What is a Majorana fermion?

Report
Robustness of Topological Superconductivity in
Proximity-Coupled Topological Insulator
Nanoribbons
Tudor D. Stanescu
West Virginia University
Collaborators:
Brasov
September, 2014
Piyapong Sitthison
(WVU)
Outline
 Majorana fermions in solid state structures: status and
challenges
 Proximity-coupled topological insulator nanoribbons
• Modeling
• Low-energy states
• Phase diagram
• Proximity-induced gap
I
Majorana fermions in solid state structures
What is a Majorana fermion?
Question: Are the spinors representing spin-1/2 particles necessarily
complex ?
Majorana (1937): neutral spin-1/2 particles can
be described by a real wave equation:
Majorana fermion – an electrically neutral
particle which is its own antiparticle
Relevance:
particle physics (neutrinos ?)
Experimental status:
NOT observed
2000s: Majorana fermions can emerge as quasiparticle excitations in solid-state systems
Superconductors – the natural hosts for Majoranas
electron (-e)
Cooper pair (-2e)
hole (+e)
 charge is not an observable
 the elementary excitations are combinations of particles and holes
(Bogoliubov quasiparticles)
Particle-hole symmetry
Zero energy state
(Majorana fermion)
Spinless fermions + particle-hole symmetry
Majoranas at E=0
Practical route to realizing Majorana bound states
1D spinless p-wave superconductor
Kitaev, Physics-Uspekhi, 01
Semiconductor
nanowire
Superconductor
Sau et al., PRL’10
Alicea PRB’10
Lutchyn et al., PRL’10
Oreg et al., PRL’10
Single-channel nanowire
Spin-orbit
coupling
Zeeman
splitting
Proximity-induced
superconductivity
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)
Suppression of the gap-closing signature
TDS et al., PRB 84, 144522 (2011)
TDS et al., PRL 109, 266402 (2012)
Low-energy spectra in the presence of disorder
Interface inhomogeneity
Static disorder
TDS et al., PRB 84, 144522 (2011)
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)
II
Proximity-Coupled Topological Insulator
Nanoribbons
The topological insulator Majorana wire
Cook & Franz, PRB 86, 155431 (2012)
Theoretical modeling
Low-energy TI states
Effective TI Hamiltonian
Local potential
SC Hamiltonian
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)
V=0; F=0
V=0; F=0.5
V=0.05; F=0.5
Sitthison & TDS, PRB 90, 035313 (2014)
Low-energy states
V=0; F=0.5
V=0.05; F=0.5
Sitthison & TDS, PRB 90, 035313 (2014)
Proximity-induced quasiparticle gap
m=0.05 eV
m=-0.09 eV
Sitthison & TDS, PRB 90, 035313 (2014)
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
V=0.06 eV
V=0
V=0.03 eV
Sitthison & TDS, PRB 90, 0000 (2014)
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

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