J. P. Dahlhaus

A zero-voltage conductance peak from weak antilocalization in a Majorana nanowire

We show that weak antilocalization by disorder competes with resonant Andreev reflection from a Majorana zero mode to produce a zero-voltage conductance peak of order e2/h in a superconducting nanowire. The phase conjugation needed for quantum interference to survive a disorder average is provided by particle–hole symmetry—in the absence of time-reversal symmetry and without requiring a topologically nontrivial phase. We identify methods of distinguishing the Majorana resonance from the weak antilocalization effect.

Quantum point contact as a probe of a topological superconductor

We calculate the conductance of a ballistic point contact to a superconducting wire, produced by the s-wave proximity effect in a semiconductor with spin–orbit coupling in a parallel magnetic field. The conductance G as a function of contact width or Fermi energy shows plateaux at half-integer multiples of 4e2/h if the superconductor is in a topologically nontrivial phase. In contrast, the plateaux are at the usual integer multiples in the topologically trivial phase. Disorder destroys all plateaux except the first, which remains precisely quantized, consistent with previous results for a tunnel contact. The advantage of a ballistic contact over a tunnel contact as a probe of the topological phase is the strongly reduced sensitivity to finite voltage or temperature.

Quantized Conductance at the Majorana Phase Transition in a Disordered Superconducting Wire

Superconducting wires without time-reversal and spin-rotation symmetries can be driven into a topological phase that supports Majorana bound states. Direct detection of these zero-energy states is complicated by the proliferation of low-lying excitations in a disordered multimode wire. We show that the phase transition itself is signaled by a quantized thermal conductance and electrical shot noise power, irrespective of the degree of disorder. In a ring geometry, the phase transition is signaled by a period doubling of the magnetoconductance oscillations. These signatures directly follow from the identification of the sign of the determinant of the reflection matrix as a topological quantum number.

Fermion-parity anomaly of the critical supercurrent in the quantum spin-Hall effect.

The helical edge state of a quantum spin-Hall insulator can carry a supercurrent in equilibrium between two superconducting electrodes (separation L, coherence length ξ). We calculate the maximum (critical) current I(c) that can flow without dissipation along a single edge, going beyond the short-junction restriction L << ξ of earlier work, and find a dependence on the fermion parity of the ground state when L becomes larger than ξ. Fermion-parity conservation doubles the critical current in the low-temperature, long-junction limit, while for a short junction I(c) is the same with or without parity constraints. This provides a phase-insensitive, dc signature of the 4 π-periodic Josephson effect.

Magnetization Signatures of Light-Induced Quantum Hall Edge States.

Circularly polarized light opens a gap in the Dirac spectrum of graphene and topological insulator (TI) surfaces, thereby inducing a quantum Hall-like phase. We propose to detect the accompanying edge states and their current by the magnetic field they produce. The topological nature of the edge states is reflected in the mean orbital magnetization of the sample, which shows a universal linear dependence as a function of a generalized chemical potential-independent of the driving details and the properties of the material. The proposed protocol overcomes several typically encountered problems in the realization and measurement of Floquet phases, including the destructive effects of phonons and coupled electron baths and provides a way to occupy the induced edge states selectively. We estimate practical experimental parameters and conclude that the magnetization signature of the Floquet topological phase may be detectable with current techniques.

Random-matrix theory of Andreev reflection from a topological superconductor

We calculate the probability distribution of the Andreev reflection eigenvalues

Quantum Hall effect in a one-dimensional dynamical system

{R}_{n}

Wigner-Poisson statistics of topological transitions in a Josephson junction.

at the Fermi level in the circular ensemble of random-matrix theory. Without spin-rotation symmetry, the statistics of the electrical conductance

Emergence of Massless Dirac Fermions in Graphene's Hofstadter Butterfly at Switches of the Quantum Hall Phase Connectivity

G

Dynamics of tunneling into nonequilibrium edge states

depends on the topological quantum number