Superconductor-insulator Transition Research Articles

Quantum Criticality at the Superconductor-Insulator Transition Probed by the Nernst Effect.

The superconductor-insulator transition (SIT) is an excellent example of a quantum phase transition at zero temperature, dominated by quantum fluctuations. These are expected to be very prominent close to the quantum critical point. So far, most of the experimental studies of the SIT have concentrated on transport properties and tunneling experiments that provide indirect information on criticality close to the transition. Here we present an experiment uniquely designed to study the evolution of quantum fluctuations through the quantum critical point. We utilize the Nernst effect, which has been shown to be effective in probing superconducting fluctuation. We measure the Nernst coefficient in amorphous indium oxide films tuned through the SIT and find a large signal on both the superconducting and the insulating sides, which peaks close to the critical point. The transverse Peltier coefficient α_{xy}, which is the thermodynamic quantity extracted from these measurements, follows quantum critical scaling with critical exponents ν∼0.7 and z∼1. These exponents are consistent with a clean X-Y model in 2+1 dimensions.

Effect of structural disorder and Coulomb interactions in the superconductor-insulator transition applied to boron doped diamond

The effect of disorder, both structural (non-diagonal) and on-site (diagonal), is studied through the inhomogeneous Bogoliubov-de Gennes (BdG) theory in narrow-band disordered superconductors with a view towards understanding superconductivity in boron doped diamond (BDD) and boron-doped nanocrystalline diamond (BNCD) films. We employ the attractive Hubbard model within the mean field approximation, including the short-range Coulomb interaction between holes in the narrow acceptor band. We study substitutional boron incorporation in a triangular lattice, with disorder in the form of random potential fluctuations at the boron sites. The role of structural disorder was studied through non-uniform variation of the tight-binding coupling parameter where, following experimental findings, we incorporate the concurrent increase in structural disorder with increasing boron concentration. We illustrate stark differences between the effects of structural and on-site disorder and show that structural disorder has a much greater effect on the density of states, mean pairing amplitude and superfluid density than on-site potential disorder. We show that structural disorder can increase the mean pairing amplitude while the spectral gap in the density of states decreases with states eventually appearing within the spectral gap for high levels of disorder. This study illustrates how the effects of structural disorder can explain some of the features found in superconducting BDD and BNCD films such as a tendency towards saturation of the Tc with boron doping and deviations from the expected BCS theory in the temperature dependence of the pairing amplitude and spectral gap.

Dielectric response of Anderson and pseudogapped insulators

Using a combination of analytic and numerical methods, we study the polarizability of a (non-interacting) Anderson insulator in one-, two-, and three-dimensions and demonstrate that, in a wide range of parameters, it scales proportionally to the square of the localization length, contrary to earlier claims based on the effective-medium approximation. We further analyze the effect of electron–electron interactions on the dielectric constant in quasi-1D, quasi-2D and 3D materials with large localization length, including both Coulomb repulsion and phonon-mediated attraction. The phonon-mediated attraction (in the pseudogapped state on the insulating side of the superconductor-insulator transition) produces a correction to the dielectric constant, which may be detected from a linear response of a dielectric constant to an external magnetic field.

Superconductivity-localization interplay and fluctuation magnetoresistance in epitaxial BaPb1−xBixO3 thin films

BaPb$_{1-x}$Bi$_x$O$_3$ is a superconductor, with transition temperature $T_c=11$ K, whose parent compound BaBiO$_3$ possess a charge ordering phase and perovskite crystal structure reminiscent of the cuprates. The lack of magnetism simplifies the BaPb$_{1-x}$Bi$_{x}$O$_3$ phase diagram, making this system an ideal platform for contrasting high-$T_c$ systems with isotropic superconductors. Here we use high-quality epitaxial thin films and magnetotransport to demonstrate superconducting fluctuations that extend well beyond $T_c$. For the thickest films (thickness above $\sim100$ nm) this region extends to $\sim27$ K, well above the bulk $T_c$ and remarkably close to the higher $T_c$ of Ba$_{1-x}$K$_x$BiO$_3$ ($T_c=31$ K). We drive the system through a superconductor-insulator transition by decreasing thickness and find the observed $T_c$ correlates strongly with disorder. This material manifests strong fluctuations across a wide range of thicknesses, temperatures, and disorder presenting new opportunities for understanding the precursor of superconductivity near the 2D-3D dimensionality crossover.

