Session W33: Superconductor-Insulator Transitions

Mott transition, magnetism and d-wave superconductivity on lattices with frustration

By tuning band parameters and choosing appropriate lattices, it is possible to frustrate antiferromagnetism to reveal the competing d-wave superconducting (d-SC) phase, the normal phase and the Mott insulating phase. We study the nature of the competition between these phases by using Cellular Dynamical Mean-Field Theory for the Hubbard model on the anisotropic triangular lattice and on the square lattice with second-neighbor hopping. The phase diagram in the $T=0$ plane is drawn as a function of interaction strength $U/t$ and frustration $t'/t$. The critical interaction strength for the Mott transition is found as a function of frustration. At half-filling and for intermediate coupling we find that outside the Mott insulating phases, d-SC appears at an optimal level of frustration. We also identify spin fluctuations as the source of pair formation. We find that components of the spin susceptibility involved in binding are mostly centered in the quarter of the Brillouin zone closest to $(\pi,\pi)$. We conclude that retarded short-range spin fluctuations are crucial for d-SC even in the presence of frustration and that there are optimal values of frustration that favor d-SC.   

Superconductor-Metal-Insulator Phase Transition in Ta Films

We have reported the magnetically induced metallic phase in superconducting Ta films which intervenes the superconducting and insulating phases [1]. Recently, we studied the electronic transport properties of Ta film with various degrees of disorders which were controlled by film thickness. We found that as sample thickness decreases, the films undergo a superconductor-metal-insulator phase transition. Each phase exhibits distinct nonlinear current-voltage (I-V) characteristics, similar to those of magnetically induced superconductor-metal-insulator transition. We have measured the evolution of nonlinear I-V with changing magnetic field (B) and temperature (T), for representative samples with different degrees of disorders, which leads to the phase diagram in B-T-Disorder space. [1] Y.Qin et al., Phys. Rev. B 73, 100505(R) (2006).   

Dissipation-driven quantum phase transition in superconductor-graphene systems

We show that a system of Josephson junctions coupled via low-resistance tunneling contacts to graphene substrate(s) may effectively operate as a current switching device. The effect is based on the dissipation-driven superconductor-to-insulator quantum phase transition, which happens due to the interplay of the Josephson effect and Coulomb blockade. Coupling to a graphene substrate with gapless excitations further enhances charge fluctuations favoring superconductivity. The effect is shown to scale exponentially with the Fermi energy in graphene, which can be controlled by the gate voltage. We develop a theory, which quantitatively describes the quantum phase transition in a two-dimensional Josephson junction array, but it is expected to provide a reliable qualitative description for one-dimensional systems as well. We argue that the local effect of dissipation-induced enhancement of superconductivity is very robust and a similar sharp crossover should be present in finite Josephson junction chains.   

Superfluid response of a gated LaAlO$_3$ / SrTiO$_3$ heterostructure

Disordered two-dimensional superconductors undergo a quantum phase transition into an insulating phase, with an unusual intervening metallic phase, upon the introduction of sufficiently large amounts of disorder or the application of a sufficiently strong magnetic field. The LaAlO$_3$ / SrTiO$_3$ heterostructure, because it can be gated, provides a new opportunity: to see how two-dimensional superconductivity is destroyed continuously as a function of carrier concentration. We build on the electrical transport measurements in other works, which demonstrated the existence of a superconductor-insulator transition upon decreasing the carrier concentration, by using a two coil mutual inductance technique to measure the complex ac conductivity. We will track the superfluid density, which can be derived from the complex conductivity, throughout parts of the carrier concentration- temperature- magnetic field phase diagram, and make comparisons with data from the field-tuned superconductor-insulator transitions in MoGe and InOx. This work is supported by the DOE and the DFG via SFB484.   

Giant enhancement of superconductivity in ultrathin $a$-Pb films by a parallel magnetic field: effect of magnetic impurity

An ultrathin superconductor containing paramagnetic impurities is predicted$^{1,2}$ to exhibit \textit{enhancement} of superconductivity ($T_{c}$ and $I_{C})$ when subject to a parallel magnetic field. We have recently observed a pronounced enhancement of superconductivity in ultrathin homogeneous amorphous Pb films without any (intentionally added) magnetic impurities in the presence of a parallel magnetic field; the $T_{c}$ enhancement is as large as 13{\%} and persists in field as high as 8 T. Our experiments are carried out in a modified dilution refrigerator capable of \textit{in situ} film growth, sample rotation, and incremental deposition of magnetic (Cr) impurities, which allows for a systematic, unambiguous elucidation of the effect of paramagnetic impurities on the field-enhancement of superconductivity. With increasing Cr density on a Pb film, the magnitude of the $T_{c}$ enhancement is progressively suppressed, contrary to the theoretical predictions. $^{1}$ Kharitonov \textit{et al}., JETP Lett. 82, 473 (2005). $^{2}$ Wei \textit{et al}., Europhys. Lett. 75, 943 (2006).   

