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Register a new userFractional skyrmion and absence of low-lying Andreev bound states in a micro fractional-flux quantum vortex
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We investigate quasi-particle excitation modes and the topological number of a fractional-flux quantum vortex in a layered (multi-component) superconductor. The Bogoliubov equation for a half-flux quantum vortex is solved to show that there is no low-lying Andreev bound state near zero energy in the core of a quantum vortex, which is surprisingly in contrast to the result for an inter-flux vortex. Related to this result, there are singular excitation modes that have opposite angular momenta, moving in the opposite direction around the core of the vortex. The topological index (skyrmion number) for a fractional-flux quantum vortex becomes fractional since the topological index is divided into two parts where one from the vortex (bulk) and the other from the kink (domain wall, boundary). The topological numbers for both the vortex and the kink (domain wall) are fractional, and their sum becomes an integer. This shows an interesting analogy between this result and the index theorem for manifolds with boundary. We argue that fractional-flux quantum vortices are not commutative each other and follow non-abelian statistics. This non-abelian statistics of vortices is different from that in p-wave superconductors.
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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 present evidence that the $H_{rm P}$ for nanocrystals nucleated in samples with edges parallel to the nodal direction is larger than for the antinodal case, $sim 72$,% at low temperatures. This finding supports the theoretical proposal that surface Andreev bound states appearing in a sample with edges parallel to the nodal direction would produce an anomalous Meissner current that increases the Bean-Livingston barrier for vortex penetration.This has been detected thanks to the nucleation of vortex nanocrystals with a significant surface-to-volume ratio.
Focusing on a quantum-limit behavior, we study a single vortex in a clean s-wave type-II superconductor by self-consistently solving the Bogoliubov-de Gennes equation. The discrete energy levels of the vortex bound states in the quantum limit is discussed. The vortex core radius shrinks monotonically up to an atomic-scale length on lowering the temperature T, and the shrinkage stops to saturate at a lower T. The pair potential, supercurrent, and local density of states around the vortex exhibit Friedel-like oscillations. The local density of states has particle-hole asymmetry induced by the vortex. These are potentially observed directly by STM.
In long Josephson junctions with multiple discontinuities of the Josephson phase, fractional vortex molecules are spontaneously formed. At each discontinuity point a fractional Josephson vortex carrying a magnetic flux $|Phi|<Phi_0$, $Phi_0approx 2.07times 10^{-15}$ Wb being the magnetic flux quantum, is pinned. Each vortex has an oscillatory eigenmode with a frequency that depends on $Phi/Phi_0$ and lies inside the plasma gap. We experimentally investigate the dependence of the eigenfrequencies of a two-vortex molecule on the distance between the vortices, on their topological charge $wp=2piPhi/Phi_0$ and on the bias current $gamma$ applied to the Josephson junction. We find that with decreasing distance between vortices, a splitting of the eigenfrequencies occurs, that corresponds to the emergence of collective oscillatory modes of both vortices. We use a resonant microwave spectroscopy technique and find good agreement between experimental results and theoretical predictions.
Since the discovery of the Fractional Quantum Hall Effect in 1982 there has been considerable theoretical discussion on the possibility of fractional quantization of conductance in the absence of Landau levels formed by a quantizing magnetic field. Although various situations have been theoretically envisaged, particularly lattice models in which band flattening resembles Landau levels, the predicted fractions have never been observed. In this Letter, we show that odd and even denominator fractions can be observed, and manipulated, in the absence of a quantizing magnetic field, when a low-density electron system in a GaAs based one-dimensional quantum wire is allowed to relax in the second dimension. It is suggested that such a relaxation results in formation of a zig-zag array of electrons with ring paths which establish a cyclic current and a resultant lowering of energy. The behavior has been observed for both symmetric and asymmetric confinement but increasing the asymmetry of the confinement potential, to result in a flattening of confinement, enhances the appearance of new fractional states. We find that an in-plane magnetic field induces new even denominator fractions possibly indicative of electron pairing. The new quantum states described here have implications both for the physics of low dimensional electron systems and also for quantum technologies. This work will enable further development of structures which are designed to electrostatically manipulate the electrons for the formation of particular configurations. In turn, this could result in a designer tailoring of fractional states to amplify particular properties of importance in future quantum computation.
We calcuate electronic spin susceptibility and spin-lattice relaxation rate in singlet superconductor near a pairbreaking surface, or in a domain wall of the order parameter. We directly link presence of high-density Andreev bound states in the inhomogeneous region, combined with coherence factors, to enhancement of the susceptibility above the normal states value for certain $bf q$ vectors. Beside the dominant peak at ferromagnetic vector $q=0$, we find significant enhancement of antiferromagnetic correlations at vectors $qlesssim 2 k_f$, with $bf q$ $along$ the domain wall in $S$-wave superconductor, and $across$ domain wall in $D$-wave (nodes along the wall). These features are destroyed by applying moderate Zeeman field that splits the zero-energy peak. We solve Bogoliubov-de Gennes equations in momentum space and our results deviate from the lattice models investigated previously. Large enhancement of the spin-lattice relaxation rate $T_1^{-1}$ at the domain wall provides clear signature of the quasiparticle bound states, and is in good agreement with recent experiment in organic superconductor $kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$.
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