Influence of disorder on the superconducting critical temperature in indium-opal nanocomposites

Transport properties of bulk indium-opal and indium-porous glass superconducting nanocomposites possessing moderate and strong disorder are investigated. A strongly nonmonotonous dependence of the global critical temperature Tc versus normal state conductivity of samples is found. The maximum, which is observed at moderate disorder, has Tc higher than that of clean bulk indium. The increasing part can be explained by the Eliashberg equations with disorder and an additional mechanism of interaction between superconducting and dielectric granules. The descending part of the maximum at higher disorder can be explained by the increasing of long-range Coulomb repulsion due to diffusion of charges. Negative slope in magnetic field dependence of resistivity and a peak in the temperature dependence of resistivity, observed in the sample near the proximity to the disorder-induced superconductor–insulator transition (SIT). A large difference between the onset temperature of superconducting fluctuations, Tcon, and global critical temperature Tc is found and considered in the framework of the weak multifractal theory. Slow time-logarithmic relaxation of the resistivity between Tc and Tcon is observed, which assumes existence of the precursor state near the SIT. This unusual state is discussed in the scope of the many-body localization theory.

Charge Berezinskii-Kosterlitz-Thouless transition in superconducting NbTiN films

Three decades after the prediction of charge-vortex duality in the critical vicinity of the two-dimensional superconductor-insulator transition (SIT), one of the fundamental implications of this duality—the charge Berezinskii-Kosterlitz-Thouless (BKT) transition that should occur on the insulating side of the SIT—has remained unobserved. The dual picture of the process points to the existence of a superinsulating state endowed with zero conductance at finite temperature. Here, we report the observation of the charge BKT transition on the insulating side of the SIT in 10 nm thick NbTiN films, identified by the BKT critical behavior of the temperature and magnetic field dependent resistance, and map out the magnetic-field dependence of the critical temperature of the charge BKT transition. Finally, we ascertain the effects of the finite electrostatic screening length and its divergence at the magnetic field-tuned approach to the superconductor-insulator transition.

Superconductor-Insulator transition in sputtered amorphous MoRu and MoRuN thin films

This work shows the experimental results of the superconductor-insulator (S-I) transition for amorphous molybdenum ruthenium (MoRu) and molybdenum ruthenium nitride (MoRuN) films. These amorphous films onto c-plane sapphire substrates have been interpreted to be homogeneous by XRD and AFM measurements. Electrical and superconducting properties measurements were carried out on MoRu and MoRuN thin films deposited by reactive sputtering technique. We have analysed the data on Rsq (T) based on excess conductivity of superconducting films by the AL and MT term and weak localization and electron-electron interaction for the conductance. MoRu films which offer the most homogeneous film morphology, showed a critical sheet resistance of transition, Rc, of ∼ 2 kΩ. This values is smaller than those previously our reported for quench-condensed MoRu films on SiO underlayer held at liquid He temperature.

Tc depression and superconductor-insulator transition in molybdenum nitride thin films

We have studied that the Tc depression and the superconductor-insulator transition (SIT) in molybdenum nitride (MoN) thin films. Thin films were fabricated by reactive DC magnetron sputtering method onto (100) MgO substrates in the mixture of Ar and N2 gases. Several dozen MoN thin films were prepared in the range of 3 nm < thickness d < 60 nm. The resistance was measured by a DC four-probe technique. It is found that Tc decreases from 6.6 K for thick films with increase of the normal state sheet resistance and experimental data were fitted to the Finkel’stein formula using the bulk superconducting transition temperature Tc0 = 6.45 K and the elastic scattering time of electron τ = 1.6 × 10−16 s. From this analysis the critical sheet resistance Rc is found about 2 kΩ, which is smaller than the quantum sheet resistance RQ. This value of Rc is almost the same as those for 2D NbN films. The value of τ for MoN films is also the similar value for NbN films 1.0 × 10−16 s, while Tc0 is different from that for NbN films 14.85 K. It is indicated that the mechanism of SIT for MoN films is similar to that of NbN films, while the mean free path ℓ for MoN films is larger than that for NbN films.

Quantum phase transitions in highly crystalline two-dimensional superconductors

Superconductor–insulator transition is one of the remarkable phenomena driven by quantum fluctuation in two-dimensional (2D) systems. Such a quantum phase transition (QPT) was investigated predominantly on highly disordered thin films with amorphous or granular structures using scaling law with constant exponents. Here, we provide a totally different view of QPT in highly crystalline 2D superconductors. According to the magneto-transport measurements in 2D superconducting ZrNCl and MoS2, we found that the quantum metallic state commonly observed at low magnetic fields is converted via the quantum Griffiths state to the weakly localized metal at high magnetic fields. The scaling behavior, characterized by the diverging dynamical critical exponent (Griffiths singularity), indicates that the quantum fluctuation manifests itself as superconducting puddles, in marked contrast to the thermal fluctuation. We suggest that an evolution from the quantum metallic to the quantum Griffiths state is generic nature in highly crystalline 2D superconductors with weak pinning potentials.

