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Topologically non-trivial superconductivity in spin–orbit-coupled systems: bulk phases and quantum phase transitions

TitleTopologically non-trivial superconductivity in spin–orbit-coupled systems: bulk phases and quantum phase transitions
Publication TypeJournal Article
Year of Publication2011
AuthorsS. Tewari, T. D. Stanescu, J. D. Sau, and S. Das Sarma
JournalNew J. Phys.
Date Publishedjun
Keywords2011, Single Fellow

Topologically non-trivial superconductivity has been predicted to occur in superconductors with a sizable spin-orbit coupling in the presence of an external Zeeman splitting. Two such systems have been proposed: (a) s-wave superconductor pair potential is proximity induced on a semiconductor, and (b) pair potential naturally arises from an intrinsic s-wave pairing interaction. As is now well known, such systems in the form of a 2D film or 1D nano-wires in a wire-network can be used for topological quantum computation. When the external Zeeman splitting \$\backslash Gamma\$ crosses a critical value \$\backslash Gamma\_c\$, the system passes from a regular superconducting phase to a non-Abelian topological superconducting phase. In both cases (a) and (b) we consider in this paper the pair potential \$\backslash Delta\$ is strictly s-wave in both the ordinary and the topological superconducting phases, which are separated by a topological quantum critical point at \$\backslash Gamma\_c = \backslash sqrt\{\backslash Delta\^{}2 + \backslash mu\^{}2\}\$, where \$\backslash mu (>> \backslash Delta)\$ is the chemical potential. On the other hand, since \$\backslash Gamma\_c >> \backslash Delta\$, the Zeeman splitting required for the topological phase (\$\backslash Gamma > \backslash Gamma\_c\$) far exceeds the value (\$\backslash Gamma \backslash sim \backslash Delta\$) above which an s-wave pair potential is expected to vanish (and the system to become non-superconducting) in the absence of spin-orbit coupling. We are thus led to a situation that the topological superconducting phase appears to set in a parameter regime at which the system actually is non-superconducting in the absence of spin-orbit coupling. In this paper we address the question of how a pure s-wave pair potential can survive a strong Zeeman field to give rise to a topological superconducting phase. We show that the spin-orbit coupling is the crucial parameter for the quantum transition into and the robustness of the topologically non-trivial superconducting phase realized for \$\backslash Gamma >> \backslash Delta\$.