Interplay of exciton condensation and quantum spin Hall effect in InAs/GaSb bilayers

We study the phase diagram of the inverted InAs/GaSb bilayer quantum wells. For small tunneling amplitude between the layers, we find that the system is prone to formation of an s-wave exciton condensate phase, where the spin-structure of the order parameter is uniquely determined by the small spin-orbit coupling arising from the bulk inversion asymmetry. The phase is topologically trivial and does not support edge transport. On the contrary, for large tunneling amplitude, we obtain a topologically non-trivial quantum spin Hall insulator phase with a p-wave exciton order parameter, which enhances the hybridization gap. These topologically distinct insulators are separated by an insulating phase with spontaneously broken time-reversal symmetry. Close to the phase transition between the quantum spin Hall and time-reversal broken phases, the edge transport shows quantized conductance in small samples, whereas in long samples the mean free path associated with the backscattering at the edge is temperature independent, in agreement with recent experiments.Comment: v. 2, 9 pages, 5 figure

Extended topological group structure due to average reflection symmetry

We extend the single-particle topological classification of insulators and superconductors to include systems in which disorder preserves average reflection symmetry. We show that the topological group structure of bulk Hamiltonians and topological defects is exponentially extended when this additional condition is met, and examine some of its physical consequences. Those include localization-delocalization transitions between topological phases with the same boundary conductance, as well as gapless topological defects stabilized by average reflection symmetry.Comment: 8 pages, 5 figures, 1 table; improved section 4 "Extended topological classification" incl. example of stacked QSH layer

X-shaped and Y-shaped Andreev resonance profiles in a superconducting quantum dot

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 $N\times N$ 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 $\propto\sqrt{N}$ 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).Comment: Contribution for the JETP special issue in honor of A.F. Andreev's 75th birthday. 9 pages, 8 figure

Bimodal conductance distribution of Kitaev edge modes in topological superconductors

A two-dimensional superconductor with spin-triplet p-wave pairing supports chiral or helical Majorana edge modes with a quantized (length $L$-independent) thermal conductance. Sufficiently strong anisotropy removes both chirality and helicity, doubling the conductance in the clean system and imposing a super-Ohmic $1/\sqrt{L}$ decay in the presence of disorder. We explain the absence of localization in the framework of the Kitaev Hamiltonian, contrasting the edge modes of the two-dimensional system with the one-dimensional Kitaev chain. While the disordered Kitaev chain has a log-normal conductance distribution peaked at an exponentially small value, the Kitaev edge has a bimodal distribution with a second peak near the conductance quantum. Shot noise provides an alternative, purely electrical method of detection of these charge-neutral edge modes.Comment: 11 pages, 13 figure

Phase-locked magnetoconductance oscillations as a probe of Majorana edge states

We calculate the Andreev conductance of a superconducting ring interrupted by a flux-biased Josephson junction, searching for electrical signatures of circulating edge states. Two-dimensional pair potentials of spin-singlet d-wave and spin-triplet p-wave symmetry support, respectively, (chiral) Dirac modes and (chiral or helical) Majorana modes. These produce h/e-periodic magnetoconductance oscillations of amplitude \simeq (e^{2}/h)N^{-1/2}, measured via an N-mode point contact at the inner or outer perimeter of the grounded ring. For Dirac modes the oscillations in the two contacts are independent, while for an unpaired Majorana mode they are phase locked by a topological phase transition at the Josephson junction.Comment: 10 pages, 6 figures. New appendix on the gauge invariant discretization of the Bogoliubov-De Gennes equation. Accepted for publication in PR