Abstract
We consider theoretically a 1D-semiconducting wire with strong Rashba interaction in proximity with s-wave superconductor, driven into topological phase by external magnetic field. Additionally, we take into account on-site Coulomb interactions inside the wire. The system is modelled by a tight binding Hamiltonian with Rashba hopping term and induced s-wave superconductivity. Calculations are performed utilizing recursive Green’s function method, and Coulomb interactions are treated selfconsistently within Hubbard I approximation. For the Hubbard levels residing within p-wave superconducting gap, particle–hole symmetric four-resonance structure develops in the density of states, apart from Majorana resonance. One pair of particle–hole symmetric resonances is created by the discrete II-Hubbard levels of the particular site, and the second pair of Hubbard sub-bands originates from recursive summation over the sites of the wire. Quantum interference between both types of pairs of states creates in-gap charge-conjugated Fano resonances with opposite asymmetry factors. We demonstrate that when quantum interference is dominated by two-particle tunneling, the Majorana resonance is strongly diminished, while it is not altered when single-particle tunneling dominates in interference process. We also discuss some consequences for experimental distinction of true Majorana states, and show that on-site Coulomb interactions support the appearance of topological phase.
Highlights
In solid state heterostructures they appear as quasiparticles, so called Majorana zero-modes (MZM)4
When the wire is driven into topological phase by switching on large spin-orbit interaction, both particle and hole Fano resonances appear in the density of states of the common chirality, determined by the direction of external magnetic field
We have shown that on-site Coulomb interactions in 1D-topological wire exhibit local and global effects in its density of states
Summary
Exotic quantum particles being their own antiparticles, were proposed by Ettore Majorana as a real solution of Dirac equation. In the present paper we demonstrate, how the coexistence of quantum interference and Coulomb interactions in a 1D-topological wire influences the formation of Majorana resonance in the density of states. As a result of quantum interference between the particle-hole symmetric pairs of local in-gap quasiparticle Hubbard resonances and pairs of in-gap quasiparticle Hubbard sub-bands, characteristic particle-hole symmetric Fano resonances with opposite q-asymmetry parameters, form inside the topological superconducting gap. This quantum interference is mediated by propagation of superconditing pairs at Fermi energy, and it influences the formation of the Majorana resonance. The last section includes conclusions, and the details of calculations are presented in Appendices
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