Quantum critical singularities in two-dimensional metallic XY ferromagnets

An important problem in contemporary physics concerns quantum-critical fluctuations in metals. A scaling function for the momentum, frequency, temperature, and magnetic field dependence of the correlation function near a 2D-ferromagnetic quantum-critical point (QCP) is constructed, and its singularities are determined by comparing to the recent calculations of the correlation functions of the dissipative quantum XY model (DQXY). The calculations are motivated by the measured properties of the metallic compound ${\mathrm{YFe}}_{2}{\mathrm{Al}}_{10}$, which is a realization of the DQXY model in 2D. The frequency, temperature, and magnetic field dependence of the scaling function as well as the singularities measured in the experiments are given by the theory without adjustable exponents. The same model is applicable to the superconductor-insulator transitions, classes of metallic AFM-QCPs, and as fluctuations of the loop-current ordered state in hole-doped cuprates. The results presented here lend credence to the solution found for the 2D-DQXY model and its applications in understanding quantum-critical properties of diverse systems.

Superconductor-insulator transition in fccGeSb2Te4at elevated pressures

We show that polycrystalline GeSb2Te4 in the fcc phase (f-GST), which is an insulator at low temperature at ambient pressure, becomes a superconductor at elevated pressures. Our study of the superconductor to insulator transition versus pressure at low temperatures reveals a second order quantum phase transition with linear scaling (critical exponent close to unity) of the transition temperature with the pressure above the critical zero-temperature pressure. In addition, we demonstrate that at higher pressures the f-GST goes through a structural phase transition via amorphization to bcc GST (b-GST), which also become superconducting. We also find that the pressure regime where an inhomogeneous mixture of amorphous and b-GST exists, there is an anomalous peak in magnetoresistance, and suggest an explanation for this anomaly.

Microwave Properties of Superconductors Close to the Superconductor-Insulator Transition.

Strongly disordered pseudogapped superconductors are expected to display arbitrarily high values of kinetic inductance close to the superconductor-insulator transition (SIT), which make them attractive for the implementation of large dissipationless inductance. We develop the theory of the collective modes in these superconductors and discuss associated dissipation at microwave frequencies. We obtain the collective mode spectra dependence on the disorder level and conclude that collective modes become a relevant source of dissipation and noise in the outer proximity of the SIT.

Field-tuned superconductor–insulator transitions and Hall resistance in thin polycrystalline MoN films

We report on the superconductor–insulator transitions (SITs) of disordered molybdenum nitride (MoN) thin films on (1 0 0) MgO substrates as a function of the film thickness and magnetic fields. The Tc of the superconducting MoN films, which exhibit a sharp superconducting transition, monotonically decreases as the normal state Rsq increases with a decreasing film thickness. For several films with different thicknesses, we estimate the critical field Hc and the product zν ≃ 0.6 of the dynamical exponent z and the correlation length exponent ν using a finite scaling analysis. The value of this product can be explained by the (2 + 1) XY model. We found that the Hall resistance ΔRxy(H) is maximized when the magnetic field satisfies HHP(T) |1 − T/TC0| in the superconducting state and also in the normal states owning to the superconducting fluctuation corresponding to the ghost critical magnetic field. We measured the Hall conductivity δσxy(H) = σxy(H) − and fit the Gaussian approximation theory for δσxy(H) to the experimental data. Agreement between the data and the theory beyond Hc suggests the survival of the Cooper pair in the insulating region of the SIT.

Exact Boson-Fermion Duality on a 3D Euclidean Lattice.

The idea of statistical transmutation plays a crucial role in descriptions of the fractional quantum Hall effect. However, a recently conjectured duality between a critical boson and a massless two-component Dirac fermion extends this notion to gapless systems. This duality sheds light on highly nontrivial problems such as the half-filled Landau level, the superconductor-insulator transition, and surface states of strongly coupled topological insulators. Although this boson-fermion duality has undergone many consistency checks, it has remained unproven. We describe the duality in a nonperturbative fashion using an exact UV mapping of partition functions on a 3D Euclidean lattice.

Vortex variable range hopping in a conventional superconducting film

The behavior of a disordered amorphous thin film of superconducting Indium Oxide has been studied as a function of temperature and magnetic field applied perpendicular to its plane. A superconductor-insulator transition has been observed, though the isotherms do not cross at a single point. The curves of resistance vs. temperature on the putative superconducting side of this transition, where the resistance decreases with decreasing temperature, obey two-dimensional Mott variable-range hopping of vortices over wide ranges of temperature and resistance. To estimate the parameters of hopping, the film is modeled as a granular system and the hopping of vortices is treated in a manner analogous to hopping of charges. The reason the long range interaction between vortices over the range of magnetic fields investigated does not lead to a stronger variation of resistance with temperature than that of two-dimensional Mott variable-range hopping remains unresolved.

