Superconductor-insulator Quantum Phase Transition Research Articles

Quantum critical scaling and holographic bound for transport coefficients near Lifshitz points

The transport behavior of strongly anisotropic systems is significantly richer compared to isotropic ones. The most dramatic spatial anisotropy at a critical point occurs at a Lifshitz transition, found in systems with merging Dirac or Weyl point or near the superconductor-insulator quantum phase transition. Previous work found that in these systems a famous conjecture on the existence of a lower bound for the ratio of a shear viscosity to entropy is violated, and proposed a generalization of this bound for anisotropic systems near charge neutrality involving the electric conductivities. The present study uses scaling arguments and the gauge-gravity duality to confirm the previous analysis of universal bounds in anisotropic Dirac systems. We investigate the strongly-coupled phase of quantum Lifshitz systems in a gravitational Einstein-Maxwell-dilaton model with a linear massless scalar which breaks translations in the boundary dual field theory and sources the anisotropy. The holographic computation demonstrates that some elements of the viscosity tensor can be related to the ratio of the electric conductivities through a simple geometric ratio of elements of the bulk metric evaluated at the horizon, and thus obey a generalized bound, while others violate it. From the IR critical geometry, we express the charge diffusion constants in terms of the square butterfly velocities. The proportionality factor turns out to be direction-independent, linear in the inverse temperature, and related to the critical exponents which parametrize the anisotropic scaling of the dual field theory.

Superconductor-insulator transition in capacitively coupled superconducting nanowires.

We investigate superconductor–insulator quantum phase transitions in ultrathin capacitively coupled superconducting nanowires with proliferating quantum phase slips. We derive a set of coupled Berezinskii–Kosterlitz–Thouless-like renormalization group equations demonstrating that interaction between quantum phase slips in one of the wires gets modified due to the effect of plasma modes propagating in another wire. As a result, the superconductor–insulator phase transition in each of the wires is controlled not only by its own parameters but also by those of the neighboring wire as well as by mutual capacitance. We argue that superconducting nanowires with properly chosen parameters may turn insulating once they are brought sufficiently close to each other.

Deficiency of the scaling collapse as an indicator of a superconductor-insulator quantum phase transition

Finite-size scaling analysis is a well-accepted method for identification and characterization of quantum phase transitions (QPTs) in superconducting, magnetic, and insulating systems. We formally apply this analysis in the form suitable for QPTs in two-dimensional (2D) superconducting films to magnetic-field-driven superconductor-metal transition in one-dimensional (1D) MoGe nanowires. Despite being obviously inapplicable to nanowires, the 2D scaling equation leads to a high-quality scaling collapse of the nanowire resistance in the temperature and resistance ranges comparable or better to what is accepted in the analysis of the films. Our results suggest that the appearance and the quality of the scaling collapse by itself is not a definitive indicator of a QPT. We have also observed a sign change of the zero-bias anomaly (ZBA) in the nonlinear resistance, occurring exactly at the critical field of the accidental QPT. This behavior is often taken as an additional confirmation of the transition. We argue that in nanowires, the nonlinearity is caused by electron heating and has no relation to the critical fluctuations. Our observation suggests that similar to the scaling collapse, the sign change of ZBA can be a misleading indicator of QPT.

Strain-induced superconductor-insulator transition on a Lieb lattice

We report the numerical investigation of strain induced superconductor-insulator quantum phase transition on a Lieb lattice. Based on a non perturbative Monte Carlo technique, we show that in two dimensions an s-wave superconductor undergoes transition to a highly correlated bosonic insulator under the influence of strain, applied as staggered hopping amplitudes. We further demonstrate a strain induced BCS-BEC like crossover in the superconducting state, such that the superconductor-insulator transition takes place between a bosonic superconductor and a bosonic insulator. Our results suggest that it is the contribution of the dispersive bands towards the superconducting order, which dictates this crossover. To the best of our knowledge, this is the first work to report theoretical investigation of "disorder free" superconductor-insulator phase transition in systems with Lieb lattice structure. With the recent experimental realization of the Lieb lattice in ultracold atomic gases, photonic lattices as well as in solid state systems, we believe that the results presented in this paper would be of importance to initiate experimental investigation of such novel quantum phase transitions. We further discuss the fate of such systems at finite temperature, highlighting the effect of fluctuations on the superconducting pair formations, thermal scales and quasiparticle behavior. Our non perturbative numerical approach to the problem enables us to capture the thermal scales of the system accurately and provides us with mean field estimates of the ground state properties. The high temperature quasiparticle signatures discussed in this paper are expected to serve as benchmarks for experiments such as radio frequency and momentum resolved radio frequency spectroscopy measurements carried out on systems such as ultracold atomic gases.

