Abstract
We obtain exact expressions for the first three moments of the heat conductance of a quantum chain that crosses over from a superconducting quantum dot to a superconducting disordered quantum wire. Our analytic solution provides exact detailed descriptions of all crossovers that can be observed in the system as a function of its length, which include ballistic-metallic and metallic-insulating crossovers. The two Bogoliubov-de Gennes (BdG) symmetry classes with time-reversal symmetry are accounted for. The striking effect of total suppression of the insulating regime in systems with broken spin-rotation invariance is observed at large length scales. For a single channel system, this anomalous effect can be interpreted as a signature of the presence of the elusive Majorana fermion in a condensed matter system.
Highlights
Random-matrix theory (RMT) has been widely used in the study of phase-coherent complex quantum systems and has been successful in uncovering universal properties of quantum transport in chaotic and disordered systems [1]
Much of the success of RMT in quantum transport is due to the strong correspondence between the statistical properties of random-matrix ensembles and the fluctuations of measured observables of complex quantum systems as a function of some control parameter, such as energy or magnetic field
It has been established that these symmetries lead to a classification of RMT ensembles into ten universal classes [2, 3], which are divided into three categories: (i) WignerDyson (WD, three classes), appropriate to describe normal disordered conductors, (ii) chiral (Ch, three classes), appropriate for systems with a purely off-diagonal disorder, and (iii)
Summary
Random-matrix theory (RMT) has been widely used in the study of phase-coherent complex quantum systems and has been successful in uncovering universal properties of quantum transport in chaotic and disordered systems [1]. The thermal conductivity, on the other hand, despite maybe not containing direct information of topological invariants, as can be seen from their randommatrix description [9], can still provide valuable information about topological phase transitions [10] It was, in the study of disordered quantum wires that evidence of the presence of condensed matter Majorana modes emerged most clearly. In the study of disordered quantum wires that evidence of the presence of condensed matter Majorana modes emerged most clearly These can be traced back to the prediction [11] that for quantum wires in the chiral classes (for odd N open scattering channels) and in the superconducting D and DIII classes there is no exponential localization, since, unlike its behavior in the standard classes, the average conductance falls off in the limit of long distances L ≫ Nl as 1/√L, which is a kind of super-ohmic behavior. If the system is realized as a single channel topological superconductor with broken spin-rotation invariance, we can interpret the total suppression of the insulating regime as a signature of the presence of a condensed matter Majorana fermion
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