A direct transition between a Neel ordered Mott insulator and a $d_{x2-y2}$ superconductor on the square lattice

In this paper we study a bandwidth-controlled direct, continuous, phase transition from a Mott insulator, with easy plane Neel order, to a fully gapped $d_{x2-y2}$ superconductor with a doubled unit cell on the square lattice, a transition that is forbidden according to the Landau paradigm. This transition is made possible because the vortices of the antiferromagnet are charged and the vortices of the superconductor carry spins. These nontrivial vortex quantum numbers arise because the ordered phases are intimately related to a topological band insulator. We describe the lattice model as well as the effective field theory.   

Superconductor to Quantum Metal Transitions in Ultra Thin Films

Homogeneous films of amorphous bismuth have been continuously tuned from the superconducting state by increasing a perpendicular magnetic field. Electrical transport and Hall measurements show that the non-superconducting states of the films are quantum-corrected metals. In the vicinity of transition field, the resistance can be fit by an Arrhenius type of conduction at high temperatures but this form fails at lower temperatures where the resistance is a non-monotonic function of temperature. This suggests that a two-phase regime develops near criticality. Theories suggest that this is in the form of superconducting puddles embedded in a normal matrix$^{1,2}$. $^{1}$B. Spivak, P. Oreto, and S. A. Kivelson, Phys. Rev. B \textbf{77}, 214523 (2008) $^{2}$Y. Dubi, Y. Meir, and Y. Avishai, Nature \textbf{449}, 876-880 (2007)   

The superconductor-insulator transition: is there a new insulating state?

We present nonlinear conductivity measurements on the insulating side of the superconductor-insulator transition in amorphous indium oxide. The results agree with previous data$^{1,2}$, and show conductance jumps at well-defined voltage bias thresholds. The current in the sample changes by as much as a factor of 10$^ {6}$ at the threshold, from our noise floor of 3x10$^{-14}$A to over 10$^{-8}$A. The jumps disappear above a magnetic-field- dependent temperature T$^{*}$, which is 0.11K or lower. The threshold voltage changes from 20$\mu$V to over 0.2V (4 orders of magnitude) by application of a magnetic field. We ask whether a true zero conductance state exists in our samples. DC measurements reveal pseudo-exponential I-V characteristics, which can be extrapolated to find the high Ohmic resistance of these samples at low temperatures. The extrapolated R(T) curves typically show a sub-activated trend at low T. Our results suggest that our samples have zero conductance only at the absolute zero of temperature. \\[4pt] (1) Sambandamurthy et al. PRL 92, 107005\\[0pt] (2) Baturina et al. Nature Letters 452, p613   

Metal-insulator transition and superconductivity in the Mott insulator GaTa$_{4}$Se$_{8}$ : towards a tuning of the Mott transition by electric pulses

We have recently discovered the existence of a non-volatile electric-pulse-induced resistive switching (EPI-RS) in the spinel Mott insulator GaTa$_{4}$Se$_{8}$ [1]. The origin of this effect is different from other EPI-RS mechanisms identified to date [2]. A granular superconducting state below $T_{C}$ = 5-7 K, ascertained by critical current and critical field data obtained on single crystals, appears in the EPI ``metallic'' state. This transition is reminiscent of the bulk superconductivity at 5-8 K obtained under pressure [3]. Interestingly, STM experiments have revealed a puzzling electromechanical coupling between the tip voltage and the GaTa$_{4}$Se$_{8}$ sample surface. All these results may therefore indicate that, beside electronic doping and pressure, electric pulses, through an electrostrictive effect, could be a relevant parameter to tune the Mott metal-insulator transition. [1] C. Vaju \textit{et al.}, Adv. Mater. 20, 2760 (2008) [2] R. Waser, M. Aono, Nature Mat. 6, 833 (2007) [3] M.M. Abd-Elmeguid \textit{et al.}, PRL 93, 126403 (2004)   

Enhanced Suppression of Superconductivity in Amorphous Films with Nanoscale Patterning

We have measured the thickness dependence of the superconducting critical temperature, $T_c(d_{\rm Bi})$, in amorphous Bi/Sb films patterned with a regular array of holes as well as nanoscale thickness variations. We find that the mean field $T_c$ is suppressed relative to simultaneously produced unstructured films of the same thickness. Surprisingly, however, the functional form for $T_c(d_{\rm Bi})$, remains unaffected. The role of the thickness variations in suppressing $T_c$ is compared to the role of the holes, through parameterization of the surface, as measured through AFM/SEM and a proximity effect calculation. These results suggest that these two nanoscale modifications suppress $T_c$ about equally and are consistent with $T_c$ being determined on a microscopic length scale.   