Quantum electrodynamics of a superconductor–insulator phase transition

A chain of Josephson junctions implements one of the simplest many-body models undergoing a superconductor-insulator (SI) quantum phase transition between states with zero and infinite resistance. Apart from zero resistance, the superconducting state is necessarily accompanied by a sound-like mode due to collective oscillations of the phase of the complex-valued order parameter. Exciting this phase mode results in transverse photons propagating along the chain. Surprisingly little is known about the fate of this mode upon entering the insulating state, where the order parameter's amplitude remains non-zero, but the phase ordering is "melted" by quantum fluctuations. Here we report momentum-resolved radio-frequency spectroscopy of collective modes in nanofabricated chains of Al/AlOx/Al tunnel junctions. We find that the phase mode survives remarkably far into the insulating regime, such that $\textrm{M}\Omega$-resistance chains carry $\textrm{GHz}$-frequency alternating currents as nearly ideal superconductors. The insulator reveals itself through broadening and random frequency shifts of collective mode resonances, originated from intrinsic interactions. By pushing the chain parameters deeper into the insulating state, we achieved propagation with the speed of light down to $8\times 10^5~\textrm{m/s}$ and the wave impedance up to $23~\textrm{k}\Omega$. The latter quantity exceeds the predicted critical impedance by an order of magnitude, which opens the problem of quantum electrodynamics of a Bose glass insulator for both theory and experiment. Notably, the effective fine structure constant of such a 1D vacuum exceeds a unity, promising transformative applications to quantum science and technology.

Temperature dependence of the magnetoresistance peak in highly disordered superconductors

Highly disordered superconductors have a rich phase diagram. At a moderate magnetic field (B) the samples go through the superconductor-insulator quantum phase transition. In the insulating phase, the resistance increases sharply with B up to a magneto-resistance peak beyond which the resistance drops with B. In this manuscript we follow the temperature (T) evolution of this magneto-resistance peak. We show that as T is reduced, the peak appears at lower B's approaching the critical field of the superconductor-insulator transition. Due to experimental limitations we are unable to determine whether the T=0 limiting position of the peak matches that of the critical field or is at comparable but slightly higher B. We show that, although the peak appears at different B values, its resistance follows an activated T dependence over a large T range with a prefactor that is very similar to the quantum of resistance for cooper-pairs.

Superconductor-insulator transition in disordered Josephson-junction chains

We study the superconductor-insulator quantum phase transition in disordered Josephson junction chains. To this end, we derive the field theory from the lattice model that describes a chain of superconducting islands with a capacitive coupling to the ground ($C_0$) as well as between the islands ($C_1$). We analyze the theory in the short-range ($C_1 \ll C_0$) and in the long-range ($C_1 \gg C_0$) limits. The transition to the insulating state is driven by the proliferation of quantum phase slips. The most important source of disorder originates from trapped charges in the substrate that suppress the coherence of phase slips, thus favoring superconducting correlations. Using the renormalization-group approach, we determine the phase diagram and evaluate the temperature dependence of the dc conductivity and system-size dependence of the resistance around the superconductor-insulator transition. These dependences have in general strongly non-monotonic character, with several distinct regimes reflecting an intricate interplay of superconductivity and disorder.

