Quasiclassical Eilenberger theory of the topological proximity effect in a superconducting nanowire

Abstract

We use the quasiclassical Eilenberger theory to study the topological superconducting proximity effects between a segment of a nanowire with a p-wave order parameter and a metallic segment. This model faithfully represents key qualitative features of an experimental setup, where only a part of a nanowire is in immediate contact with a bulk superconductor, inducing topological superconductivity. It is shown that the Eilenberger equations represent a viable alternative to the Bogoliubov-de Gennes theory of the topological superconducting heterostructures and provide a much simpler quantitative description of some observables. For our setup, we obtain exact analytical solutions for the quasiclassical Green's functions and the density of states as a function of position and energy. The correlations induced by the boundary involve terms associated with both p-wave and odd-frequency pairing, which are intertwined and contribute to observables on an equal footing. We recover the signatures of the standard Majorana mode near the end of the superconducting segment, but find no such localized mode induced in the metallic segment. Instead, the zero-bias feature is spread out across the entire metallic part in accordance with the previous works. In shorter wires, the Majorana mode and delocalized peak split up away from zero energy. For long metallic segments, non-topological Andreev bound states appear and eventually merge together, giving rise to a gapless superconductor.

11 pages, 8 figures

References in corpus (17)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• A spin triplet supercurrent through the half-metallic ferromagnet CrO2
• Non-Abelian quantum order in spin-orbit-coupled semiconductors: The search for topological Majorana particles in solid state systems
• Towards a realistic transport modeling in a superconducting nanowire with Majorana fermions
• Theory of the proximity effect in junctions with unconventional superconductors
• Odd-frequency pairing in normal metal/superconductor junctions
• Splitting of Majorana modes due to intervortex tunneling in a p + ip superconductor
• Majorana Fermions and Odd-frequency Cooper Pairs in a Nano Wire
• Odd Triplet Pairing in clean Superconductor/Ferromagnet heterostructures
• Tunneling of anyonic Majorana excitations in topological superconductors
• Model for Vortex-core tunneling spectroscopy of chiral p-wave superconductors via odd-frequency pairing states
• Emergent Odd-Frequency Superconducting Order Parameter near Boundaries in Unconventional Superconductors
• Effects of finite superconducting coherence lengths and of phase gradients in topological SN and SNS junctions and rings

Cited by in corpus (20)

• Fermion Fractionalization to Majorana Fermions in Dimerized Kitaev Superconductor
• Symmetry Protected Topological Superfluids and Superconductors --- From the Basics to ${}^3$He ---
• Superconducting proximity effect in three-dimensional topological insulators in the presence of a magnetic field
• Odd-frequency superconducting states with different types of Meissner response: Problem of coexistence
• Proximity-Induced Odd-Frequency Superconductivity in a Topological Insulator
• Bulk disorder in the superconductor affects proximity-induced topological superconductivity
• Odd-frequency pair in topological superconductivity of 1D magnetic chain
• Odd-Frequency Pairs in Chiral Symmetric Systems: Spectral Bulk-Boundary Correspondence and Topological Criticality
• General framework for transport in spin-orbit-coupled superconducting heterostructures: Nonuniform spin-orbit coupling and spin-orbit-active interfaces
• Topological superconductivity in nanowires proximate to a diffusive superconductor-magnetic insulator bilayer
• Generalized Eilenberger theory for Majorana zero-mode-carrying disordered $p$-wave superconductors
• Theory of proximity effect in two-dimensional unconventional superconductor with Rashba spin-orbit interaction
• Odd-frequency pairing and Ising spin susceptibility in time-reversal invariant superfluids and superconductors
• Probing Majorana-like states in quantum dots and quantum rings
• Majorana zero modes in spintronics devices
• Local density of states in two-dimensional topological superconductors under a magnetic field: signature of an exterior Majorana bound state
• Effect of disorder on Majorana localization in topological superconductors: a quasiclassical approach
• Extended Majorana zero modes in a topological superconducting-normal T-junction
• Long range $p$-wave proximity effect into a disordered metal
• Odd-frequency pairs and anomalous proximity effect in nematic and chiral states of superconducting topological insulators