Vortex lattices in the superconducting phases of doped topological insulators and heterostructures
Hsiang-Hsuan Hung, Pouyan Ghaemi, Taylor L. Hughes, Matthew J. Gilbert
DOI 10.1103/PhysRevB.87.035401 · Physical Review B
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Abstract
Majorana fermions are predicted to play a crucial role in condensed matter realizations of topological quantum computation. These heretofore undiscovered quasiparticles have been predicted to exist at the cores of vortex excitations in topological superconductors and in heterostructures of superconductors and materials with strong spin-orbit coupling. In this work, we examine topological insulators with bulk s-wave superconductivity in the presence of a vortex lattice generated by a perpendicular magnetic field. Using self-consistent Bogoliubov–de Gennes calculations, we confirm that beyond the semiclassical, weak-pairing limit the Majorana vortex states appear as the chemical potential is tuned from either side of the band edge so long as the density of states is sufficient for superconductivity to form. Further, we demonstrate that the previously predicted vortex phase transition survives beyond the semiclassical limit. At chemical potential values smaller than the critical chemical potential, the vortex lattice modes hybridize within the top and bottom surfaces, giving rise to a dispersive low-energy mid-gap band. As the chemical potential is increased, the Majorana states become more localized within a single surface but spread into the bulk toward the opposite surface. Eventually, when the chemical potential is sufficiently high in the bulk bands, the Majorana modes can tunnel between surfaces and eventually a critical point is reached at which modes on opposite surfaces can freely tunnel and annihilate leading to the topological phase transition previously studied in the work of Hosur et al. [Phys. Rev. Lett. 107, 097001 (2011)].
Source-reported materials — not catalogue approval
| Formula | Reported Tc (K) | Pressure (GPa) | Type |
|---|---|---|---|
| Bi2Se3 Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula. | — | Pressure not reported | unknown |
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