It has been known that when a magnetic field is applied to some superconductors, so-called "Type-II Supercondutors", a quantized magnetic flux penetrates into the matter.
This flux suppresses the superconductivity locally, and the current flows round the flux line.
This is called the "Vortex".
Bound States around a Vortex
Around the vortex, the superconductivity, namely, the superconducting pair potential is suppressed, and this potential works as if it is a kind of quantum well.
Quasiparticles are bounded in the vortex.
There exist excitations at the vortex.
Then, the vortex has been traditionally considered to be a Core of the Normal State.
This normal-core picture of the vortex is, however, correct only for "dirty" superconductors, which heavily contain impurities or defects.
Hess's Success of STM observation of Vortices
In 1989, Hesset al. first succeeded in observing the bound states, namely, local density of states (LDOS), around a vortex with Scanning Tunneling Microscope (STM) [Phys. Rev. Lett. 62, 214 (1989)].
They revealed true electronic structure of the vortex in a clean type-II superconductor, 2H-NbSe2.
An existence of a striking zero-bias peak at the vortex center was found by Hess et al.
Splitting of the Zero-bias peak
Motivated by Hess's successful experiment, several theoretical works were done.
A theoretical group of Shore, Huang, Dorsey, and Sethna predicted that the zero-bias peak should split into two, if STM spectra are taken at some distance from the vortex center along a radial line [Phys. Rev. Lett. 62, 3089 (1989)].
The splitting indicates that the bounded quasiparticle around a vortex has a dispersion relation between its angular momentum and energy.
The theoretical prediction was actually confirmed by later experiments by Hess.
The zero-bias peak and its splitting along a radial line show that the vortex has rich internal electronic structure.
The naive normal-core picture of vortices does break down in clean type-II superconductors.
Star-shaped Local Density of States
Hess's beautiful STM experiments further revealed very exciting properties of vortices.
They found that the LDOS around the vortex is shaped like a "star" at a fixed energy and its orientation is dependent on the energy, that is, the sixfold star shape rotates as the bias voltage varies [Phys. Rev. Lett. 64, 2711 (1990)].
Soon after this observation, Gygi and Schlueter proposed an explanation for this rotation of the star-shaped LDOS [Phys. Rev. Lett. 65, 1820 (1990)].
On the basis of a sixfold perturbation, they explained that the lower and higher energy stars are interpreted as bonding or antibonding states.
However, while they explained certain aspects of the observation, some features of the star-shaped LDOS observed in later STM experiments could not be sufficiently understood by this perturbation scheme.
Mysteries of the Star-shaped LDOS
According to precise STM experiments by Hess, a 'ray' of the star splits into a pair of nearly parallel rays at the intermediate energy [a corresponding theoretical result (see below) is shown in the above image of this page, the middle one].
In spectral evolutions along radial lines which cross the vortex center, the zero-bias peak doesn't split into two, but into three or more ones.
Also the peaks vary with the angle of the direction in which the spectral evolution is taken.
These experimental findings have not been able to be sufficiently explained for a long time.
Gap Anisotropy ?!
We (Hayashi, Ichioka, and Machida) attempted to understand these experimental findings on the basis of the following effects: (1) an anisotropy of superconducting gap; (2) the vortex lattice; and (3) an anisotropic Fermi surface (or an anisotropy of the underlying crystal lattice).
Using the quasiclassical theory of superconductivity, we calculated the LDOS around a vortex for each case.
Then, we tentatively concluded that the item (1), anisotropic gap effect, is the most probable.
The above images of this page are those obtained in the case of an anisotropic s-wave gap.
It was shown that the complicated structure of peaks in the STM spectra can be explained in terms of quasiparticle trajectories (see the reference #3 below).
We also predicted the existence of extra peaks in spectral evolutions, which is characteristic of the gap anisotropy.
Gap or Crystal Lattice ?
There, however, remains an uncertainty.
Our recent calculation showed that the crystal lattice effect on the vortex bound states, which Gygi and Schlueter originally considered, also reproduces qualitatively the detail of the STM results, if non-perturbation method is adopted.
Further investigation and comparison are now in progress.
If the above predicted extra peaks are observed in future STM, it will be an evidence of the gap anisotropy.
Future problems...
The low-temperature STM experiments have successfully revealed the rich internal electronic structure of individual vortices in a clean type-II superconductor, 2H-NbSe2.
Future STM experiments on various superconductors are greatly expected.
On the other hand, it has been found by STM that the vortex in clean type-II superconductors has richer electronic structure than a traditional "normal core" does.
It might be appropriate that the vortex is called the Superconducting Vortex rather than the Normal-state Vortex Core.
(We recommend an interesting paper by Rainer, Sauls, and Waxman [Phys. Rev. B 54, 10094 (1996)]. Especially their Introduction is appropriate.)
It is expected to investigate effects of the superconducting vortex on various physical phenomena such as the Thermal conductivity and Nuclear spin-Lattice relaxation..
I. Guillamon, H. Suderow, S. Vieira, L. Cario, P. Diener, and P. Rodiere,
arXiv:0807.1809 Phys. Rev. Lett. 101, 166407 (2008). Difference is interesting! Radially symmetric vortex core in
2H-NbS2 and Sixfold star-shaped one in 2H-NbSe2.
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