Odd-frequency superconducting pairing in Kitaev-based junctions

We investigate odd-frequency superconducting correlations in normal-superconductor (NS) and short superconductor-normal-superconductor (SNS) junctions with the S region described by the Kitaev model of spinless fermions in one dimension. We demonstrate that, in both the trivial and topological phases, Andreev reflection is responsible for the coexistence of even- and odd-frequency pair amplitudes at interfaces, while normal reflections solely contribute to odd-frequency pairing. At NS interfaces we find that the odd-frequency pair amplitude exhibits large, but finite, values in the topological phase at low frequencies. This enhancement is due to the emergence of a Majorana zero mode at the interface, but notably there is no divergence and a finite odd-frequency pair amplitude also exists outside the topological phase. We also show that the local density of states and local odd-frequency pairing can be characterized solely by Andreev reflections deep in the topological phase. Moreover, in the topological phase of short SNS junctions, we find that both even- and odd-frequency amplitudes capture the emergence of topological Andreev bound states. For a superconducting phase difference $0<\phi<\pi$ the odd-frequency magnitude exhibits a linear frequency ($\sim |\omega|$) dependence at low-frequencies, while at $\phi=\pi$ it develops a resonance peak ($\sim 1/|\omega|$) due to the protected Majorana zero modes.Comment: 12 pages, 7 figures + 7 pages of supplemental material. Published versio

SNS junctions in nanowires with spin-orbit coupling: role of confinement and helicity on the sub-gap spectrum

We study normal transport and the sub-gap spectrum of superconductor-normal-superconductor (SNS) junctions made of semiconducting nanowires with strong Rashba spin-orbit coupling. We focus, in particular, on the role of confinement effects in long ballistic junctions. In the normal regime, scattering at the two contacts gives rise to two distinct features in conductance, Fabry-Perot resonances and Fano dips. The latter arise in the presence of a strong Zeeman field $B$ that removes a spin sector in the leads (\emph{helical} leads), but not in the central region. Conversely, a helical central region between non-helical leads exhibits helical gaps of half-quantum conductance, with superimposed helical Fabry-Perot oscillations. These normal features translate into distinct subgap states when the leads become superconducting. In particular, Fabry-Perot resonances within the helical gap become parity-protected zero-energy states (parity crossings), well below the critical field $B_c$ at which the superconducting leads become topological. As a function of Zeeman field or Fermi energy, these zero-modes oscillate around zero energy, forming characteristic loops, which evolve continuously into Majorana bound states as $B$ exceeds $B_c$. The relation with the physics of parity crossings of Yu-Shiba-Rusinov bound states is discussed.Comment: 12 pages main article, 14 figures + 5 pages supplementary material, 5 figures. Added new appendix. Other minor changes. Published versio

Non-Hermitian phase-biased Josephson junctions

We study non-Hermitian Josephson junctions formed by conventional superconductors with a finite phase difference under non-Hermiticity naturally appearing due to coupling to normal reservoirs. Depending on the structure of non-Hermiticity, captured here in terms of retarded self-energies, the low-energy spectrum hosts topologically stable exceptional points either at zero or finite real energies as a function of the superconducting phase difference. Interestingly, we find that the corresponding phase-biased supercurrents acquire divergent profiles at such exceptional points, an instance that turns out to be a natural and unique non-Hermitian effect that signals a possible way to enhance the sensitivity of Josephson junctions. Our work thus opens the way for realizing unique non-Hermitian phenomena due to the interplay between non-Hermitian topology and the Josephson effect.Comment: 8 pages, 4 figures + 2 pages supplemental materia

Multiple Andreev reflection and critical current in topological superconducting nanowire junctions

We study transport in a voltage biased superconductor-normal-superconductor (SNS) junction made of semiconducting nanowires with strong spin-orbit coupling, as it transitions into a topological superconducting phase for increasing Zeeman field. Despite the absence of a fractional steady-state ac Josephson current in the topological phase, the dissipative multiple Andreev reflection (MAR) current I_dc at different junction transparencies is particularly revealing. It exhibits unique features related to topology, such as the gap inversion, the formation of Majorana bound states, and fermion-parity conservation. Moreover, the critical current I_c, which remarkably does not vanish at the critical point where the system becomes gapless, provides direct evidence of the topological transition.Comment: Published version, 21 pages, 7 figures, 3 appendice

Confinement-induced zero-bias peaks in conventional superconductor hybrids

Majorana bound states in topological superconductors have been predicted to appear in the form of zero-bias conductance peaks of height 2e2/h, which represents one of the most studied signatures so far. Here, we show that quasi-zero-energy states, similar to Majorana bound states, can naturally form in any superconducting hybrid junction due to confinement effects, in the absence of spin fields and, thus, without relation to topology. Remarkably, these topologically trivial quasi-zero-energy states produce zero-bias conductance peaks, that could be similar to Majorana signatures, but develop a different peak height ((4e2/h) and are less stable under gating or depletion of the confined region. Our results put forward confinement as an alternative mechanism to explain the ubiquitous presence of trivial zero-bias peaks and quasi-zero-energy states in superconductor hybrid

Exceptional odd-frequency pairing in non-Hermitian superconducting systems

We first show the realization of exceptional points in a non-Hermitian superconducting system based on a conventional superconductor and then demonstrate that, surprisingly, the system hosts odd-frequency pairing, solely generated by the non-Hermiticity. While there is a coexistence of even- and odd-frequency pairs under general conditions, we find that the even-frequency term vanishes at the exceptional degeneracies, leaving only odd-frequency pairing. This exceptional odd-frequency pairing is directly given by the imaginary part of the eigenvalues at the exceptional points and can be measured from the spectral function. Our results thus put forward non-Hermitian systems as a powerful platform to realize odd-frequency superconducting pairing.Comment: 6 pages, 4 figures + 4 pages supplemental materia

Hybrid superconductor-semiconductor nanowire junctions as useful platforms to study Majorana bound states

Tesis Doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Física de la Materia Condensada. Fecha de lectura: 20-05-2016Esta tesis tiene embargado el acceso al texto completo hasta el 20-11-201