Superconductivity in multiple phases of compressed GeSb2Te4

Here we report the discovery of superconductivity in multiple phases of the compressed GeSb2Te4 (GST) phase change memory alloy, which has attracted considerable attention for the last decade due to its unusual physical properties with many potential applications. Superconductivity is observed through electrical transport measurements, both for the amorphous (a-GST) and for the crystalline (c-GST) phases. The superconducting critical temperature, TC, continuously increases with the applied pressure reaching a maximum Tc =6K at P=20 GPa for a-GST, whereas the critical temperature of the cubic phase reaches a maximum Tc =8 K at 30 GPa. This new material system, exhibiting a superconductor-insulator quantum phase transition (SIT) has an advantage over disordered metals since it has a continuous control of the crystal structure and the electronic properties using pressure as an external stimulus, which was lacking in SIT studies until today.

Parity effect and single-electron injection for Josephson junction chains deep in the insulating state

We have made a systematic investigation of charge transport in one-dimensional chains of Josephson junctions where the characteristic Josephson energy is much less than the single-junction Cooper-pair charging energy, ${E}_{J}\ensuremath{\ll}{E}_{CP}$. Such chains are deep in the insulating state, where superconducting phase coherence across the chain is absent, and a voltage threshold for conduction is observed at the lowest temperatures. We find that Cooper-pair tunneling in such chains is completely suppressed. Instead, charge transport is dominated by tunneling of single electrons, which is very sensitive to the presence of BCS quasiparticles on the superconducting islands of the chain. Consequently, we observe a strong parity effect, where the threshold voltage vanishes sharply at a characteristic parity temperature ${T}^{*}$, which is significantly lower than the critical temperature ${T}_{c}$. A measurable and thermally activated zero-bias conductance appears above ${T}^{*}$, with an activation energy equal to the superconducting gap, confirming the role of thermally excited quasiparticles. Conduction below ${T}^{*}$ and above the voltage threshold occurs via injection of single electrons/holes into the Cooper-pair insulator, forming a nonequilibrium steady state with a significantly enhanced effective temperature. Our results explicitly show that single-electron transport dominates deep in the insulating state of Josephson junction arrays. This conduction process has mostly been ignored in previous studies of both superconducting junction arrays and granular superconducting films below the superconductor-insulator quantum phase transition.

Two-dimensional superconductor-insulator quantum phase transitions in an electron-doped cuprate

We use ionic liquid-assisted electric field effect to tune the carrier density in an electron-doped cuprate ultrathin film and cause a two-dimensional superconductor-insulator transition (SIT). The low upper critical field in this system allows us to perform magnetic field (B)-induced SIT in the liquid-gated superconducting film. Finite-size scaling analysis indicates that SITs induced both by electric and magnetic field are quantum phase transitions and the transitions are governed by percolation effects - quantum mechanical in the former and classical in the latter case. Compared to the hole-doped cuprates, the SITs in electron-doped system occur at critical sheet resistances (Rc) much lower than the pair quantum resistance RQ=h/(2e)2=6.45 k{\Omega}, suggesting the possible existence of fermionic excitations at finite temperature at the insulating phase near SITs.

Length-scale dependent superconductor-insulator quantum phase transitions in one dimension

We study the dissipation physics of a one dimensional mesoscopic superconducting quantum interference device array using the field-theoretical renormalization group method. We observe length scale dependent, superconductor-insulator quantum phase transition at very low temperature and also observe the dual behavior of the system for higher and lower values of magnetic field. At a critical magnetic field, we also observe a critical behavior where the resistance is independent of length.

From quantum corrections to magnetic-field-tuned superconductor–insulator quantum phase transition in TiN films

Results of the measurements of the magnetic-field-dependent resistance of ultrathin superconducting TiN films with different degrees of disorder are presented. The main features of the isomagnetic data R ( T , B = const ) and isotherms R ( B , T = const ) observed in all samples are: fan-shaped structure of R ( T , B = const ) curves, a negative magnetoresistance at high magnetic fields, the presence of an intersection point ( B c , R c ), and the possibility of a scaling data presentation. The analysis of the data reveals that such behavior, previously regarded as the main evidence of the magnetic-field-tuned superconductor–insulator transition, can actually be observed for a usual thermodynamic superconductor–normal metal transition, provided that the behavior of this metal is controlled, to a considerable degree, by the quantum corrections to the conductivity.

Quantum fluctuations in thin superconducting wires of finite length.