Giant enhancement of superconductivity in ultrathin $a$-Pb films by a parallel magnetic field: effect of film thickness

We have observed a pronounced enhancement of superconductivity in ultrathin homogeneously disordered amorphous Pb films in the presence of a parallel magnetic field. Our experiments are carried out in a modified dilution refrigerator capable of \textit{in situ} film growth and sample rotation, thus allowing for a detailed examination of the effects of perpendicular and parallel magnetic field on the same film at incrementally larger thicknesses. With increasing thickness, the film is tuned from an insulator to a superconductor where its zero-field T$_{c}$ increases with the thickness. For these films we observe enhancement of T$_{c}$ by a parallel magnetic field, while a perpendicular magnetic field of any strength causes a degradation of T$_{c}$. The magnitude of the T$_{c}$ enhancement appears to exhibit a non-monotonic dependence on the film thickness (zero-field T$_{c})$. The enhancement is as large as 13{\%} and persists in fields as high as 8 T for certain thicknesses. We will discuss the possible origin of the field-enhancement of superconductivity.   

Superconductor-insulator transitions in films patterned with a disordered nanohoneycomb hole array

On both sides of the Superconductor-Insulator Transition (SIT), ultrathin Bi films patterned with an ordered array of holes exhibit magnetoresistance (MR) oscillations with a period set by the superconducting flux quantum$[1]$. This observation implies that the insulating phase consists of localized Cooper pairs. To probe further this localized Cooper pair phase we have investigated samples patterned with disordered hole arrays. We have found that disorder reduces the number of MR oscillations and weakens the magnetic field tuned SIT. We will present these results and discuss their implications for the Cooper pair insulating phase. \\ $[1]$ M.D Stewart, Jr., A. Yin, J.M. Xu, and J.M. Valles, Jr., Science \textbf{318}, 1273 (2007)   

High field magnetoresistance peak near the superconductor insulator transition in amorphous Bi films patterned with a nanohoneycomb array of holes

The spectacular magnetoresistance (MR) peak that appears on the insulating side of the Superconductor-Insulator Transition (SIT) in In Oxide films [1] has received much attention. It has been taken as a sign that Cooper pairs persist into their insulating phase. We have observed a similar MR peak in ultrathin amorphous Bi films patterned with a disordered nanohoneycomb array of holes. This peak increases in magnitude with decreasing thickness and moves to lower field with decreasing temperature. Most importantly, it coexists with MR oscillations at lower fields that reveal the presence of Cooper pairs [2]. We will present our latest investigations of this peak and contrast our results with the behavior of unpatterned amorphous film systems.\\[3pt] [1] G. Sambandamurthy, \textit{et al.}, \textit{Phys. Rev. Lett.} \textbf{92}, 107005 (2004). \\[0pt] [2] M. D. Stewart, Jr., \textit{et al.}, \textit{Science} \textbf{318}, 1273 (2007).   

Superconductor-Insulator Phase Transitions in Current-Biased Arrays of Small Josephson Junctions

We present a variational approach to treat the metastable superconducting state in an array of small Josephson junctions driven by an applied current. The approach is a generalization of one previously used to treat such an array at zero applied current. The array Hamiltonian is treated variationally using the Gibbs-Bogoliubov inequality, using a set of harmonic ``phase phonons'' as the variational state. We find that, for a given J/U, where J and U are the Josephson and charging energies, a superconducting (S) to insulating (I) transition occurs as a function of applied current, or by varying the direction of the applied current at fixed magnitude. The critical values of J/U are calculated for a square, triangular, and simple cubic lattices of Josephson junctions as a function of bias current. The resulting critical J/U is found to be highly sensitive to changes in bias current magnitude, and somewhat less sensitive to current direction, for all geometries studied.   

Biot-Savart correlations in layered superconductors

We discuss the superconductor to normal phase transition in an infinite layered type-II superconductor in the limit where Josephson coupling between layers is negligible. We model each plane as a neutral gas of thermally excited pancake vortices and assume the Biot-Savart interaction between vortices is the dominant mechanism for coupling the layers. Using the real-space renormalization group, we demonstrate that the transition in this model is a Kosterlitz-Thouless transition driven by the unbinding of pancake vortices. We study the high temperature phase using a Debye-Huckel type mean field theory. We find that while the long range interaction leads to correlations between the planes, the screening within the individual layers is not significantly different from an isolated two-dimensional system. This overall picture places some claims expressed in the literature on a more secure analytical footing and also resolves some conflicting views. Experimental implications will be discussed.