Quantum Vortex Liquid Research Articles

Resistivity in Quantum Vortex Liquid of Clean Two-Dimensional Superconductor

Resistivity in Quantum Vortex Liquid of Clean Two-Dimensional Superconductor

Expanded quantum vortex liquid regimes in the electron nematic superconductors FeSe1−xSx and FeSe1−xTex

The quantum vortex liquid (QVL) is an intriguing state of type-II superconductors in which intense quantum fluctuations of the superconducting (SC) order parameter destroy the Abrikosov lattice even at very low temperatures. Such a state has only rarely been observed, however, and remains poorly understood. One of the key questions is the precise origin of such intense quantum fluctuations and the role of nearby non-SC phases or quantum critical points in amplifying these effects. Here we report a high-field magnetotransport study of FeSe1−xSx and FeSe1−xTex which show a broad QVL regime both within and beyond their respective electron nematic phases. A clear correlation is found between the extent of the QVL and the strength of the superconductivity. This comparative study enables us to identify the essential elements that promote the QVL regime in unconventional superconductors and to demonstrate that the QVL regime itself is most extended wherever superconductivity is weakest.

Quantum Criticality inside the Anomalous Metallic State of a Disordered Superconducting Thin Film.

The field-induced superconductor-insulator transition (SIT) in two-dimensional (2D) systems is a famous example of a quantum phase transition. However, an emergence of an anomalous metallic state induced by field has been a long-standing problem in 2D superconductors. While theories predicted that the emergence is attributed to strong phase fluctuations of the superconducting order parameter due to quantum fluctuations, usual resistance measurements have not probed them directly. Here, using Nernst effect measurements, we uncover superconducting fluctuations in the vicinity of the field-induced metallic state in an amorphous Mo_{x}Ge_{1-x} thin film. The field range where the vortex Nernst signals are detectable remains nonzero toward zero temperature, and it locates inside the metallic state defined by the magnetoresistance, indicating that the metallic state results from quantum vortex liquid (QVL) with phase fluctuations due to quantum fluctuations. Slow decay of transport entropy of vortices in the QVL with decreasing temperature suggests that the metallic state originates from broadening of a quantum critical point in SIT.

Equilibrium and Dynamic Vortex States near Absolute Zero in a Weak Pinning Amorphous Film

By developing and employing a mode-locking measurement with pulsed currents, we successfully determine the dynamic melting field \(B_{\text{c,dyn}}^{\infty }(T)\) for a driven vortex lattice of an amorphous MoxGe1−x film in the limit of zero temperature (T → 0) and complete a dynamic as well as a static vortex phase diagram. At T = 0, the mixed state in the absence of pinning comprises vortex-lattice and quantum-vortex-liquid (QVL) phases, and the melting field separating the two phases is identified as \(B_{\text{c,dyn}}^{\infty }(0)\). Comparison of the dynamic and static phase diagrams reveals that, when the weak pinning is introduced into the pin-free system, a disordered phase emerges just above the vortex-lattice phase and a threshold field separating the two phases is slightly suppressed from \(B_{\text{c,dyn}}^{\infty }(0)\), indicative of defect-induced disordering of the lattice. By contrast, a melting field into QVL is much enhanced from \(B_{\text{c,dyn}}^{\infty }(0)\) up to a point near the ...

The Quantuam Melting Transitions with the Magnetic Field in Weakly Disordered Josephson Junction Arrays

Using the resistively shunted junction model, we study the magnetic field induced dynamic melting transitions of a current-driven vortex system in two-dimensional weakly disordered Josephson junction arrays at zero temperature. From the unified model simulations, we find that the intrinsic quantum vortex liquid (QVL) phenomenon, which consistent with the recent experimental reports in disordered and superconducting MoGe films. The enhancement of critical current in the QVL phase arises from intrinsic quantum fluctuations in the moving vortex flow.

