Volume 116, Number 1, October 2016
|Number of page(s)||6|
|Section||Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties|
|Published online||14 November 2016|
Topological phase transitions in the 1D multichannel Dirac equation with random mass and a random matrix model
1 LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay - 91405 Orsay cedex, France
2 École Normale Supérieure de Cachan - 94235 Cachan cedex, France
3 School of Mathematics, University of Bristol - Bristol BS8 1TW, UK
Received: 4 July 2016
Accepted: 10 October 2016
We establish the connection between a multichannel disordered model —the 1D Dirac equation with matrix random mass— and a random matrix model corresponding to a deformation of the Laguerre ensemble. This allows us to derive exact determinantal representations for the density of states and identify its low-energy behaviour . The vanishing of the exponent α for N specific values of the averaged mass over disorder ratio corresponds to N phase transitions of topological nature characterised by the change of a quantum number (Witten index) which is deduced straightforwardly in the matrix model.
PACS: 73.63.Nm – Quantum wires / 72.15.Rn – Localization effects (Anderson or weak localization) / 02.50.-r – Probability theory, stochastic processes, and statistics
© EPLA, 2016
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