding samples ohmic conductance (resistance proportional to length) is reached for any finite density of decoherence sites, if the chemical potential of the contacts is within a conducting band. If is outside a band, or if due to disorder, no bands form, for high decoherence densities still ohmic conductance is reached, where is a critical decoherence density. For , the sample resistance increases exponentially with the length. INTRODUCTION Resistance of electrical current is caused by momentum relaxation of the electrons. Therefore, in classical Drude theory, the value of the resistivity is governed by the phenomenological momentum relaxation time. Also in semi-classical Boltzmann transport theory it is a common ansatz to model the collision integral using the same relaxation time [2]. On the other hand, in quantum transport there is no momentum relaxation for coherent electrons. The resistance as given by the Landauer-Büttiker formula [3] does not necessarily increase with the system length. Therefore, a natural way to obtain material specific resistivities is to include decoherence into the description of electron transport. Using coherent transport formalism this can be done by attaching fictitious reservoirs (Büttiker probes) to the sample [4-7]. Within the scattering matrix formalism, the sample can be divided into parts and random phase fluctuations can be added to the scattering matrices of the parts thus to obtain decoherence [8,9]. Another approach is to apply the nonequilibrium Green’s function (NEGF) method for the non-coherent case, which for explicit modeling of the interaction [10] computationally is very demanding, therefore also phenomenological models for the self-energy caused by interaction have been proposed [11]. Here we use a statistical model for the effects of decoherence [1] which assumes that electronic transport occurs coherently in between of stochastically distributed “decoherence regions” where the phase information is completely lost. To these decoherence regions we assign electron energy distribution functions which are interrelated by rate equations. The transition *
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rates themselves are calculated by applying the coherent transport formalism. Thus we use a twoscale modeling approach. Microscopically we apply quantum transport formalism, and on the total system scale a classical rate equation describes the transport. In this paper as the samples we consider linear chains described by a ti
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