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We investigate the behavior of vortex bound states in the quantum limit by self-consistently solving the Bogoliubov-de Gennes equation. We find that the energies of the vortex bound states deviates from the analytical result $E_mu=muDelta^2/E_F$ with the half-integer angular momentum $mu$ in the extreme quantum limit. Specifically, the energy ratio for the first three orders is more close to $1:2:3$ instead of $1:3:5$ at extremely low temperature. The local density of states reveals an Friedel-like behavior associated with that of the pair potential in the extreme quantum limit, which will be smoothed out by thermal effect above a certain temperature even the quantum limit condition, namely $T/T_c<Delta/E_F$ is still satisfied. Our studies show that the vortex bound states can exhibit very distinct features in different temperature regimes, which provides a comprehensive understanding and should stimulate more experimental efforts for verifications.
We investigate the vortex lattice and vortex bound states in CsFe$_2$As$_2$ single crystals by scanning tunneling microscopy/spectroscopy (STM/STS) under various magnetic fields. A possible structural transition or crossover of vortex lattice is obse
Majorana quasi-particles may arise as zero-energy bound states in vortices on the surface of a topological insulator that is proximitized by a conventional superconductor. Such a system finds its natural realization in the iron-based superconductor F
We study the penetration field $H_{rm P}$ for vortex nanocrystals nucleated in micron-sized samples with edges aligned along the nodal and anti-nodal directions of the d-wave superconducting parameter of Bi$_2$Sr$_2$CaCu$_2$O$_{8 - delta}$. Here we p
We report the observation of discrete vortex bound states with the energy levels deviating from the widely believed ratio of 1:3:5 in the vortices of an iron based superconductor KCa2Fe4As4F2 through scanning tunneling microcopy (STM). Meanwhile Frie
The helical electron states on the surface of topological insulators or elemental Bismuth become unstable toward superconducting pairing formation when coupled to the charge or magnetic fluctuations. The latter gives rise to pairing instability in ch