Vortex states in mesoscopic superconductors

The results of theoretical investigations of the electronic structure and transport properties of vortex states in mesoscopic superconductors with sizes of several coherence lengths are reviewed. The features of the electronic spectra of multiquantum vortices and vortex molecules, as well as mechanisms of thermal transport along vortex lines, are considered by taking into account boundary effects.     

Singularity of the vortex density of states in d-wave superconductors

In d-wave superconductors, the electronic density of states (DOS) induced by a vortex exhibits a divergence at low energies: N _vortex(E) ∼1/|E|. This divergence is the result of gap nodes in the spectrum of excitation outside the vortex core. The heat capacity in two regimes, T ²/T _c ² ≫ B/B _c 2 and T ²/T _c ² ≪ B/B _c 2, is discussed. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 9, 641–645 (10 November 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Application of nano-scale Josephson junction as phase sensitive detector for analysis of vortex states in mesoscopic superconductors

We study phase shifts in a Josephson junction induced by vortices in superconducting mesoscopic electrodes. The position of the vortices are controlled by suitable geometry of a nano-scale Nb–Pt_1−xNi_x–Nb junction of the overlap type made by Focused Ion Beam (FIB) sculpturing. The vortex is kept outside the junction, parallel to the junction plane. From the measured Fraunhofer characteristics the entrance and exit of vortices are detected. By changing the bias current through the junction at constant magnetic field the vortices can be manipulated and the system can be switched between two consecutive vortex states which are characterized by different critical currents of the junction. A mesoscopic superconductor thus acts as a non-volatile memory cell in which the junction is used both for reading and writing information (vortex). Furthermore, we observe that the critical current density of Nb–Pt_1−xNi_x–Nb junctions decreases non-monotonously with increasing Ni concentration. It exhibits a minimum at ∼40 at.% Ni, which is an indication of switching into the π state.     

Effects of geometrical symmetry on the vortex in mesoscopic superconductors

We first systematically study the multivortex states in mesoscopic superconductors via self-consistent Bogoliubov-de Gennes equations. Our work focuses on how the geometrical symmetry affects the penetration and arrangement of vortices in mesoscopic superconductors and find that the key parameter determining the entrance of the vortex is the current density at the hot spots on the edge of sample. Through determining the spatial distribution of hot spots, the geometrical symmetry of the superconducting sample influences the nucleation and entrance of vortices. Our results propose one possible experimental approach to control and manipulate the quantum states of mesoscopic superconductors with their topological geometries, and they can be easily generalized to the confined superfluids and Bose-Einstein condensates.     

Local density of states around two nonmagnetic impurities in cuprate superconductors

The local density of states (LDOS) around two nonmagnetic impurities which are located at different sites is studied within the two-dimensional t-J-U model. The order parameters are determined in a self-consistent way with the Gutzwiller projected mean-field approximation and the Bogoliubov-de Gennes theory. When the two impurities are located one or two sites away, we find the superconductivity coherence peaks are more strongly suppressed and the zero-energy peak (ZEP) has split into two peaks. Whereas when the two impurities are located next to each other, the ZEP vanished, and LDOS does not change a lot compared with the case away from the impurities.     

Model of vortex states in hole-doped iron-pnictide superconductors

Based on a phenomenological model with competing spin-density-wave (SDW) and extended s-wave superconductivity, the vortex states in Ba(1-x)K(x)Fe2As2 are investigated by solving Bogoliubov-de Gennes equations. Our result for the optimally doped compound without induced SDW is in qualitative agreement with recent scanning tunneling microscopy experiment. We also propose that the main effect of the SDW on the vortex states is to reduce the intensity of the in-gap peak in the local density of states and transfer the spectral weight to form additional peaks outside the gap.     

Quasi-particle transport in vortex state of nodal superconductors

The quasi-classical approach has proved very useful for studying the vortex state of nodal superconductors like d-wave superconductors in high T_c cuprates. After a brief introduction, we review our work on the thermal conductivity tensor in d-wave superconductors and f-wave superconductors.     

Negative partial density of states in mesoscopic systems

Since the experimental observation of quantum mechanical scattering phase shift in mesoscopic systems, several aspects of it have not yet been understood. The experimental observations have also accentuated many theoretical problems related to Friedel sum rule and negativity of partial density of states. We address these problems using the concepts of Argand diagram and Burgers circuit. We can prove the possibility of negative partial density of states in mesoscopic systems. Such a conclusive and general evidence cannot be given in one, two or three dimensions. We can show a general connection between phase drops and exactness of semi classical Friedel sum rule. We also show Argand diagram for a scattering matrix element can be of few classes based on their topology and all observations can be classified accordingly.     

Electronic structure of edge and vortex states in chiral mesoscopic superconductor

A subgap quasiparticle spectrum in a mesoscopic disk of a chiral superconductor is studied. An exact expression has been derived for the spectrum of surface states localized at the disk edge. For an Abrikosov vortex placed at the center of a superconducting disk, the spectrum transformation near the intersection points of the surface and vortex anomalous energy branches is investigated. The resulting splitting of the anomalous branches due to the hybridization of the edge and vortex states is determined by an external magnetic field and can lead, in particular, to the formation of a set of minigaps in the quasiparticle spectrum. Tuning the external magnetic field makes it possible to control the width of the minigaps and the positions of the corresponding density of state singularities at the minigap edges. The text was submitted by the author in English.     

