Heat conduction in the vortex state of NbSe2: evidence for multiband superconductivity

The thermal conductivity kappa of the layered s-wave superconductor NbSe2 was measured down to T(c)/100 throughout the vortex state. With increasing field, we identify two regimes: one with localized states at fields very near H(c1) and one with highly delocalized quasiparticle excitations at higher fields. The two associated length scales are naturally explained as multiband superconductivity, with distinct small and large superconducting gaps on different sheets of the Fermi surface. This behavior is compared to that of the multiband superconductor MgB2 and the conventional superconductor V3Si.     

Quasiparticle density of states of 2H-NbSe2 single crystals revealed by low-temperature specific heat measurements according to a two-component model

Low-temperature specific heat in a dichalcogenide superconductor 2H-NbSe2 is measured in various magnetic fields. It is found that the specific heat can be described very well by a simple model concerning two components corresponding to vortex normal core and ambient superconducting region, separately. For calculating the specific heat outside the vortex core region, we use the Bardeen-Cooper Schrieffer （BCS） formalism under the assumption of a narrow distribution of the superconducting gaps. The field-dependent vortex core size in the mixed state of 2H-NbSe2, determined by using this model, can explain the nonlinear field dependence of specific heat coefficient γ（H）, which is in good agreement with the previous experimental results and more formal calculations. With the high-temperature specific heat data, we can find that, in the multi-band superconductor 2H-NbSe2, the recovered density of states （or Fermi surface） below Tc under a magnetic field seems not to be gapped again by the charge density wave （CDW） gap, which suggests that the superconducting gap and the CDW gap may open on different Fermi surface sheets.     

Low temperature limit of the vortex core radius and the kramer-pesch effect in NbSe2

Muon spin rotation ( &mgr;SR) has been used to measure the magnetic field distribution in the vortex state of the type-II superconductor NbSe2 ( T(c) = 7.0 K) below T = 2 K. The distribution is consistent with a highly ordered hexagonal vortex lattice with a well resolved high-field cutoff associated with the finite size of the vortex cores. The temperature dependence of the core radius is much weaker than the temperature dependence predicted from the Bogoliubov-de Gennes theory. Furthermore, the vortex radius measured by &mgr;SR near the low temperature quantum limit is about an order of magnitude larger than predicted.     

Excitations in correlated superfluids near a continuous transition into a supersolid

We study a superfluid on a lattice close to a transition into a supersolid phase and show that a uniform superflow in the homogeneous superfluid can drive the roton gap to zero. This leads to supersolid order around the vortex core in the superfluid, with the size of the modulated pattern around the core being related to the bulk superfluid density and roton gap. We also study the electronic tunneling density of states for a uniform superconductor near a phase transition into a supersolid phase. Implications are considered for strongly correlated superconductors.     

Excitations électroniques dans les supraconducteurs purs de 2ème espèce

In a pure superconductor of the second kind, with a??1, one can consider the region far from vortex lines as a BCS superconductor with a local superfluid velocity. We calculate the local density of states due to the excitations in such a superconductor, then the density of states of the excitations for the whole superconductor, except for the core regions. This density of states remains finite even near the gap and takes a non-zero value below the gap.     

Magnetic-field effects on the size of vortices below the surface of NbSe2 detected using low energy beta-NMR

A low energy radioactive beam of polarized 8Li has been used to observe the vortex lattice near the surface of superconducting NbSe2. The inhomogeneous magnetic-field distribution associated with the vortex lattice was measured using depth-resolved beta-detected NMR. Below Tc, one observes the characteristic line shape for a triangular vortex lattice which depends on the magnetic penetration depth and vortex core radius. The size of the vortex core varies strongly with the magnetic field. In particular, in a low field of 10.8 mT, the core radius is much larger than the coherence length. The possible origin of these giant vortices is discussed.     

