Quantum Vortex Liquid Research Articles

Vortex states at low temperature and disorder in thick a-Mo xSi 1− x films

We measure the DC and AC complex resistivities for two thick a-Mo x Si 1− x films with different disorder (normal-state resistivity ρ n). For both films, we can precisely determine the vortex–glass-transition line B g( T), which persists down to low enough temperatures T up to high fields B near B c2(0), where B c2(0) is an upper critical field at T=0. The finite quantum-vortex-liquid (QVL) phase at T=0 is clearly observed in the region B g(0)< B< B c2(0). The width of the T=0 QVL phase is wider for a more resistive film, indicating that disorder plays an important role in the appearance of QVL through the enhancement of quantum fluctuations. Also, we determine the crossover temperature between the thermal and quantum liquid regime in the B– T phase diagram.

Low-temperature vortex liquid states induced by quantum fluctuations in the quasi-two-dimensional organic superconductorκ−(BEDT−TTF)2Cu(NCS)2

We report the transport properties in the vortex liquid states induced by quantum fluctuations at low temperature in the layered organic superconductor kappa-(BEDT-TTF)_{2} Cu(NCS)_{2}. A steep drop of the resistivity observed below about 1 K separates the liquid state into two regions. In the low resistance state at lower temperature, a finite resistivity with weak temperature dependence persists down to 100 mK at least. The finite resistivity in the vortex state at T ~= 0 K indicates the realization of quantum vortex liquid assisted by the strong quantum fluctuations instead of the thermal one. A possible origin for separating these liquid states is a remnant vortex melting line at the original position, which is obscured and suppressed by the quantum fluctuations. A non-linear behavior of the in-plane resistivity appears at large current density in only the low resistance state, but not in another vortex liquid state at higher temperature, where the thermal fluctuations are dominant. The transport properties in the low resistance state are well understood in the vortex slush concept with a short-range order of vortices. Thus the low resistance state below 1 K is considered to be a novel quantum vortex slush state.

Quantum liquid of vortices at T=0 in thick a-Mo xSi 1− x films

Effects of disorder (or quantum fluctuations) on the vortex phase diagram at low temperature T have been studied on the basis of measurements of dc and ac complex resistivities for thick amorphous Mo x Si 1− x films with different disorder (normal-state resistivity). Irrespective of disorder, the vortex–glass transition (VGT) persists down to T∼0.05 T c0 up to B∼0.9 B c2(0), where T c0 and B c2(0) are the mean-field transition temperature and upper critical field at T=0, respectively. In the limit T=0, the VGT line B g( T) is independent of T and extrapolates to a field below B c2(0), indicative of the presence of a quantum–vortex–liquid (QVL) phase at T=0 in the regime B g(0)< B< B c2(0). The width of the T=0 QVL phase, [ B c2(0)− B g(0)]/ B c2(0), is wider for a more disordered film. This result is consistent with a view that the QVL phase is driven by quantum fluctuations, which are enhanced with increasing disorder.

Magnetic relaxation and critical current density of the new superconductor MgB2

Magnetic relaxation rate, critical current density and transport properties have been investigated on MgB2 bulks from 1.6 K to Tc at magnetic fields up to 8 T. A vortex phase diagram is depicted based on these measurements. A large separation between the bulk irreversibility field Hirr(T) and the upper critical field Hc2(T) has been found. It is thus proposed that there is a quantum vortex liquid due to strong quantum fluctuation of vortices at 0 K. It is also found that the magnetic relaxation rate is weakly dependent on temperature but strongly dependent on field indicating a trivial influence of thermal fluctuation on the vortex depinning process. Therefore, the phase line Hirr(T) is attributed to quantum vortex melting in the rather clean system at a finite temperature.

Vortex states at T=0 in disordered thin and thick films of a-Mo xSi 1− x

We measure the transport properties of highly disordered thin and thick films of amorphous (a-)Mo x Si 1− x at low temperatures T. For thin films we have observed an anomalous peak in the magnetoresistance in fields B higher than the critical field B C of the field-driven superconductor–insulator transition (SIT). This suggests the presence of localized Cooper pairs on the insulating side of the SIT. We present data supporting the view that this insulating regime may correspond to the quantum-vortex-liquid (QVL) phase. The metallic QVL phase in B< B C is not evident, most likely absent. On the other hand, for thick films the existence of the vortex-glass transition and the metallic QVL phase at T=0 has been demonstrated. Based on these data, we construct the T=0 phase diagram of disordered two-dimensional and three-dimensional superconductors.

Evidence for the quantum vortex liquid phase in thick a-Mo xSi 1− x films

We perform detailed measurements of the ac complex resistivity of thick amorphous (a-)Mo x Si 1− x films at low temperatures T to study the vortex states near T=0 K. We obtain evidence for the vortex-glass transition (VGT) down to low enough temperatures T∼0.1 K and up to high fields B near the upper critical field B c2(0) at T=0 K. In the limit T→0 K, the VGT line B g( T) becomes independent of T and extrapolates to a field B g(0) lower than B c2(0). From this result, together with the finding that B g(0) coincides with the T=0 K superconductor–metal transition, we conclude that the metallic quantum vortex liquid phase is present in the field region B g(0)< B< B c2(0).

