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Tunneling conductance due to discrete spectrum of Andreev states | | P. A. Ioselevich
; M. V. Feigel'man
; | | Date: |
12 Nov 2012 | | Abstract: | We study tunneling spectroscopy of discrete subgap Andreev states in a
superconducting system. If the tunneling coupling is weak, individual levels
are resolved and the conductance $G(V)$ at small temperatures is composed of a
set of resonant Lorentz peaks which cannot be described within perturbation
theory over tunnelling strength. We establish a general formula for their
widths and heights and show that the width of any peak scales as normal-state
tunnel conductance, while its height is $lesssim 2e^2/h$ and depends only on
contact geometry and the spatial profile of the resonant Andreev level. We also
establish an exact formula for the single-channel conductance that takes the
whole Andreev spectrum into account. We use it to study the interference of
Andreev reflection processes through different levels. The effect is most
pronounced at low voltages, where an Andreev level at $E_j$ and its conjugate
at $-E_j$ interfere destructively. This interference leads to the quantization
of the zero-bias conductance: G(0) equals $2e^2/h$ (or 0) if there is (there is
not) a Majorana fermion in the spectrum, in agreement with previous results
from $S$-matrix theory. We also study $G(eV>0)$ for a system with a pair of
almost decoupled Majorana fermions with splitting $E_0$ and show that at lowest
$E_0$ there is a zero-bias Lorentz peak of width $W$ as expected for a single
Majorana fermion (a topological NS-junction) with a narrow dip of width
$E_0^2/W$ at zero bias, which ensures $G(0)=0$ (the NS-junction remains trivial
on a very small energy scale). As the coupling $W$ gets stronger, the dip
becomes narrower, which can be understood as enhanced decoupling of the remote
Majorana fermion. Then the zero-bias dip requires extremely low temperatures
$Tlesssim E_0^2/W$ to be observed. | | Source: | arXiv, 1211.2722 | | Services: | Forum | Review | PDF | Favorites | |
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