Fermionic entropy of the vortex state in d-wave superconductors

In d-wave superconductors the electronic entropy associated with an isolated vortex diverges logarithmically with the size of the system even at low temperatures. In the vortex array the entropy per vortex per layer, S _V , is much larger than k _B and depends on the distribution of the velocity field v _s around the vortex. If there is a first-order transition upon a change of the velocity distribution, then there will be a big entropy jump ΔS _V ∼k _B at the transition. This entropy jump comes from the electronic degrees of freedom on the vortex background, which is modified by the vortex transition. This can explain the big jump in the entropy observed in the so-called vortex-melting transition [A. Junod, M. Roulin, J-Y. Genoud et al., Physica C, to be published], in which the vortex array and thus the velocity field are redistributed. The possibility of the Berezinskii-Kosterlitz-Thouless transition in the 3-dimensional d-wave superconductor due to the fermionic bound states in the vortex background is discussed. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 6, 465–469 (25 March 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Experimental evidence for giant vortex states in a mesoscopic superconducting disk

The response of a mesoscopic superconducting disk to perpendicular magnetic fields is studied by using the multiple-small-tunnel-junction method, in which transport properties of several small tunnel junctions attached to the disk are measured simultaneously. This allows us to make the first experimental distinction between the giant vortex states and multivortex states. Moreover, we experimentally find a magnetic-field induced rearrangement and combination of vortices. The experimental results are well reproduced in numerical results based on the nonlinear Ginzburg-Landau theory.     

Ubiquitous V-shape density of states in a mixed state of clean limit type II superconductors

It is demonstrated theoretically and experimentally that the low energy density of states N(E) is described by a singular V-shape form N(E)=N(0)(H)+alpha|E|+O(E2) for all clean superconductors in a vortex state, irrespective of the underlying gap structure. The linear term alpha|E| which has not been recognized so far is obtained by exactly evaluating the vortex contribution. Based on microscopic Eilenberger theory N(E) is evaluated for the isotropic gap, line, and point-node gaps to yield a V-shape N(E). Scanning tunneling spectroscopy-STM experiments on NbSe2 and YNi2B2C give direct evidence for this. We provide arguments on the significance of this finding and on the relevance to other experiments.     

Index theoretic characterization of d-wave superconductors in the vortex state

We study analytically the low energy spectrum of a lattice d-wave superconductor in the vortex lattice state. For an inversion symmetric hc/2e vortex lattice and in the presence of particle-hole symmetry we prove an index theorem that imposes a lower bound on the number of zero-energy modes. Generic cases are constructed in which this bound exceeds the number of zero modes of an equivalent lattice of hc/e vortices, despite the identical point group symmetries. The quasiparticle spectrum around the zero modes is doubly degenerate and exhibits a Dirac-like dispersion, with velocities that become universal functions of Delta(0)/t in the limit of low magnetic field. For weak particle-hole symmetry breaking, the gapped state can be characterized by a topological quantum number, related to spin-Hall conductivity, which generally differs in the cases of the hc/2e and hc/e vortex lattices.     

Experimental distinction between giant vortex and multivortex states in mesoscopic superconducting squares

We study the distinction between giant vortex states and multivortex states in a thin mesoscopic superconducting square by using the temperature dependence of the vortex expulsion fields. We find that the results agree well with those obtained from the multiple-small-tunnel-junction method, indicating that the distinction by the temperature dependence of the vortex expulsion fields is applicable to superconducting squares.     

A new vortex state with non-uniform vorticity in superconducting mesoscopic rings

A study is presented of the superconducting states in mesoscopic rings. On the basis of self-consistent solution of the Ginzburg-Landau equations, a new kind of vortex states with non-uniform vorticity is found for some cases to be thermodynamically more stable, than the solution with unique winding number for the whole ring. There are indications that the solution with non-uniform vorticity concerns a metastable state of a superconducting mesoscopic ring.     

Relaxation processes in mesoscopic superconductors

We investigate the possibility of a novel kind of optical pump probe spectroscopy where the two laser pulses are focused on different areas of the sample. The response to the destruction of the superconducting state in a large part of a mesoscopic ring is studied numerically. We use the time dependent Ginzburg-Landau equations with periodic boundary conditions and external magnetic field. We evaluate the relaxation rates of the superconducting order parameter as well as the voltage induced by the charge imbalance. Computer simulations confirm that the perturbation of superconductivity on one part of the ring induces a voltage which decelerates the superconducting electrons on the other part of the ring. This deceleration results in the decrease of the superconducting current and the superfluid density. The relaxation times are of the order of the picosecond, the induced voltage of few millivolts and the variation of the superconducting gap of 10% which we believe to be suitable for time resolved femtosecond optical spectroscopy.