In one-dimensional wires, fluctuations destroy superconducting long-range order and stiffness at finite temperatures; in an infinite wire, quasi-long-range order and stiffness survive at zero temperature if the wire's dimensionless admittance mu is large, mu>2. We analyze the disappearance of this superconductor-insulator quantum phase transition in a finite wire and its resurrection due to the wire's coupling to its environment characterized through the dimensionless conductance K.

Superconductor-insulator quantum phase transition in a single Josephson junction

The superconductor-to-insulator quantum phase transition in resistively shunted Josephson junctions is investigated by means of path-integral Monte Carlo simulations. Our numerical technique allows to directly access the regime of the Josephson-to-charging energy ratios ${E}_{J}{/E}_{C}$ of order one. Our results unambiguously support an earlier theoretical conjecture, based on renormalization-group calculations, that at $\stackrel{\ensuremath{\rightarrow}}{T}0$ the dissipative phase transition occurs at a universal value of the shunt resistance ${R}_{S}{=h/4e}^{2}$ for all values ${E}_{J}{/E}_{C}.$ On the other hand, finite-temperature effects are shown to turn this phase transition into a crossover, whose position depends significantly on ${E}_{J}{/E}_{C},$ as well as on the dissipation strength and temperature. The latter effect needs to be taken into account in order to reconcile earlier theoretical predictions with recent experimental results.

Scaling Analysis of Magnetic-Field-Tuned Phase Transitions in One-Dimensional Josephson Junction Arrays

We have studied experimentally the magnetic field-induced superconductor-insulator quantum phase transition in one-dimensional arrays of small Josephson junctions. The zero bias resistance was found to display a drastic change upon application of a small magnetic field; this result was analyzed in context of the superfluid-insulator transition in one dimension. A scaling analysis suggests a power law dependence of the correlation length instead of an exponential one. The dynamical exponents $z$ were determined to be close to 1, and the correlation length critical exponents were also found to be about 0.3 and 0.6 in the two groups of measured samples.

Superconducting alloys with weak and strong scattering: Anderson’s theorem and a superconductor-insulator transition

We have studied the effects of strong impurity scattering on disordered superconductors beyond the low impurity concentration limit. By applying the full CPA to a superconductiong A-B binary alloy, we calculated the fluctuations of the local order parameters $\Delta_{A}, \Delta_{B}$ and charge densities, $n_{A}, n_{B}$ for weak and strong on site disorder. We find that for narrow band alloy s-wav e superconductors the conditions for Anderson's theorem are satisfied in general only for the case of particle-hole symmetry. In this case it is satisfied regardless whether we are in the weak or strong scattering regimes. Interestingly, we find that strong scattering leads to band splitting and in this regime for any band filling we have a critical concentration where a superconductor-insulator quantum phase transition occurs at T=0.

Self-duality in superconductor-insulator quantum phase transitions

It is argued that close to a Coulomb interacting quantum critical point the interaction between two vortices in a disordered superconducting thin film separated by a distance r changes from logarithmic in the mean-field region to 1/r in the region dominated by quantum critical fluctuations. This gives support to the charge-vortex duality picture of the observed reflection symmetry in the current-voltage characteristics on both sides of the transition.

Thermally fluctuating superconductors in two dimensions

In many two-dimensional superconducting systems, such as Josephson-junction arrays, granular superconducting films, and the high-temperature superconductors, it appears that the electrons bind into Cooper pairs below a pairing temperature (T(P)) that is well above the Kosterlitz-Thouless temperature (T(KT)) the temperature below which there is long-range superconducting order). The electron dynamics at temperatures between T(KT) and T(P) involve a complex interplay of thermal and quantum fluctuations, for which no quantitative theory exists. Here we report numerical results for this region, by exploiting its proximity to a T = 0 superconductor-insulator quantum phase transition. This quantum critical point need not be experimentally accessible for our results to apply. We characterize the static, thermodynamic properties by a single dimensionless parameter, gamma(T). Quantitative and universal results are obtained for the frequency dependence of the conductivity, which are dependent only upon gamma(T) and fundamental constants of nature.