26 research outputs found
Effects of finite superconducting coherence lengths and of phase gradients in topological SN and SNS junctions and rings
We study the effect of a finite proximity superconducting (SC) coherence
length in SN and SNS junctions consisting of a semiconducting topological
insulating wire whose ends are connected to either one or two s-wave
superconductors. We find that such systems behave exactly as SN and SNS
junctions made from a single wire for which some regions are sitting on top of
superconductors, the size of the topological SC region being determined by the
SC coherence length. We also analyze the effect of a non-perfect transmission
at the NS interface on the spatial extension of the Majorana fermions.
Moreover, we study the effects of continuous phase gradients in both an open
and closed (ring) SNS junction. We find that such phase gradients play an
important role in the spatial localization of the Majorana fermions
Engineering and manipulating topological qubits in 1D quantum wires
We investigate the Josephson effect in TNT and NTN junctions, consisting of
topological (T) and normal (N) phases of semiconductor-superconductor 1D
heterostructures in the presence of a Zeeman field. A key feature of our setup
is that, in addition to the variation of the phase of the superconducting order
parameter, we allow the orientation of the magnetic field to change along the
junction. We find a novel magnetic contribution to the Majorana Josephson
coupling that permits the Josephson current to be tuned by changing the
orientation of the magnetic field along the junction. We also predict that a
spin current can be generated by a finite superconducting phase difference,
rendering these materials potential candidates for spintronic applications.
Finally, this new type of coupling not only constitutes a unique fingerprint
for the existence of Majorana bound states but also provides an alternative
pathway for manipulating and braiding topological qubits in networks of wires.Comment: references and a note were added in v2; 6 pages, 2 figures; v1 had
been submitted for the ICM2012 proceedings on the 31st of May 201
Z_2 Invariants of topological insulators as geometric obstructions
We consider a gapped periodic quantum system with time-reversal symmetry of fermionic (or odd) type, i.e. the time-reversal operator squares to −1. We investigate the existence of periodic and time-reversal invariant Bloch frames in dimensions 2 and 3. In 2d, the obstruction to the existence of such a frame is shown to be encoded in a Z2-valued topological invariant, which can be computed by a simple algorithm. We prove that the latter agrees with the Fu-Kane index. In 3d, instead, four Z2 invariants emerge from the construction, again related to the Fu-Kane-Mele indices. When no topological obstruction is present, we provide a constructive algorithm yielding explicitly a periodic and time-reversal invariant Bloch frame. The result is formulated in an abstract setting, so that it applies both to discrete models and to continuous ones
Mutation of Andreev into Majorana bound states in long superconductor-normal and superconductor-normal-superconductor junctions
International audienc
Topological superconductivity in the one-dimensional interacting Creutz model
We consider one-dimensional topological insulators characterized by zero energy end states. In presence of proximity induced pairing, those end states can become Majorana states. We study here the fate of those various end states when Hubbard electron-electron repulsive interactions are added, using a combination of mean-field theory and density matrix renormalization group techniques.Transport électronique dans les isolants topologiquesEtats de Majorana et d'Andreev dans des circuits hybrides combinant des matériaux magnétiques et supraconducteur
Dissipation-enabled fractional Josephson effect
The anomalous 4Ï€-periodic ac Josephson effect, a hallmark of topological Josephson junctions, was experimentally observed in a quantum spin Hall insulator. This finding is unexpected due to time-reversal symmetry preventing the backscattering of the helical edge states and therefore suppressing the 4Ï€-periodic component of the Josephson current. Here, we analyze the two-particle inelastic scattering as a possible explanation for this experimental finding. We show that a sufficiently strong inelastic scattering restores the 4Ï€-periodic component of the current beyond the short Josephson junction regime. Its signature is an observable peak in the power spectrum of the junction at half the Josephson frequency. We propose to use the exponential dependence of the peak width on the applied bias and the magnitude of the dc current as means of verifying that the inelastic scattering is indeed the mechanism responsible for the 4Ï€-periodic signal.QN/Akhmerov Grou
Effects of finite superconducting coherence lengths and of phase gradients in topological SN and SNS junctions and rings
Mutation of Andreev into Majorana bound states in long superconductor-normal and superconductor-normal-superconductor junctions
We study one-dimensional topological SN and SNS long junctions obtained by
placing a topological insulating nanowire in the proximity of either one or two
SC finite-size leads. Using the Majorana Polarization order parameter (MP)
introduced in Phys. Rev. Lett. 108, 096802 (2012)(arxiv:1109.5697) we find that
the extended Andreev bound states (ABS) of the normal part of the wire acquire
a finite MP: for a finite-size SN junction the ABS spectrum exhibits a
zero-energy extended state which carries a full Majorana fermion, while the ABS
of long SNS junctions with phase difference transform into two
zero-energy states carrying two Majorana fermions with the same MP. Given their
extended character inside the whole normal link, and not only close to an
interface, these Majorana-Andreev states can be directly detected in tunneling
spectroscopy experiments