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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
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)
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)
Theoretical modeling
Low-energy TI states
Effective TI Hamiltonian
SC Hamiltonian
Local potential
TI-SC coupling
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
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