Onedimensional spinorbit coupled Dirac system with extended $s$wave superconductivity: Majorana modes and Josephson effects
Abstract
Motivated by the spinmomentum locking of electrons at the boundaries of topological insulators, we study a onedimensional system of spinorbit coupled massless Dirac electrons with $s$wave superconducting pairing. As a result of the spinorbit coupling, our model has only two kinds of linearly dispersing modes, which we take to be rightmoving spinup and leftmoving spindown. Both lattice and continuum models are studied. In the lattice model, we find that a single Majorana zero energy mode appears at each end of a finite system provided that the $s$wave pairing has an extended form, with the nearestneighbor pairing being larger than the onsite pairing. We confirm this both numerically and analytically by calculating the winding number. Next we study a lattice version of a model with both Schrödinger and Diraclike terms and find that the model hosts a topological transition between topologically trivial and nontrivial phases depending on the relative strength of the Schrödinger and Dirac terms. We then study a continuum system consisting of two $s$wave superconductors with different phases of the pairing. Remarkably, we find that the system has a {\it single} Andreev bound state which is localized at the junction. When the pairing phase difference crosses a multiple of $2 \pi$, an Andreev bound state touches the top of the superconducting gap and disappears, and a different state appears from the bottom of the gap. We also study the AC Josephson effect in such a junction with a voltage bias that has both a constant $V_0$ and a term which oscillates with a frequency $\omega$. We find that, in contrast to standard Josephson junctions, Shapiro plateaus appear when the Josephson frequency $\omega_J= 2eV_0/\hbar$ is a rational fraction of $\omega$. We discuss experiments which can realize such junctions.
 Publication:

arXiv eprints
 Pub Date:
 July 2020
 arXiv:
 arXiv:2007.00357
 Bibcode:
 2020arXiv200700357U
 Keywords:

 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Superconductivity
 EPrint:
 16 pages, 9 figures