Probing Majorana modes in the tunneling spectra of a resonant level

Abstract

Unambiguous identification of Majorana physics presents an outstanding problem whose solution could render topological quantum computing feasible. We develop a numerical approach to treat finite-size superconducting chains supporting Majorana modes, which is based on iterative application of a two-site Bogoliubov transformation. We demonstrate the applicability of the method by studying a resonant level attached to the superconductor subject to external perturbations. In the topological phase, we show that the spectrum of a single resonant level allows us to distinguish peaks coming from Majorana physics from the Kondo resonance.

Classical impurities and boundary Majorana zero modes in quantum chains

“…7, are in a qualitative agreement with the results of a recent numerical work 23 , where the spectrum of a resonant level attached to the edge of a 1D triplet superconductor was calculated. However, local thermodynamic properties of this system have not been addressed in Ref.…”

“…The main features of the spectral weight A(ω) in the strong localization limit, |m| > Γ, shown schematically in the last plot of Fig. 7, are in a qualitative agreement with the results of a recent numerical work 23 , where the spectrum of a resonant level attached to the edge of a 1D triplet superconductor was calculated. However, local thermodynamic properties of this system have not been addressed in Ref.…”

“…If the temperature is kept finite and h 0 → 0, m 0;< follows a Curie law, m 0;< = χ < (T )h 0 , where χ < (T ) is given by (23). The zero-temperature value of m 0;< displays the expected discontinuity at h 0 → ±0: m 0;< = µ eff sgn(h 0 ).…”

“…This expression yields the picture of a boundary spin µ eff σ z 0 , where µ eff = √ Z is the effective magnetic moment. If the temperature is kept finite and h 0 → 0, m 0;< follows a Curie law, m 0;< = χ < (T )h 0 , where χ < (T ) is given by (23). The zero-temperature value of m 0;< displays the expected discontinuity at h 0 → ±0: m 0;< = µ eff sgn(h 0 ).…”

“…( 24), where µ eff was expressed as the matrix element of the operator σ z 0 between the two degenerate ground states. A renormalized but finite local free-spin susceptibility (23) in the disordered phase reflects the fact that the two ground states only differ locally, that is, in a finite number of degrees of freedom. This shows that in this phase the origin of the exact spectral degeneracy is purely local, and accordingly, cannot be seen in measurements which only probe degrees of freedom far from the impurity.…”