Superconductor–Insulator Transition in NbTiN Films

Experimental results indicating a direct disorder-induced superconductor–insulator transition in NbTiN thin films have been reported. It has been shown that an increase in the resistance per square in the normal state is accompanied by the suppression of the critical temperature of the superconducting transition Tc according to the fermion mechanism of suppression of superconductivity by disorder. At the same time, the temperature of the Berezinskii–Kosterlitz–Thouless transition is completely suppressed at a nonzero critical temperature and, then, the ground state changes to insulating, which is characteristic of the boson model of suppression of superconductivity by disorder. It has been shown that the temperature dependences of the resistance of insulating films follow the Arrhenius activation law.

Random gauge models of the superconductor-insulator transition in two-dimensional disordered superconductors

We study numerically the superconductor-insulator transition in two-dimensional inhomogeneous superconductors with gauge disorder, described by four different quantum rotor models: a gauge glass, a flux glass, a binary phase glass and a Gaussian phase glass. The first two models, describe the combined effect of geometrical disorder in the array of local superconducting islands and a uniform external magnetic field while the last two describe the effects of random negative Josephson-junction couplings or $\pi$ junctions. Monte Carlo simulations in the path-integral representation of the models are used to determine the critical exponents and the universal conductivity at the quantum phase transition. The gauge and flux glass models display the same critical behavior, within the estimated numerical uncertainties. Similar agreement is found for the binary and Gaussian phase-glass models. Despite the different symmetries and disorder correlations, we find that the universal conductivity of these models is approximately the same. In particular, the ratio of this value to that of the pure model agrees with recent experiments on nanohole thin film superconductors in a magnetic field, in the large disorder limit.

Magnetotransport in Ultrathin 2-D Superconducting Mo2C Crystals

Ultrathin transition metal carbides are a class of emerging 2-D materials with many intriguing properties and applications. Here, we report the transport measurements on high-quality ultrathin Mo2C crystals, which are synthesized by a chemical vapor deposition method. We demonstrate 2-D nature of the observed superconductivity in ultrathin Mo2C crystals, being consistent with a Berezinskii–Kosterlitz–Thouless transition. As the sample thickness decreases, the Mo2C crystals exhibit negative magnetoresistance behavior at low magnetic fields deep in the superconducting state. We attribute these results to strong phase fluctuations of the superconducting order parameters near the superconductor–insulator transition. Our results demonstrate that these high-quality ultrathin Mo2C crystals provide an appealing platform to gain insights into 2-D superconductivity in a clean system.

Possible observation of the Berezinskii-Kosterlitz-Thouless transition in boron-doped diamond films

The occurrence of the Berezinskii-Kosterlitz-Thouless (BKT) transition is investigated in heavily boron-doped nanocrystalline diamond films through a combination of current-voltage and resistance measurements. We observe transport features suggesting a robust BKT transition along with transport features related to vortex pinning in nanocrystalline diamond films with smaller grain size. The vortex core energy determined through analysis of the resistance temperature curves was found to be anti-correlated to the BKT transition temperatures. It is also observed that the higher BKT temperature is related to an increased vortex-antivortex binding energy derived from the activated transport regions. Further, the magnetic field induced superconductor insulator transition shows the possibility of the charge glass state. The consequences of granularity such as localization and vortex pinning can lead to tuneable BKT temperatures and strongly affects the field induced insulating state.

Superconductor to weak-insulator transitions in disordered tantalum nitride films

We study the two-dimensional superconductor-insulator transition (SIT) in thin films of tantalum nitride. At zero magnetic field, films can be disorder-tuned across the SIT by adjusting thickness and film stoichiometry; insulating films exhibit classical hopping transport. Superconducting films exhibit a magnetic field-tuned SIT, whose insulating ground state at high field appears to be a quantum-corrected metal. Scaling behavior at the field-tuned SIT shows classical percolation critical exponents $z \nu \approx$ 1.3, with a corresponding critical field $H_c \ll H_{c2}$. The Hall effect shows a crossing point near $H_c$, but with a non-universal critical value $\rho_{xy}^c$ comparable to the normal state Hall resistivity. We propose that high-carrier density metals will always exhibit this pattern of behavior at the boundary between superconducting and (trivially) insulating ground states.