• Corpus ID: 220280262

Majorana modes for a one-dimensional spin-orbit coupled Dirac system with extended $s$-wave superconductivity

@article{Udupa2020MajoranaMF,
  title={Majorana modes for a one-dimensional spin-orbit coupled Dirac system with extended \$s\$-wave superconductivity},
  author={Adithi Udupa and Abhishek Banerjee and K Sengupta and Diptiman Sen},
  journal={arXiv: Mesoscale and Nanoscale Physics},
  year={2020}
}

• Adithi Udupa, A. Banerjee, +1 author D. Sen
• Published 1 July 2020
• Physics
• arXiv: Mesoscale and Nanoscale Physics

We study a one-dimensional system of spin-orbit coupled Dirac electrons with $s$-wave superconducting pairing. Both lattice and continuum models are studied. In the lattice model, we find that zero energy end modes appear provided that the $s$-wave pairing has an extended form, and the nearest-neighbor pairing is larger than the on-site pairing. We confirm this both numerically and analytically by calculating the winding number. We find that the continuum model also has zero energy end modes. Next we study a lattice version of a model with both Schrodinger and Dirac-like terms and find that the model hosts a topological transition between topologically trivial and non-trivial phases depending on the relative strength of the Schrodinger and Dirac terms. Finally, we study a continuum system consisting of two $s$-wave superconductors with different phases of the pairing, with a $\delta$-function potential barrier lying at the junction of the two superconductors. We find that the system has a 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 junctions 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.