Bimodal conductance distribution of Kitaev edge modes in topological superconductors

Abstract

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.

11 pages, 13 figures

References in corpus (5)

• Topological Insulators with Inversion Symmetry
• Anderson Transitions
• Localization in disordered superconducting wires with broken spin-rotation symmetry
• Topological indices, defects and Majorana fermion in chiral superconductors
• Thermal metal-insulator transition in a helical topological superconductor

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• Statistical Majorana Bound State Spectroscopy
• Wiedemann-Franz-type relation between shot noise and thermal conduction of Majorana surface states in a three-dimensional topological superconductor
• Topological reflection matrix
• Asymmetric $d$-wave superconducting topological insulator in proximity with a magnetic order
• Detrimental effects of disorder in two-dimensional time-reversal invariant topological superconductors
• Persistent current in 2D topological superconductors
• Quantum theory for edge current and noise in two-dimensional topological superconductors