Vortex State And Quasi-particle In Multiband Superconductors And Superconductor Heterostructures

Multicomponent superconductivity is realized in multiband superconductors when an interband pairing interaction is considerably weaker than the intraband interactions.There is a new quantum phase that originates from the interband phase difference in this superconducting condensate.Firstly,we discuss the applicability of this physical viewpoint for known multiband superconductors.Secondly,topics related to the interband phase difference are treated.Finally,we mention that the Bardeen–Cooper–Schrieffer formalism and the Ginzburg–Landau formalism may not be fully guaranteed in the presence of a fluctuation in the interband phase difference.We also address plausible new superconducting electronics using the interband phase difference.The time-dependent Ginzburg–Landau equations(TDGL)model a thin-film superconductor of finite size under a magnetic field.For numerical computation,we use a staggered grid discretization,a technique well known in numerical fluid mechanics.Some properties of the solutions are established.In our simulations,we impose natural boundary conditions at the edge of the superconductor.With suitable choices of parameters(corresponding to type II superconductors)and the strength of the external magnetic field,the steady-state solutions exhibit vortices.We show that the nonlocal interband coupling can lead to the breaking of translation symmetry and the axial rotation symmetry of the conventional Abrikosov vortex states,resulting in a novel vortex structure comprising a mixture of triangle and square-like vortex lattices that have no counterparts in the single-band superconductors.Half-quantized vortices and stable vortex-antivortex pairs are found.The origin of the vortex-core states in s-wave and p-wave superconductors is investigated by means of some selected numerical experiments.By relaxing the self-consistency condition in the Bogoliubov–de Gennes equations and tuning the order parameter in the core region,it is shown that the suppression of the superfluiddensity in the core is not a necessary condition for the core states to form.This excludes “potential well” types of interpretations for the core states.The topological defect in the phase of the order parameter,however,plays a crucial role.For p-wave superconductors,It shows that either an s-wave or the mixed d-and s-wave state with odd-frequency and spin-triplet symmetry is induced at the vortex core,depending both on the chirality of the pairing states and on the vortex topology.It is also found that the odd-frequency triplet even parity(OTE)bound state can be manipulated with a local non-magnetic potential.Interestingly,with an appropriate potential amplitude,the zero-energy OTE bound state can be stabilized at a distance from the vortex core and from the local potential.Possible existences of the Majorana fermion modes are expected if the particle-hole symmetry property is applied to the zero-energy OTE bound state.We study the robustness of Majorana zero energy modes and minigaps of quasiparticle excitations in a vortex by numerically solving Bogoliubov-de Gennes equations in a heterostructure composed of an s-wave superconductor,a spin-orbit-coupled semiconductor thin film,and a magnetic insulator.This heterostructure was proposed recently as a platform for observing non-Abelian statistics and performing topological quantum computation.The dependence of the Majorana zero energy states and the minigaps on various physics parameters Zeeman field,chemical potential,spin-orbit coupling strength is characterized.We find the minigaps depend strongly on the spin-orbit coupling strength.In certain parameter region,the minigaps are linearly proportional to the s-wave superconducting pairing gap,which is very different from the dependence in a regular s-or p-wave superconductor.We characterize the zero energy chiral edge state at the boundary and calculate the scanning tunneling microscopy signal in the vortex core that shows a pronounced zero energy peak.We show that the Majorana zero energy states are robust in the presence of various types of impurities.We find the existence of impurity potential may increase the minigaps and thus benefit topological quantumcomputation.The supercurrent through a holmium/cobalt/holmium-based Josephson junction is investigated by using the extended the Blonder-Tinkham-Klapwijk(BTK)approach.It is found that the spiral magnetism of the Ho layer can induce both spin-split and spin-flip scatterings,which control the conversion between the spin-singlet and equal spin-triplet pairing correlations,generating a tunable long-range spin-triplet pair ordering.Spin-triplet current sharp peaks variations with the Ho layer thickness as well as a slow decay of the current amplitude with the Co layer thickness are revealed.The theoretical results are in good agreement with the relevant experimental observations.