The vortex physics which comes from the vortex core

A theoretical view of vortex core states and of their effects on physics of vortices in clean s- and d-wave-type II superconductors is presented based on a semi-classical picture of a vortex core as an Andreev potential well containing many quasiparticle states. We discuss the density of states, the vortex dissipation, Hall effect, and the vortex mass. The dynamic characteristics are determined by relaxation of core excitations driven by a moving vortex. In a d-wave superconductor, gap nodes make the core states more extended and introduce novel features into thermodynamics and kinetics of vortices.     

Chirality sensitive effect on surface states in chiral p-wave superconductors

We study the local density of states at the surface of a chiral p-wave superconductor in the presence of a weak magnetic field. As a result, the formation of low-energy Andreev bound states is either suppressed or enhanced by an applied magnetic field, depending on its orientation with respect to the chirality of the p-wave superconductor. Similarly, an Abrikosov vortex, which is situated not too far from the surface, leads to a zero-energy peak of the density of states, if its chirality is the same as that of the superconductor, and to a gap structure for the opposite case. We explain the underlying principle of this effect and propose a chirality sensitive test on unconventional superconductors.     

Core states and spectral flow in vortex dynamics

I review the semi-classical picture of how states bound in the core of a vortex in an S-wave superconductor respond to relative motion between the vortex and the condensate. I show how the momentum absorbed as a result of the Magnus force acting on the core leads to a change in the distribution of occupied states (“spectral flow”). In the simplest relaxation time approximation this modified distribution gives rise to the Kopnin–Kravtsov force on the vortex.     

Tunneling spectroscopy and vortex imaging in boron-doped diamond

We present the first scanning tunneling spectroscopy study of single-crystalline boron-doped diamond. The measurements were performed below 100 mK with a low temperature scanning tunneling microscope. The tunneling density of states displays a clear superconducting gap. The temperature evolution of the order parameter follows the weak-coupling BCS law with Delta(0)/kBTc approximately 1.74. Vortex imaging at low magnetic field also reveals localized states inside the vortex core that are unexpected for such a dirty superconductor.     

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.     

NMR relaxation time around a vortex in stripe superconductors

Site-dependent NMR relaxation time T1(r) is calculated in the vortex state using the Bogoliubov-de Gennes theory, taking account of possible "field-induced stripe" states in which the magnetism arises locally around a vortex core in d-wave superconductivity. The recently observed huge enhancement T-11(r) below T(c) at a core site in Tl2Ba2CuO6 is explained. The field-induced stripe picture explains consistently other relevant STM and neutron experiments.     

Bound and continuum states of a vortex line in a pure type-II superconductor

The Bogoliubov equations for the quasi-particle excitations of an isolated vortex line in a pure type-II superconductor are solved by means of a method due to Bardeenet al. The low lying energy levels of the bound states are found to have the form of Landau levels where the effective field is determined by the pair potential and the magnetic field in the core region of the vortex. From the solutions of the continuum states of high energy simple expressions for the phase shifts are derived. The contributions of the continuum states to the pair potential and the current density are calculated. The pair potential is shown to tend to the BCS gap parameter, and thus to be serf-consistent, at large distances from the vortex axis.     

Comment on vortex mass and quantum tunneling of vortices

Vortex mass in Fermi superfluids and superconductors and its influence on quantum tunneling of vortices are discussed. The vortex mass is essentially enhanced due to the fermion zero modes in the core of the vortex: the bound states of the Bogoliubov quasiparticles localized in the core. These bound states form the normal component, which is nonzero even in the low-temperature limit. In the collisionless regime ω ₀ τ≫1 the normal component trapped by the vortex is unbound from the normal component in a bulk superfluid/superconductor and adds to the inertial mass of the moving vortex. In a d-wave superconductor the vortex mass has an additional factor of (B _c2/B)^1/2 due to the gap nodes. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 2, 201–206 (25 January 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Anomalous Hall effect in the mixed state of high-temperature superconductors

The Hall effect in the mixed state of high-T_c superconductors (HTSC) is of an anomalous nature: near the transition there is a range of temperatures and of magnetic fields where the sign of the Hall effect is opposite to that in the normal state. The universality of the phenomenon in question is indicative of its connection with some general properties of the mixed state of type-II superconductors, namely, with peculiarities of motion of magnetic flux vortex lines (vortices) in these superconductors. This work puts forward a model accounting for a number of vortex motion specific features and providing a possibility to obtain the characteristics of the anomalous Hall effect.