Peak effect and dynamic melting transitions of driven vortex system in weakly disordered Josephson junction arrays

Using the resistively shunted junction model, we study the magnetic frustration induced dynamic melting transitions of a current-driven vortex system in two-dimensional weakly disordered Josephson juction arrays at zero temperature and very low temperatures. From the unified model simulations, we simultaneously obtain two kinds of dynamic melting transitions of the vortex flow, just below the vortex glass phase and above a dynamic melting threshold, respectively. The reenter pinned dilute vortex liquid behavior and the intrinsic quantum vortex liquid (QVL) phenomenon are also obtained, consistent with the recent experimental reports in disordered and superconducting MoGe films. The peak effect of critical current in the vortex glass is induced by intrinsic collective pinning effects in the plastic flow and the enhancement of critical current and voltage noise in the QVL phase arises from intrinsic quantum fluctuations in the moving vortex flow.

Theoretical analysis of drag resistance in amorphous thin films exhibiting superconductor-insulator transitions

The magnetical field tuned superconductor-insulator transition in amorphous thin films, e.g., Ta and InO, exhibits a range of yet unexplained curious phenomena, such as a putative low-resistance metallic phase intervening the superconducting and the insulating phase, and a huge peak in the magnetoresistance at large magnetic field. Qualitatively, the phenomena can be explained equally well within several significantly different pictures, particularly the condensation of quantum vortex liquid, and the percolation of superconducting islands embedded in normal region. Recently, we proposed and analyzed a new measurement that should be able to decisively point to the correct picture: a drag resistance measurement in an amorphous thin-film bilayer setup. Neglecting interlayer tunneling, we found that the drag resistance within the vortex paradigm has opposite sign and is orders of magnitude larger than that in competing paradigms. For example, two identical films as in Sambandamurthy et al. 2004 with 25 nm layer separation at 0.07 K would produce a drag resistance $\sim10^{-4}\Omega$ according the vortex theory, but only $\sim10^{-12}\Omega$ for the percolation theory. We provide details of our theoretical analysis of the drag resistance within both paradigms, and report some new results as well.

Vortex Quantum Dynamics of Two Dimensional Lattice Bosons

We study hard-core lattice bosons in a magnetic field near half filling. The bare vortex hopping rate is extracted from exact diagonalizations of square clusters. We deduce a quantum melting of the vortex lattice above vortex density of 6.5x10(-3) per lattice site. The Hall conductivity reverses sign abruptly as the density crosses half filling, where its characteristic temperature scale vanishes. We prove that at precisely half filling, each vortex carries a spin-1/2 quantum number ("v spin"). Experimental implications of these results are discussed.

VORTEX PHASE DIAGRAM AND DYNAMICS NEAR T = 0 IN THE LIQUID PHASE OF A THICK a-MoxGe1-x FILM

We report on the equilibrium vortex phase diagram and vortex dynamics driven by dc current in the low-temperature liquid phase of thick amorphous (a-) Mo x Ge 1-x and a- Mo x Si 1-x films containing weak and moderately strong pinning, respectively. The solid state for the a- Mo x Ge 1-x film is an ordered vortex lattice or Bragg glass, which is different from the disordered vortex glass for the a- Mo x Si 1-x films. We find that the liquid state is similar to each other, involving the quantum-vortex-liquid (QVL) phase at low temperature. The width of the QVL phase is not enhanced by reduced pinning strength. In both systems we detect the unusual vortex flow in (near) the QVL phase.

Vortex phase diagram and vortex dynamics at low temperature in a thick a-Mg xB 1− x film

We report on the equilibrium vortex phase diagram and vortex dynamics at low temperature T in a thick amorphous (a-)Mg x B 1− x film based on the measurements of the dc resistivity ρ and time ( t)-dependent component of the flux-flow voltage, δ V( t), respectively. Both ρ( T) in perpendicular fields and the vortex phase diagram are qualitatively similar to those for the a-Mo x Si 1− x films, in which evidence for the quantum-vortex-liquid (QVL) phase has been obtained. In either material system we observe anomalous vortex flow with the asymmetric distribution of δ V( t) in the QVL phase, suggesting that the anomalous flow is a universal phenomenon commonly observed for disordered amorphous films, independent of material.

