Superconductor-to-insulator Transition Research Articles

Topological Gauge Theory of Josephson Junction Arrays: The Discovery of Superinsulation

We review the topological gauge theory description of Josephson junction arrays (JJA), fabricated systems which exhibit the superconductor-to-insulator transition (SIT). This description revealed the topological nature of the phases around the SIT and led to the discovery of a new state of matter, the superinsulator, characterized by infinite resistance, even at finite temperatures, due to linear confinement of electric charges. This discovery is particularly relevant for the physics of superconducting films with emergent granularity, which are modeled with JJAs and share the same phase diagram.

Superconducting fluctuations and giant negative magnetoresistance in a gate-voltage tuned two-dimensional electron system with strong spin-orbit impurity scattering

We present a quantitative theory of the gate-voltage tuned superconductor-to-insulator transition (SIT) observed experimentally in the 2D electron system created in the (111) interface between crystalline ${\mathrm{Sr}\mathrm{Ti}\mathrm{O}}_{3}$ and ${\mathrm{La}\mathrm{Al}\mathrm{O}}_{3}$. Considering two fundamental opposing effects of Cooper-pair fluctuations---the critical conductivity enhancement, known as paraconductivity, and its suppression associated with the loss of unpaired electrons due to Cooper-pairs formation---we generalize the standard thermal fluctuations theory to include interaction between fluctuations within the self-consistent field approximation and quantum tunneling between mesoscopic superconducting puddles within a phenomenological approach. Relying on the quantitative agreement found between our theory and a large body of experimental sheet-resistance data, we conclude that spin-orbit scatterings, via significant enhancement of the interaction between fluctuations, strongly enhance the sheet resistance peak at high fields and reveal anomalous metallic behavior at low fields, due to mixing of relatively heavy electron bands with a light electron band near a Lifshitz point. The large enhancement of the interaction between fluctuations at high fields, where the sheet resistance is strongly amplified, is shown to result in localization of Cooper-pair fluctuations within mesoscopic puddles.

Superconductor-insulator transition in the absence of disorder

We provide a microscopic-level derivation of earlier results showing that, in the critical vicinity of the superconductor-to-insulator transition (SIT), disorder and localization become negligible and the structure of the emergent phases is determined by topological effects arising from the competition between two quantum orders, superconductivity and superinsulation. We find that, around the critical point, the ground state is a composite incompressible quantum fluid of Cooper pairs and vortices coexisting with an intertwined Wigner crystal for the excess (with respect to integer filling) excitations of the two types.

Microscopic charging and in-gap states in superconducting granular aluminum

Following the emergence of superconducting granular aluminum (grAl) as a material for high-impedance quantum circuits, future development hinges on a microscopic understanding of its phase diagram, and whether the superconductor-to-insulator transition (SIT) is driven by disorder or charging effects. Beyond fundamental relevance, these mechanisms govern noise and dissipation in microwave circuits. Although the enhancement of the critical temperature, and the SIT in granular superconductors have been studied for more than fifty years, experimental studies have so far provided incomplete information on the microscopic phenomena. Here we present scanning tunneling microscope measurements of the local electronic structure of superconducting grAl. We confirm an increased superconducting gap in individual grains both near and above the Mott resistivity $\rho_\mathrm{M} \approx 400\ \mu \Omega cm$. Above $\rho_\mathrm{M}$ we find Coulomb charging effects, a first indication for decoupling, and in-gap states on individual grains, which could contribute to flux noise and dielectric loss in quantum devices. We also observe multiple low-energy states outside the gap, which may indicate bosonic excitations of the superconducting order parameter.

Superconducting properties of tungsten nanowires fabricated using focussed ion beam technique

We report superconducting properties of tungsten meander structures fabricated using the focussed ion beam (FIB) induced technique. Three meander structures with individual line widths of ∼70, ∼300 and ∼450 nm were fabricated for evaluation and comparison of the superconducting properties. The resistance-temperature characteristics of the meanders were measured and analysed down to a temperature of 100 mK. The superconducting properties such as critical temperature (TC) and upper-critical field (HC2) of these wires are in comparison to the reported values of FIB deposited tungsten available in literature. While the normal state resistance increases sharply as the width of the wire decreases, the superconducting transition temperature registered a slight decrease. Significant amount of residual resistance (3.8% of normal state value at 100 mK) was observed for the sample with the lowest width (70 nm). The residual resistance trails as function of temperature was analysed invoking theoretical models governing the phase slip induced dissipations in superconducting nanowires. The results indicated signature of phase slips as the width of the wire decreases: thermally activated phase slips dominant near to the TC and quantum phase slip (QPS) near to TC as well as much below to the TC. The magneto-resistance isotherms indicated quantum phase transitions (QPT); typical of a superconductor-to-insulator transition (SIT) driven by magnetic field. The SIT transition which originates from the intrinsic disorder present in the sample can be tuned by an external parameter such as magnetic field, and can be modelled by standard theories of QPT for quasi 2D or (2 + 1) D XY models. The successful fabrication of meander structures of W using FIB and the demonstration of superconductivity suggest that FIB deposited W can be exploited for many of the technological applications of superconducting nanowires such as superconducting nanowire single photon detectors, bolometers, transition edge sensors and even for quantum current standard employing the QPS phenomenon.