The work is based on the phenomenologically generalized results of Bardeen-Stephen and Nozieres-Vinen, supplemented with an allowance for a new mechanism of vortex “friction” associated with Andreev electron reflection on the interface between the normal core and the superconducting periphery of a vortex. Within the framework of the model suggested, magnetic field (and temperature) dependences of the longitudinal and Hall resistances of a mixed state superconductor have been calculated at temperatures nearing T_c. At certain quite realistic parameters which define the forces acting on the vortices, there is a range of magnetic fields and temperatures where the sign of the Hall effect is opposite to that in the normal state. The lower limit of this range is the irreversibility line and the upper critical field.     

Collective multivortex states in periodic arrays of traps

We examine the vortex states in a 2D superconductor interacting with a square array of pinning sites. As a function of increasing pinning size or strength we find a series of novel phases including multivortex and composite superlattice states such as aligned dimer and trimer configurations at individual pinning sites. Interactions of the vortices give rise to an orientational ordering of the internal vortex structures in each pinning site. We also show that these vortex states can give rise to a multistage melting behavior.     

Scanning tunneling spectroscopy in the superconducting state and vortex cores of the beta-pyrochlore KOs2O6

We performed the first scanning tunneling spectroscopy measurements on the pyrochlore superconductor KOs2O6 (T(c)=9.6 K) in both zero magnetic field and the vortex state at several temperatures above 1.95 K. This material presents atomically flat surfaces, yielding spatially homogeneous spectra which reveal fully gapped superconductivity with a gap anisotropy of 30%. Measurements performed at fields of 2 and 6 T display a hexagonal Abrikosov flux line lattice. From the shape of the vortex cores, we extract a coherence length of 31-40 A, in agreement with the value derived from the upper critical field H(c2). We observe a reduction in size of the vortex cores (and hence the coherence length) with increasing field which is consistent with the unexpectedly high and unsaturated upper critical field reported.     

Near-oscillatory relaxation behavior of levitation force in infiltration and growth processed bulk YBCO/Ag superconducting composites

Time relaxation behavior of levitation force has been studied in IGP bulk YBCO/Ag superconductor using levitation force measurements as these measurements throw light on the magnetic relaxation in superconductors and the underlying vortex dynamics, pinning mechanisms and the nature of pinning forces. The measurements have revealed a hitherto unknown near-oscillatory relaxation of the levitation force with varying magnetic field. This kind of behavior is found to be more pronounced at smaller gap distances between the permanent magnet and the superconductor. A switch-type polarity bistable equilibrium model for the supercurrent structure has been proposed based on the understanding that even the permanent magnet gets magnetized in the presence of the superconductor, which has also been verified and reported here. This model satisfactorily explains the observed oscillatory behavior of relaxation rates.     

Temperature dependence of the magnetic penetration depth in the vortex state of the pyrochlore superconductor,Cd2Re2O7

We report transverse-field and zero-field muon spin rotation and relaxation studies of the superconducting rhenium oxide pyrochlore, Cd2Re2O7. Transverse-field measurements (H=0.007 T) show line broadening below T(c), which is characteristic of a vortex state, demonstrating conclusively the type-II nature of this superconductor. The penetration depth is seen to level off below about 400 mK (T/T(c) approximately 0.4), with a rather large value of lambda(T=0) approximately 7500 A. The temperature independent behavior below approximately 400 mK is consistent with a nodeless superconducting energy gap. Zero-field measurements indicate no static magnetic fields developing below the transition temperature.