Download - Robustness of Topological Superconductivity in Proximity-Coupled Topological Insulator Nanoribbons
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