Low-temperature vortex liquid in La2−xSrxCuO4

In the cuprates, the lightly-doped region is of major interest because superconductivity, antiferromagnetism, and the pseudogap state \cite{Timusk,Lee,Anderson} come together near a critical doping value $x_c$. These states are deeply influenced by phase fluctuations \cite{Emery} which lead to a vortex-liquid state that surrounds the superconducting region \cite{WangPRB01,WangPRB06}. However, many questions \cite{Doniach,Fisher,FisherLee,Tesanovic,Sachdev} related to the nature of the transition and vortex-liquid state at very low tempera- tures $T$ remain open because the diamagnetic signal is difficult to resolve in this region. Here, we report torque magnetometry results on $\rm La_{2-x}Sr_xCuO_4$ (LSCO) which show that superconductivity is lost at $x_c$ by quantum phase fluctuations. We find that, in a magnetic field $H$, the vortex solid-to-liquid transition occurs at field $H_m$ much lower than the depairing field $H_{c2}$. The vortex liquid exists in the large field interval $H_m \ll H_{c2}$, even in the limit $T\to$0. The resulting phase diagram reveals the large fraction of the $x$-$H$ plane occupied by the quantum vortex liquid.

Vortex flow and shot noise in the quantum-liquid phase of thick amorphous superconducting films

We measure the fluctuations (noise) of the vortex-flow voltage in the low-temperature liquid phase of thick amorphous $(a\text{\ensuremath{-}}){\mathrm{Mg}}_{x}{\mathrm{B}}_{1\ensuremath{-}x}$ and $a\text{\ensuremath{-}}{\mathrm{Mo}}_{x}{\mathrm{Si}}_{1\ensuremath{-}x}$ films with different transition temperatures and widths of the quantum-vortex-liquid (QVL) phase. An anomalous vortex flow with an asymmetric distribution of (real-time) voltage fluctuations is commonly observed in the QVL phase, independent of material as well as strength of quantum fluctuations. In the QVL phase we observe the Lorentzian-type noise spectra indicative of shot noise, whose origin is attributed to the vortex bundles that are depinned and pinned randomly in the stationary flow of QVL.

Anomalous vortex flow and noise in the quantum liquid phase of amorphous films

We measure the fluctuating component of the flux-flow voltage, δV(t), about the average voltage in the low-temperature (T) liquid phase of amorphous MoxSi1−x films. For the 100-nm-thick film δV(t) originating from the vortex motion is clearly visible in the quantum-vortex-liquid (QVL) phase, where the distribution of δV(t) is asymmetric, suggestive of the unusual vortex motion. For the thin (6 and 4nm) films, in which the QVL phase is not determined from the T dependence of the resistance, the similar unusual (avalanche-like) vortex motion is observed in nearly the same reduced-T regime. These results support the view that vortex dynamics in the low-T liquid phase of thick and thin films is dominated by common physical mechanisms related to quantum-fluctuation effects.

Unusual vortex dynamics in the quantum-liquid phase of a-MoxSi1−x films

We find the unusual vortex dynamics in the low-temperature liquid phase of amorphous MoxSi1−x films by measuring the fluctuating component of the flux-flow voltage δV(t) about the average voltage. For the thick film, in which the quantum vortex liquid (QVL) phase has been well-determined in the field-temperature plane, δV(t) originating from the vortex motion is clearly visible in the QVL phase, where the distribution of δV(t) is anomalously asymmetric, implying large velocity and/or number fluctuations of driven vortices. For the thin film, in which the QVL phase has not been determined from the static transport measurements, similar unusual vortex motion is observed in nearly the same reduced-temperature regime. We suggest that vortex dynamics in the low-temperature liquid phase of thick and thin films is dominated by common physical mechanisms related to quantum-fluctuation effects.

Electronic transport at low temperature below the field-driven superconductor–insulator transition in thin a-Mo xSi 1− x films

We have shown so far that thin amorphous (a-)Mo x Si 1− x films exhibit the field-driven superconductor–insulator transition (SIT) at zero temperature ( T = 0), while the existence of a metallic quantum–vortex–liquid at T = 0 has been reported in several thin amorphous films. Here we reexamine the possibility of the metallic phase by measuring the T dependence of resistance R( T) for the thin a-Mo x Si 1− x films with various transition temperatures T c0 in fields B below the critical field of the “SIT”. We find that the value of T c0 dominates R( T) at low T. For films with T c0 larger than 1.0 K, the activation energy U derived from the slope of the Arrhenius plot of R is constant over the whole T region, while for films with T c0 < 1.0 K, U exhibits a discontinuous decrease below about 0.1 K; however, U remains constant and positive down to the lowest T. All of the data are consistent with the picture of the field-driven SIT.

