44 research outputs found
Stability of flat zero-energy states at the dirty surface of a nodal superconductor
We discuss the stability of highly degenerate zero-energy states tha appear
at the surface of a nodal superconductor preserving time-reversal symmetry. The
existence of such surface states is a direct consequence of the nontrivial
topological numbers defined in the restricted Brillouin zones in the clean
limit. In experiments, however, potential disorder is inevitable near the
surface of a real superconductor, which may lift the high degeneracy at zero
energy. We show that an index defined in terms of the chiral eigenvalues of the
zero-energy states can be used to measure the degree of degeneracy at zero
energy in the presence of potential disorder. We also discuss the relationship
between the index and the topological numbers.Comment: 12 pages, 7 figure
Symmetry conditions of a nodal superconductor for generating robust flat-band Andreev bound states at its dirty surface
We discuss the symmetry property of a nodal superconductor that hosts robust
flat-band zero-energy states at its surface under potential disorder. Such
robust zero-energy states are known to induce the anomalous proximity effect in
a dirty normal metal attached to a superconductor. A recent study has shown
that a topological index describes the number of
zero-energy states at the dirty surface of a -wave superconductor. We
generalize the theory to clarify the conditions required for a superconductor
that enables . Our results show that is realized in a topological material that belongs to
either the BDI or CII class. We also present two realistic Hamiltonians that
result in .Comment: 9 pages, 3 figure
Tunable -Josephson junction with a quantum anomalous Hall insulator
We theoretically study the Josephson current in a superconductor/quantum
anomalous Hall insulator/superconductor junction by using the lattice Green
function technique. When an in-plane external Zeeman field is applied to the
quantum anomalous Hall insulator, the Josephson current flows without a
phase difference across the junction . The phase shift
appealing in the current-phase relationship ) is
proportional to the amplitude of Zeeman fields and depends on the direction of
Zeeman fields. A phenomenological analysis of the Andreev reflection processes
explains the physical origin of . A quantum anomalous Hall insulator
breaks time-reversal symmetry and mirror reflection symmetry simultaneously.
However it preserves magnetic mirror reflection symmetry. Such characteristic
symmetry property enable us to have a tunable -junction with a quantum
Hall insulator.Comment: 10pages, 9figure
Quantization of Conductance Minimum and Index Theorem
We discuss the minimum value of the zero-bias differential conductance
in a junction consisting of a normal metal and a nodal
superconductor preserving time-reversal symmetry. Using the quasiclassical
Green function method, we show that is quantized at in the limit of strong impurity scatterings in the
normal metal. The integer represents the number of perfect
transmission channels through the junction. An analysis of the chiral symmetry
of the Hamiltonian indicates that corresponds to the
Atiyah-Singer index in mathematics.Comment: 5 pages, 1 figur
Josephson effect in two-band superconductors
We study theoretically the Josephson effect between two time-reversal
two-band superconductors, where we assume the equal-time spin-singlet -wave
pair potential in each conduction band. %as well as the band asymmetry and the
band hybridization in the normal state. The superconducting phase at the first
band and that at the second band characterize a
two-band superconducting state. We consider a Josephson junction where an
insulating barrier separates two such two-band superconductors. By applying the
tunnel Hamiltonian description, the Josephson current is calculated in terms of
the anomalous Green's function on either side of the junction. We find that the
Josephson current consists of three components which depend on three types of
phase differences across the junction: the phase difference at the first band
, the phase difference at the second band ,
and the difference at the center-of-mass phase .
A Cooper pairs generated by the band hybridization carries the last current
component. In some cases, the current-phase relationship deviates from the
sinusoidal function as a result of time-reversal symmetry breaking down.Comment: 6 page, 2 figure
Strong anomalous proximity effect from spin-singlet superconductors
The proximity effect from a spin-triplet -wave superconductor to a dirty
normal-metal has been shown to result in various unusual electromagnetic
properties, reflecting a cooperative relation between topologically protected
zero-energy quasiparticles and odd-frequency Cooper pairs. However, because of
a lack of candidate materials for spin-triplet -wave superconductors,
observing this effect has been difficult. In this paper, we demonstrate that
the anomalous proximity effect, which is essentially equivalent to that of a
spin-triplet -wave superconductor, can occur in a semiconductor/high-
cuprate superconductor hybrid device in which two potentials coexist: a
spin-singlet -wave pair potential and a spin--orbit coupling potential
sustaining the persistent spin-helix state. As a result, we propose an
alternative and promising route to observe the anomalous proximity effect
related to the profound nature of topologically protected quasiparticles and
odd-frequency Cooper pairs.Comment: 6 pages, 4 figure