Flux dynamics and vortex phase diagram of the new superconductor MgB 2

Magnetic relaxation, critical current density and transport properties have been investigated on MgB 2 bulks from 1.6 K to T c at magnetic fields up to 8 T. A vortex phase diagram is depicted based on these measurements. Two phase boundaries H irr bulk( T) and H irr g( T) characterizing different irreversible flux motions are found. The H irr bulk( T) is characterized by the appearance of the linear resistivity. A large separation between the bulk irreversibility field at 0 K and the upper critical field H c2(0) has been found, it is interpreted as either due to a quantum vortex liquid induced by strong quantum fluctuation of vortices at 0 K, or flux flow through weak-link channels. It is further found that the magnetic relaxation rate is weakly dependent on temperature but strongly dependent on field indicating a trivial influence of thermal fluctuation on the vortex depinning process. Therefore the phase line H irr bulk( T) may be attributed to quantum vortex melting in the rather clean system at a finite temperature. The second boundary H irr g( T) reflects the irreversible flux motion in some local regions due to either very strong pinning or the surface barrier on the tiny grains.

Possible vortex phase diagram at zero temperature in disordered 2D superconductors

We study transport properties of highly disordered thin films of amorphous Mo x Si 1− x at low temperatures. For superconducting films we observe an anomalous peak in the magnetoresistance suggesting the presence of localized Cooper pairs on the insulating side ( B> B C) of the field-driven superconductor–insulator transition. In contrast, for thick films, or for thin films in parallel fields the MR is always positive. These results may suggest the presence of insulating quantum-vortex-liquid (QVL) phase in the region B> B C. In B< B C the metallic QVL phase is not evident, most likely absent, which is in contrast to the results reported by other groups.

Vortex glass transition and quantum vortex liquid at low temperature in a thick a- MoxSi1-x film.

We present measurements of ac complex resistivity, as well as dc resistivity, for a thick amorphous MoxSi1-x film at low temperatures ( T>0.04 K) in various constant fields B. We find that the vortex glass transition (VGT) persists down to T approximately 0.04Tc0 up to B approximately 0.9Bc2(0), where Tc0 and Bc2(0) are the mean-field transition temperature and upper critical field at T = 0, respectively. In the limit T-->0, the VGT line Bg(T) extrapolates to a field below Bc2(0), while the dc resistivity rho(T) tends to the finite nonzero value in fields just above Bg(0). These results indicate the presence of a metallic quantum vortex liquid at T = 0 in the regime Bg(0)<B<Bc2(0).

Vortices and collective excitations in rotating BECs

Vortices in atom trap condensates are expected to be quantum objects in the limit of large coherence length. By exactly solving small systems we demonstrate that there is a quantum vortex liquid. The states have an alternative interpretation in terms of fractional vortices and collective excitations.

Superinsulator Phase of Two-Dimensional Superconductors

Using path-integral quantum Monte Carlo we study the low-temperature phase diagram of a two-dimensional superconductor within a phenomenological model, where vortices have a finite mass and move in a dissipative environment modeled by a Caldeira-Leggett term. The quantum vortex liquid at high magnetic fields exhibits superfluidity and thus corresponds to a superinsulating phase which is characterized by a nonlinear voltage-current law for an infinite system in the absence of pinning. This superinsulating phase is shifted to higher magnetic fields in the presence of dissipation.

Simulation of quantum melting of the vortex lattice and of fractional quantum Hall-like states of the quantum vortex liquid in 2D superconductors

We present results of quantum path-integral Monte Carlo studies of quantum melting of the Abrikosov vortex lattice in a two-dimensional (2D), undamped, Magnus-force model superconductor. The dependence of the melting field, B m , on the vortex mass, is found to obey the simple scaling law proposed by Magro and Ceperley. In the quantum vortex liquid state for B > B m , we find a series of maxima in the vortex-vortex correlation function, measured through the intensity of the first Bragg peak, as a function of the strength of the Magnus force in the underdamped limit. These provide the first evidence of the existence of fractional quantum Hall-like states for the 2D quantum vortex liquid.

QUANTUM SUPERCONDUCTING FLUCTUATIONS AND DISSIPATION IN VORTEX STATES

Quantum effects on renormalized superconducting fluctuations are studied in the context of vortex states. It is argued by taking account of existing resistivity data that inclusion of dissipative (metallic) dynamics is indispensable at any nonzero temperature. Analysis is largely based on simple extensions of the usual time-dependent Ginzburg–Landau (TDGL) dynamics to quantum regime. First, phase diagram and dc conductivities resulting from a quantum GL action with purely dissipative dynamics are investigated, and it is noticed that, on (or, in the vicinity of) the transition line between the vortex lattice and the resulting quantum vortex liquid regime, the inverse of vortex flow conductance becomes a nearly universal value of the order of R q = 6.45 ( k Ω) and independent of material parameters. On the other hands, based on the usual Feynman graph analysis of Kubo formula, the superconducing (i.e. fluctuation) contribution to dc diagonal conductance decreases upon cooling in the disordered phase affected by quantum fluctuations, and becomes zero in T = 0 liquid regime [and above Hc2 (0)] irrespective of the details of dynamics. Reflecting these theoretical results, calculated resistance curves show the behavior quite similar to those observed in homogeneously disordered thin films, even though the presence of a field-tuned insulator–superconductor transition at T = 0 is neglected and the dynamics is purely dissipative. Phenomena in systems with quantum fluctuation of moderate strength are also considered. Analysis is also extended to the cases with other dynamical terms. It is pointed out that the usual (mean field) vortex flow Hall conductivity is never found in any nondissipative T = 0 liquid regime, and argued that, in general, the superconducting Hall effect itself is absent there at low enough fields irrespective of the presence of particle–hole assymmetry. Therefore, in contrast to the thermal vortex states with no pinning disorder, the dc transport phenomena at T = 0 are quite sensitive to the corresponding phase diagram, and hence, discussions based on the single vortex dynamics are even qualitatively invalid in the liquid regime at extremely low temperatures.