Robustness of Topological Superconductivity in Proximity-Coupled Topological Insulator

Nanoribbons

Tudor D. Stanescu

West Virginia University

Collaborators: Piyapong Sitthison (WVU)

Brasov September, 2014

Outline

Majorana fermions in solid state structures: status and challenges

Proximity-coupled topological insulator nanoribbons• Modeling• Low-energy states• Phase diagram• Proximity-induced gap

IMajorana fermions in solid state structures

Experimental status: NOT observed

Majorana (1937): neutral spin-1/2 particles can be described by a real wave equation:

Question: Are the spinors representing spin-1/2 particles necessarily complex ?

Relevance: particle physics (neutrinos ?)

2000s: Majorana fermions can emerge as quasi-particle excitations in solid-state systems

Majorana fermion – an electrically neutral particle which is its own antiparticle

What is a Majorana fermion?

electron (-e)

hole (+e)

Cooper pair (-2e)

charge is not an observable the elementary excitations are combinations of particles and holes (Bogoliubov quasiparticles)

Superconductors – the natural hosts for Majoranas

Particle-hole symmetry

Zero energy state (Majorana fermion)

Spinless fermions + particle-hole symmetry Majoranas at E=0

1D spinless p-wave superconductorKitaev, Physics-Uspekhi, 01

Sau et al., PRL’10Alicea PRB’10

Semiconductornanowire

SuperconductorLutchyn et al., PRL’10Oreg et al., PRL’10

Spin-orbitcoupling

Zeemansplitting

Proximity-inducedsuperconductivity

Single-channel nanowire

Practical route to realizing Majorana bound states

Probing Majorana bound states: tunneling spectroscopy

Sau et al., PRB 82, 214509 (2010)

TDS et al., PRB 84, 144522 (2011)

Experimental signatures of Majorana physics

Mourik et al., Science 336, 1003 (2012)

TDS et al., PRB 84, 144522 (2011)

Suppression of the gap-closing signature

TDS et al., PRL 109, 266402 (2012)

Low-energy spectra in the presence of disorder

TDS et al., PRB 84, 144522 (2011)

Static disorder

Interface inhomogeneity

Takei et al., PRL 110, 186803 (2013)

What is responsible for the selective qp broadening?

Proximity effect in a NM-SM-SC hybrid structure

TDS et al., PRB 90, 085302 (2014)

The soft gap in dI/dV and LDOS

TDS et al., PRB 90, 085302 (2014)

IIProximity-Coupled Topological Insulator

Nanoribbons

The topological insulator Majorana wire

Cook & Franz, PRB 86, 155431 (2012)

Theoretical modeling

Low-energy TI states

Effective TI Hamiltonian

SC Hamiltonian

Local potential

TI-SC coupling

Effective Green function

BdG equation

Low-energy TI spectrum (3D)

Sitthison & TDS, PRB 90, 035313 (2014)

Low-energy TI spectrum (2D)

Sitthison & TDS, PRB 90, 035313 (2014)

Low-energy TI spectrum (1D)

Sitthison & TDS, PRB 90, 035313 (2014)

V=0; F=0 V=0; F=0.5 V=0.05; F=0.5

Low-energy states

Sitthison & TDS, PRB 90, 035313 (2014)

V=0; F=0.5 V=0.05; F=0.5

Proximity-induced quasiparticle gap

Sitthison & TDS, PRB 90, 035313 (2014)

=0.05 m eV

=-0.09 m eV

Phase diagram

Sitthison & TDS, PRB 90, 035313 (2014)

Induced qp gap as function of m and F

Sitthison & TDS, PRB 90, 035313 (2014)

Single interface structures

Sitthison & TDS, PRB 90, 0000 (2014)

V=0V=0.03 eV

V=0.06 eV

Tuning the chemical potential using gates

Sitthison & TDS, PRB 90, 0000 (2014)

Conclusions

Details matter; the unambiguous demonstration of Majorana bound states realistic modelling & controlled exp. conditions

TI-SC structures; the realization of robust topological SC phases (and Majorana bound states) over a wide range of m is not a straightforward task

Main problem: intrinsic or applied bias potentials may push some of the low-energy states away from the interface

Possible solution: symmetric TI-SC structures