Vortex excitations in the insulating state of an oxide interface

In two-dimensional (2D) superconductors an insulating state can be induced either by applying a magnetic field, $H$, or by increasing disorder. Many scenarios have been put forth to explain the superconductor to insulator transition (SIT): dominating fermionic physics after the breaking of Cooper pairs, loss of phase coherence between superconducting islands embedded in a metallic or insulating matrix and localization of Cooper pairs with concomitant condensation of vortex-type excitations. The difficulty in characterizing the insulating state and its origin stems from the lack of a continuous mapping of the superconducting to insulating phase diagram in a single sample. Here we use the two-dimensional (2D) electron liquid formed at the interface between the two insulators (111) SrTiO$_3$ and LaAlO$_3$ to study the superconductor to insulator transition. This crystalline interface surprisingly exhibits very strong features previously observed only in amorphous systems. By use of electrostatic gating and magnetic fields, the sample is tuned from the metallic region, where supeconductivity is fully manifested, deep into the insulating state. Through examination of the field dependence of the sheet resistance and comparison of the response to fields in different orientations we identify a new magnetic field scale, H$_{pairing}$, where superconducting fluctuations are muted. Our findings show that vortex fluctuations excitations and Cooper pair localization are responsible for the observed SIT and that these excitations surprisingly persist deep into the insulating state.

Sequential superconductor–Bose insulator–Fermi insulator phase transitions in quasi-two-dimensional α -WSi

A zero-temperature magnetic-field-driven superconductor to insulator transition (SIT) in quasi-two-dimensional superconductors is expected to occur when the applied magnetic field crosses a certain critical value [S. L. Sondhi, S. M. Girvin, J. P. Carini, and D. Shahar, Rev. Mod. Phys. 69, 315 (1997); A. M. Goldman, Int. J. Mod. Phys. B 24, 4081 (2010)]. A fundamental question is whether this transition is due to the localization of Cooper pairs or due to the destruction of them. Here we address this question by studying the SIT in amorphous WSi. Transport measurements reveal the localization of Cooper pairs at a quantum critical field ${B}_{c}^{1}$ (Bose insulator), with a product of the correlation length and dynamical exponents $z\ensuremath{\nu}\ensuremath{\sim}4/3$ near the quantum critical point. Beyond ${B}_{c}^{1}$, superconducting fluctuations still persist at finite temperatures. Above a second critical field ${B}_{c}^{2}>{B}_{c}^{1}$, the Cooper pairs are destroyed and the film becomes a Fermi insulator. The different phases all merge at a tricritical point at finite temperatures with $z\ensuremath{\nu}=2/3$. Our results suggest a sequential superconductor to Bose insulator to Fermi insulator phase transition, which differs from the conventional scenario involving a single quantum critical point.

Superconductor to Mott insulator transition in YBa2Cu3O7/LaCaMnO3 heterostructures.

The superconductor-to-insulator transition (SIT) induced by means such as external magnetic fields, disorder or spatial confinement is a vivid illustration of a quantum phase transition dramatically affecting the superconducting order parameter. In pursuit of a new realization of the SIT by interfacial charge transfer, we developed extremely thin superlattices composed of high Tc superconductor YBa2Cu3O7 (YBCO) and colossal magnetoresistance ferromagnet La0.67Ca0.33MnO3 (LCMO). By using linearly polarized resonant X-ray absorption spectroscopy and magnetic circular dichroism, combined with hard X-ray photoelectron spectroscopy, we derived a complete picture of the interfacial carrier doping in cuprate and manganite atomic layers, leading to the transition from superconducting to an unusual Mott insulating state emerging with the increase of LCMO layer thickness. In addition, contrary to the common perception that only transition metal ions may respond to the charge transfer process, we found that charge is also actively compensated by rare-earth and alkaline-earth metal ions of the interface. Such deterministic control of Tc by pure electronic doping without any hindering effects of chemical substitution is another promising route to disentangle the role of disorder on the pseudo-gap and charge density wave phases of underdoped cuprates.

