Wiedemann-Franz-type relation between shot noise and thermal conduction of Majorana surface states in a three-dimensional topological superconductor

Abstract

We compare the thermal conductance $G_{\mathrm{thermal}}$ (at temperature $T$) and the electrical shot noise power $P_{\mathrm{shot}}$ (at bias voltage $V\gg k_{\mathrm{B}}T/e$) of Majorana fermions on the two-dimensional surface of a three-dimensional topological superconductor. We present analytical and numerical calculations to demonstrate that, for a local coupling between the superconductor and metal contacts, $G_{\mathrm{thermal}}/P_{\mathrm{shot}}=\mathcal{L}T/eV$ (with $\mathcal{L}$ the Lorenz number). This relation is ensured by the combination of electron-hole and time-reversal symmetries, irrespective of the microscopics of the surface Hamiltonian, and provides for a purely electrical way to detect the charge-neutral Majorana surface states. A surface of aspect ratio $W/L\gg 1$ has the universal shot-noise power $P_{\mathrm{shot}}=(W/L)\times (e^2/h)\times (eV/2\pi )$

11 pages, 9 figures

References in corpus (7)

• Quantum-limited shot noise in graphene
• Local Measurements of the Superconducting Pairing Symmetry in CuxBi2Se3
• A road to reality with topological superconductors
• Topological protection, disorder, and interactions: Survival at the surface of 3D topological superconductors
• Bimodal conductance distribution of Kitaev edge modes in topological superconductors
• Surface transport coefficients for three-dimensional topological superconductors
• Helical Majorana surface states of strongly disordered topological superconductors with time-reversal symmetry

Cited by in corpus (2)

• Thermoelectric transport through Majorana bound states and violation of Wiedemann-Franz law
• Mixed electrical-heat noise spectrum in a quantum dot