The quasi-bound states of a superconducting quantum dot that is weakly coupled to a normal metal appear as resonances in the Andreev reflection probability, measured via the differential conductance. We study the evolution of these Andreev resonances
when an external parameter (such as magnetic field or gate voltage) is varied, using a random-matrix model for the $Ntimes N$ scattering matrix. We contrast the two ensembles with broken time-reversal symmetry, in the presence or absence of spin-rotation symmetry (class C or D). The poles of the scattering matrix in the complex plane, encoding the center and width of the resonance, are repelled from the imaginary axis in class C. In class D, in contrast, a number $proptosqrt{N}$ of the poles has zero real part. The corresponding Andreev resonances are pinned to the middle of the gap and produce a zero-bias conductance peak that does not split over a range of parameter values (Y-shaped profile), unlike the usual conductance peaks that merge and then immediately split (X-shaped profile).
We calculate the conductance of a two-dimensional bilayer with inverted electron-hole bands, to study the sensitivity of the quantum spin Hall insulator (with helical edge conduction) to the combination of electrostatic disorder and a perpendicular m
agnetic field. The characteristic breakdown field for helical edge conduction splits into two fields with increasing disorder, a field $B_{c}$ for the transition into a quantum Hall insulator (supporting chiral edge conduction) and a smaller field $B_{c}$ for the transition to bulk conduction in a quasi-metallic regime. The spatial separation of the inverted bands, typical for broken-gap InAs/GaSb quantum wells, is essential for the magnetic-field induced bulk conduction --- there is no such regime in HgTe quantum wells.
We show how a quantum dot with a ballistic single-channel point contact to a superconductor can be created by means of a gate electrode at the edge of a quantum spin Hall insulator (such as an InAs/GaSb quantum well). A weak perpendicular magnetic fi
eld traps a Majorana zero-mode, so that it can be observed in the gate-voltage-averaged differential conductance <dI/dV> as a 4e^2/h zero-bias peak above a (2/3{pi}^2 - 4)e^2/h background. The one-dimensional edge does not permit the braiding of pairs of Majorana fermions, but this obstacle can be overcome by coupling opposite edges at a constriction, allowing for a demonstration of non-Abelian statistics.
We calculated the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between the magnetic impurities mediated by electrons in nanoribbons. It was shown that the RKKY interaction is strongly dependent on the width of the nanoribbon and the transverse po
sitions of the impurities. The transverse confinement of electrons is responsible for the above size effect of the RKKY interaction. It provides a potential way to control the RKKY interaction by changing nanostructure geometry.