Ground State of Underdoped Cuprates in Vicinity of Superconductor-to-Insulator Transition

When an insulating underdoped cuprate is doped beyond a critical concentration (x c), high-temperature superconductivity emerges. We have synthesized a series of La 2−x Sr x CuO 4 (LSCO) samples using the combinatorial spread technique that allows us to traverse the superconductor-to-insulator transition (SIT) in extremely fine doping steps, Δx≈0.00008. We have measured the Hall resistivity (ρ H) as a function of temperature down to 300 mK in magnetic fields up to 9 T. At very low temperatures, ρ H shows an erratic behavior, jumps and fluctuations exceeding 100 %, hysteresis, and memory effects, indicating that the insulating ground state is a charge-cluster glass (CCG). Based on the phase diagram depicted in our experiment, we propose a unified picture to account for the anomalous electric transport in the vicinity of the SIT, suggesting that the CCG is in fact a disordered and glassy version of the charge density wave.

Composite fermions and the field-tuned superconductor-insulator transition

In several two-dimensional films that exhibit a magnetic field-tuned superconductor to insulator transition (SIT), stable metallic phases have been observed. Building on the `dirty boson' description of the SIT, we suggest that the metallic region is analogous to the composite Fermi liquid observed about half-filled Landau levels of the two-dimensional electron gas. The composite fermions here are mobile vortices attached to one flux quantum of an emergent gauge field. The composite vortex liquid is a 2D non-Fermi liquid metal, which we argue is stable to weak quenched disorder. We describe several experimental consequences of the emergent composite vortex liquid.

Finite-size effects in amorphous indium oxide

We study the low temperature magneto-transport properties of several highly disordered amorphous Indium oxide(a:InO) samples. Simultaneously fabricated devices comprising a 2-dimensional (2D) film and 10 $\mu$m long wires of different widths were measured to investigate the effect of size as we approach the 1D limit, which is around 4 times the correlation length, and happens to be around 100 nm for a:InO. The film and the wires showed magnetic field ({\it B}) induced superconductor to insulator transition (SIT). In the superconducting side, the resistance increased with decrease in wire width, whereas, an opposite trend is observed in the insulating side. We find that this effect can be explained in light of charge-vortex duality picture of the SIT. Resistance of the 2D film follows an activated behavior over the temperature ($T$), whereas, the wires show a crossover from the high-$T$ activated to a $T$-independent behavior. At high temperature regime the wires' resistance follow the film's until they deviate and became independent of $T$. We find that temperature at which this deviation occurs evolve with magnetic field and the width of the wire, which show the effect of finite size on the transport.

Fate of the Bose insulator in the limit of strong localization and low Cooper-pair density in ultrathin films

A Bose insulator composed of a low density of strongly localized Cooper pairs develops at the two-dimensional superconductor to insulator transition (SIT) in a number of thin film systems. Investigations of ultrathin amorphous PbBi films far from the SIT described here provide evidence that the Bose insulator gives way to a second insulating phase with decreasing film thickness. At a critical film thickness ${d}_{c}$ the magnetoresistance changes sign from positive, as expected for boson transport, to negative, as expected for fermion transport, signs of local Cooper-pair phase coherence effects on transport vanish, and the transport activation energy exhibits a kink. Below ${d}_{c}$ pairing fluctuation effects remain visible in the high-temperature transport while the activation energy continues to rise. These features show that Cooper pairing persists and suggest that the localized unpaired electron states involved in transport are interspersed among regions of strongly localized Cooper pairs in this strongly localized, low Cooper-pair density phase.

Magnetic field tuned superconductor-to-insulator transition at theLaAlO3/SrTiO3interface

We present a study of the magnetic field tuned superconductor-to-insulator transition (SIT) in the electron gas that forms at the LaAlO$_3$/SrTiO$_3$ interface. We find that the magnetic field induces a transition into a weakly insulating state, as is observed for the electrostatically tuned SIT at this interface. Finite size scaling of the magnetoresistance yields the critical exponent product $z\nu \simeq$ 7/3, indicating that the transition is governed by quantum percolation effects. While such critical exponents have been reported previously for high resistance films, they have not been reported for a low resistance system like ours, with a maximum sheet resistance of $\approx$ 1.5 k$\Omega$, much less than the quantum of resistance $R_Q \equiv h/4e^2 = 6.45$ k$\Omega$.

Effect of Coulomb interactions on the disorder-driven superconductor-insulator transition

We have studied the evolution of the superconducting energy gap of indium oxide through the disorder-driven superconductor-to-insulator transition (SIT) using two distinct experimental methods that allow us to test the influence of metallic screening: tunneling spectroscopy in which a metallic electrode is adjacent to the studied sample, thus screening Coulomb interactions, and contactless terahertz spectroscopy which probes the unperturbed sample. The tunneling measurements reveal a similar superconducting gap on both sides of the SIT and at temperatures above and below ${T}_{c}$. Terahertz measurements detect the superconducting gap below but not above the critical temperature nor in the insulating state. This difference between the two spectroscopy methods is attributed to the effect of Coulomb interactions which are screened in the tunneling experiments. Our study reveals the importance of Coulomb interactions on the energy gap of disordered superconductors.

