Time-delay matrix, midgap spectral peak, and thermopower of an Andreev billiard

Abstract

We derive the statistics of the time-delay matrix (energy derivative of the scattering matrix) in an ensemble of superconducting quantum dots with chaotic scattering (Andreev billiards), coupled ballistically to $M$ conducting modes (electron-hole modes in a normal metal or Majorana edge modes in a superconductor). As a first application we calculate the density of states ${\rho }_0$ at the Fermi level. The ensemble average $⟨{\rho }_0⟩={\delta }_0^{-1}M[\max (0,M+2\alpha /\beta ){]}^{-1}$ deviates from the bulk value $1/{\delta }_0$ by an amount depending on the Altland-Zirnbauer symmetry indices $\alpha ,\beta$. The divergent average for $M=1,2$ in symmetry class D ($\alpha =-1$, $\beta =1$) originates from the mid-gap spectral peak of a closed quantum dot, but now no longer depends on the presence or absence of a Majorana zero-mode. As a second application we calculate the probability distribution of the thermopower, contrasting the difference for paired and unpaired Majorana edge modes.

13 pages, 6 figures

References in corpus (9)

• Zero-bias anomaly in a nanowire quantum dot coupled to superconductors
• Nonlocal Thermoelectric Effects and Nonlocal Onsager Relations in a Three-Terminal Proximity-Coupled Superconductor-Ferromagnet Device
• Transport Through Andreev Bound States in a Graphene Quantum Dot
• Surface States, Edge Currents and the Angular Momentum of Chiral p-wave Superfluids
• Andreev billiards
• Thermopower induced by a supercurrent in superconductor-normal-metal structures
• Theory of a large thermoeffect in superconductors doped with magnetic impurities
• Disentangling Majorana fermions from conventional zero energy states in semiconductor quantum wires
• Superconducting proximity effect in quantum wires without time-reversal symmetry

Cited by in corpus (5)

• Separation of heat and charge currents for boosted thermoelectric conversion
• Efficient semiclassical approach for time delays
• X-shaped and Y-shaped Andreev resonance profiles in a superconducting quantum dot
• Random matrix theory of quantum transport in chaotic cavities with non-ideal leads
• Effect of chiral symmetry on chaotic scattering from Majorana zero modes