Probing vortex Majorana fermions and topology in semiconductor-superconductor heterostructures

Abstract

We investigate the local density of states, spectral function, and superconducting pair amplitudes for signatures of Majorana fermions in vortex cores in ferromagnetic and spin-orbit coupled semiconductor-superconductor heterostructures. We show that the Majorana fermion quasiparticle momentum distribution is always symmetrically distributed at a finite radius around a high symmetry point, thereby providing a necessary condition for a low-energy state to be a Majorana fermion. In real space profiles of the local density of states through the vortex core the Majorana fermion, together with other finite-energy vortex states, form a characteristic x-shape structure only present at non-trivial topology. Moreover, we find that the Mexican hat band structure property of the topologically non-trivial phase translates into multiple high-intensity band edges and also vortex core states located above the superconducting gap in the local density of states. Finally, we find no strong correlation between odd-frequency pairing and the appearance of Majorana fermions, but odd-frequency pairing exists as soon as ferromagnetism is present. In fact, we find that the only vortex superconducting pair amplitude directly related to any phase transition, is the appearance of certain spin-triplet $p$-wave pairing components in the vortex core at a pre-topological vortex core widening transition.

12 pages, 10 figures

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• Spin-polarized edge currents and Majorana fermions in one- and two-dimensional topological superconductors
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• Pinning of Andreev bound states to zero energy in two-dimensional superconductor-semiconductor Rashba heterostructures
• Superconducting order parameter $\pi$-phase shift in magnetic impurity wires
• Disorder-robust $p$-wave pairing with odd frequency dependence in normal metal-conventional superconductor junctions
• Majorana fermions at odd junctions in a wire network of ferromagnetic impurities
• Manifestation of chirality in the vortex lattice in a two-dimensional topological superconductor
• Probing chiral edge states in topological superconductors through spin-polarized local density of state measurements
• Self-consistent study of Abelian and non-Abelian order in a two-dimensional topological superconductor
• Coherent coupling between vortex bound states and magnetic impurities in 2D layered superconductors
• Probing the chirality of 1D Majorana edge states around a 2D nanoflake in a superconductor
• Local density of states in two-dimensional topological superconductors under a magnetic field: signature of an exterior Majorana bound state
• Spectroscopic and optical response of odd-frequency superconductors
• Topological $d$-wave Superconductivity and Nodal Line-Arc Intersections in Weyl Semimetals
• Temperature dependent energy gap for Yu-Shiba-Rusinov states at the quantum phase transition