The phenomenon of voltage controlled switching in disordered superconductors

The superconductor-to-insulator transition (SIT) is a phenomenon occurring in highly disordered superconductors and may be useful in the development of superconducting switches. The SIT has been demonstrated to be induced by different external parameters: temperature, magnetic field, electric field, etc. However, the electric field induced SIT (ESIT), which has been experimentally demonstrated for some specific materials, holds particular promise for practical device development. Here, we demonstrate, from theoretical considerations, the occurrence of the ESIT. We also propose a general switching device architecture using the ESIT and study some of its universal behavior, such as the effects of sample size, disorder strength and temperature on the switching action. This work provides a general framework for the development of such a device.

Effect of annealing on the superconducting properties ofa-NbxSi1−xthin films

$a$-Nb${}_{x}$Si${}_{1\ensuremath{-}x}$ thin films with thicknesses down to 25 \AA{} have been structurally characterized by transmission electron microscopy measurements. As-deposited or annealed films are shown to be continuous and homogeneous in composition and thickness, up to an annealing temperature of 500 ${}^{\ensuremath{\circ}}\mathrm{C}$. We have carried out low-temperature transport measurements on these films close to the superconductor-to-insulator transition (SIT) and shown a qualitative difference between the effect of annealing or composition and a reduction of the film thickness on the superconducting properties of $a$-NbSi. These results question the pertinence of the sheet resistance ${R}_{\ensuremath{\square}}$ as the relevant parameter to describe the SIT.

Collapse of the Cooper pair phase coherence length at a superconductor-to-insulator transition

We present investigations of the superconductor to insulator transition (SIT) of uniform a-Bi films using a technique sensitive to Cooper pair phase coherence. The films are perforated with a nanohoneycomb array of holes to form a multiply connected geometry and subjected to a perpendicular magnetic field. Film magnetoresistances on the superconducting side of the SIT oscillate with a period dictated by the superconducting flux quantum and the areal hole density. The oscillations disappear close to the SIT critical point to leave a monotonically rising magnetoresistance that persists in the insulating phase. These observations indicate that the Cooper pair phase coherence length, which is infinite in the superconducting phase, collapses to a value less than the interhole spacing at this SIT. This behavior is inconsistent with the gradual reduction of the phase coherence length expected for a bosonic, phase fluctuation driven SIT. This result starkly contrasts with previous observations of oscillations persisting in the insulating phase of other films implying that there must be at least two distinct classes of disorder tuned SITs.

Critical Resistance at the Superconductor-Insulator Transition in Hole-Doped Cuprates

Here, we show that in several p-type cuprates, the superconductor-to-insulator transition (SIT) occurs at the critical sheet resistance approximately equal to the quantum resistance of pairs, RQ=h/4$e^{2}$=6.5 kΩ. In a relatively broad range of temperatures and doping levels near the quantum critical point, the sheet resistance shows universal behavior and scaling characteristic of two-dimensional quantum phase transition.

Evidence for charge–vortex duality at the LaAlO3/SrTiO3 interface

The concept of duality has proved extremely powerful in extending our understanding in many areas of physics. Charge-vortex duality has been proposed as a model to understand the superconductor to insulator transition in disordered thin films and Josephson junction arrays. In this model, on the superconducting side, one has delocalized Cooper pairs but localized vortices; while on the insulating side, one has localized Cooper pairs but mobile vortices. Here we show a new experimental manifestation of this duality in the electron gas that forms at the interface between LaAlO(3) and SrTiO(3). The effect is due to the motion of vortices generated by the magnetization dynamics of the ferromagnet that also forms at the same interface, which results in an increase in resistance on the superconducting side of the transition, but an increase in conductance on the insulating side.

Increase inTcupon Reduction of Doping inLixZrNClSuperconductors

We revealed a detailed phase diagram of the very lightly doped regime in Li-intercalated superconductors, LixZrNCl, to which previous studies have never gained access owing to the difficulty in synthesizing single-phase samples. A continuous and uniform Li intercalation without any indication of phase separation was carefully confirmed by means of synchrotron x-ray diffraction and Raman scattering experiments. Upon reducing the carrier density below x=0.12, we found a rapid increase in the superconducting transition temperature (Tc) immediately followed by the superconductor-to-insulator transition (SIT). Such an increase in Tc on the verge of SIT seems to be difficult to explain by the conventional theory, but may be indicative of the charge fluctuation contribution to superconductivity in low-carrier-density systems.