Crossover from thermal to quantum-liquid regime in a thick amorphous film

To study the change in vortex dynamics associated with the change in equilibrium vortex states from the thermal to quantum-vortex-liquid (QVL) upon cooling, we have performed measurements of the fluctuating [time ( t)-dependent] component of flux-flow voltage V( t), δ V( t)≡ V( t)− V 0, about the average voltage V 0 using a thick amorphous Mo x Si 1− x film. Only in the QVL phase, large δ V( t) is observed. The distribution of δ V( t) is asymmetric having a tail along the direction of flux motion [δ V( t)>0], suggesting the presence of anomalous flux-flow motion in the QVL phase.

Quantum Fluctuations and Vortex Phase Diagram in Uniformly Disordered Amorphous Films

We have studied effects of microscopic disorder (normal-state resistivity ρn) and dimensionality (film thickness t) on the vortex phase diagram at low temperature T on the basis of measurements of DC and AC complex resistivities for amorphous (a)- Mo x Si 1-x films with different ρn and t. For thick films (t=100 nm ) we have commonly observed the vortex-glass transition (VGT) down to low T~0.05Tc0 and high fields up to B~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) is independent of T and extrapolates to a field below Bc2(0), indicative of the presence of a quantum-vortex-liquid (QVL) phase at T=0 in the regime Bg(0)&lt;B&lt;Bc2(0). We find that the width of the T=0 QVL phase, [Bc2(0)-Bg(0)]/Bc2(0), grows as the film becomes more resistive. This result is consistent with the view that the QVL phase is driven by strong quantum fluctuations, which are enhanced with increasing disorder. In the mixed state of the 6-nm-thick film, both the DC resistivity and vortex relaxation time follow the activated T dependence, suggestive of two-dimensional VGT.

Enhancement of the quantum-liquid phase by increased resistivity in thick a-MoxSi1-x films.

Effects of normal-state resistivity rho(n) on the vortex phase diagram at low temperature T have been studied based on dc and ac complex resistivities for thick amorphous MoxSi(1-x) films. It is commonly observed irrespective of rho(n) that, in the limit T=0, the vortex-glass-transition line B(g)(T) is independent of T and extrapolates to a field below the T=0 upper critical field B(c2)(0), indicative of the quantum-vortex-liquid (QVL) phase in the regime B(g)(0)<B<B(c2)(0). The relative width of the QVL phase increases along the B and T axes approximately proportional to rho(n). This result is consistent with a view that the QVL phase is caused by strong quantum fluctuations, which are enhanced with increasing rho(n).

Effects of disorder and dimensionality on the vortex phase diagram at low temperature in amorphous films

We present measurements of dc and ac complex resistivities for amorphous Mo x Si 1− x films with different disorder and dimensionality (film thickness t). For thicker films with t=100 and 30 nm we determine the vortex-glass-transition (VGT) 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, B g(0)< B< B c2(0), is observed for these films. We find a trend for the QVL phase to increase as the film becomes more resistive and/or thinner. This result is consistent with a view that the QVL phase is driven by strong quantum fluctuations, which are enhanced with increasing disorder and with decreasing dimensionality. For the thinnest film with t=6 nm, both the dc resistivity and vortex relaxation time follow the activated T dependence, suggestive of two-dimensional VGT.

Quantum vortex liquid state in the quasi-two-dimensional organic superconductor κ-(BEDT-TTF)2Cu(NCS)2

We report the transport properties in the quantum vortex liquid (QVL) state of the layered organic superconductor κ-(BEDT-TTF)2Cu(NCS)2. A steep change of the resistivity in the vortex liquid state is observed below about 1 K. In the low resistance state at lower temperatures, finite resistivity persists at least down to 100 mK. The finite residual resistivity may result in QVL assisted by the strong quantum fluctuations. A non-ohmic behavior appears only in the low resistance state, but not in the thermal vortex liquid state at high temperatures. These transport properties are similar to the observations discussed as the vortex slush state in the high-Tc oxides.