Exact analytical solution of a time-reversal-invariant topological superconducting wire

Abstract

We consider a model proposed before for a time-reversal-invariant topological superconductor (TRITOPS) which contains a hopping term $t$, a chemical potential $\mu$, an extended $s$-wave pairing $\Delta$ and spin-orbit coupling $\lambda$. We show that for $|\Delta |=|\lambda |$, $\mu =t=0$, the model can be solved exactly defining new fermion operators involving nearest-neighbor sites. The many-body ground state is four-fold degenerate due to the existence of two zero-energy modes localized exactly at the first and the last site of the chain. These four states show entanglement in the sense that creating or annihilating a zero-energy mode at the first site is proportional to a similar operation at the last site. By continuity, this property should persist for general parameters. Using these results we correct some statements related with the so called "time-reversal anomaly". Addition of a small hopping term for a chain with an even number of sites breaks the degeneracy and the ground state becomes unique with an even number of particles. We also consider a small magnetic field applied to one end of the chain. We compare the many-body excitation energies and spin projection along the spin-orbit direction for both ends of the chains with numerical results %for a small chain obtaining good agreement.

11 pages, 2 figures, 1 figure, more calculations and references added, accepted for publication in Phys. Rev. B

References in corpus (15)

• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Classification of topological insulators and superconductors in three spatial dimensions
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Majorana bound states in a coupled quantum-dot hybrid-nanowire system
• Kramers Pairs of Majorana Fermions and Parafermions in Fractional Topological Insulators
• Majorana bound states and non-local spin correlations in a quantum wire on an unconventional superconductor
• Topological superconductivity and unconventional pairing in oxide interfaces
• DIII Topological Superconductivity with Emergent Time-Reversal Symmetry
• Deterministic teleportation of electrons in a quantum dot nanostructure
• Catalogue of Andreev spectra and Josephson effects in structures with time-reversal-invariant topological superconductor wires
• Proximity induced time-reversal topological superconductivity in Bi2Se3 films without phase tuning
• Time-reversal-invariant topological superconductivity
• Influence of an embedded quantum dot on the Josephson effect in the topological superconducting junction with Majorana doublets

Cited by in corpus (2)

• Tomography of zero-energy end modes in topological superconducting wires
• Josephson junctions of 2D time-reversal invariant superconductors: signatures of the topological phase