Superconductor-insulator Transition Research Articles

Bose–Einstein condensation of two-dimensional spin-1 Cooper pairs in a uniform magnetic field

Bose–Einstein condensation of two-dimensional spin-1 Cooper pairs in a uniform magnetic field is investigated within the framework of quantum statistical mechanics. We derive an exact analytical solution of two-dimensional spin-1 Cooper pairs in a uniform magnetic field, which involves a q-digamma function in mathematics. In two dimensions, it is found that the critical temperature and condensate fraction are monotonically increasing functions of magnetic field B, Landé factor g, and number density σ. Our investigation in two dimensions provides an example of the magnetic-field-tuned insulator-superconductor quantum phase transition.

Universal relation between doping content and normal-state resistance in gate voltage tuned ultrathin Bi2Sr2CaCu2O8+x flakes

Gate voltage tunable ultrathin high-${T}_{c}$ cuprates supply a unique platform to investigate the electronic phase diagram and superconductor-insulator transition. One of the challenges in this field is the precise determination of the doping content in the underdoped nonsuperconducting region. Here we report the discovery of a universal relation between the doping content $p$ and the normal-state resistance at a fixed temperature $R({T}_{f})$, $p=\ensuremath{\alpha}+\ensuremath{\beta}\phantom{\rule{4pt}{0ex}}\mathrm{ln}[1/R({T}_{f})]$, in the ultrathin ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+x}$ flakes. The in-depth analysis shows that the evolution of carrier scattering probability with doping content and the change of effective mass caused by superconductor-insulator transition are two key factors leading to this logarithmic relation. Based on our finding, the more precise electronic phase diagram can be established. In addition, the superconductor-insulator transition is verified to be a quantum phase transition using a finite size scaling analysis. The scaling exponent $z\ensuremath{\nu}$ is found to have a close correlation with the disorder levels. The present result provides an important foundation to investigate the fascinating electronic states in the ultra-thin cuprates.

Zero temperature superconductor–edge metal–insulator transition in two-dimensional bosonic systems

Motivated by the recent experimental observation of an intermediate bosonic metallic state in the two-dimensional superconductor-insulator transition at $T=0$, we study an extended Bose Hubbard model in the limit of large number of particles per site. Using a representation of this in terms of two coupled $XY$ models, we find, in addition to an insulating phase and a $(2+1)D$ superfluid phase, two other phases. One phase is a $2D$ superfluid phase where a crossover from $(2+1)D$ to $2D$ has taken place as a result of incipient charge ordering, signaled by $\theta$ disordering, and which is closely related to a supersolid phase. The other new phase is an edge metal state characterized by zero superfluid stiffness, zero charge ordering, and zero bulk compressibility. However, the edge compressibility of the system is nonzero. While we do not find any intermediate state with $2D$ metallic conductivity, we are able to connect these results to STM experiments on $\mathrm{MoS_2}$ showing brims of finite density of states around the entire edge of $2D$ $\mathrm{MoS_2}$ samples.

Correlated disorder as a way towards robust superconductivity

Ordinary superconductors are widely assumed insensitive to small concentrations of random nonmagnetic impurities, whereas strong disorder suppresses superconductivity and even makes superconductor-insulator transition occur. In between these limiting cases, a most fascinating regime can take place where disorder enhances superconductivity. Hitherto, almost all theoretical studies have been conducted under the assumption that disorder is completely independent and random. In real materials, however, positions of impurities and defects tend to correlate with each other. This work shows that these correlations have a strong impact on superconductivity making it more robust and less sensitive to the disorder potential. Superconducting properties can therefore be controlled not only by the overall density of impurities and defects, but by their spatial correlations as well.

Soft-mode-phonon-mediated insulator–superconductor transition in doped two-dimensional topological insulator RuC

Recently, the search of superconducting materials with topological states has attracted extensive interest due to their exotic properties. By using first-principles calculations, we predict that RuC monolayer is a two-dimensional topological insulator (TI) and shows a TI–superconductor transition under electron doping, leading to a superconducting transition temperature Tc of 1.4 K. Further analysis reveals that the emergence of superconductivity in RuC depends critically on the existence of flatband optical phonons as well as the appearance of multiple electron-pockets and phonon mode softening induced by doping. Moreover, we find that Li-intercalated RuC (LiRuC) is a thermal dynamically stable, superconducting material with a high Tc of 9.8 K, benefitting from the strong electron–phonon coupling. Many other superconductors with flat phonon bands are also predicted via elemental substitution in LiRuC. Our results will broaden the research interest in exploring more superconductors and modulating their physical properties through flat phonon bands.

Manipulating high-temperature superconductivity by oxygen doping in Bi2Sr2CaCu2O8+δ thin flakes.

Harnessing the fascinating properties of correlated oxides requires precise control of their carrier density. Compared to other methods, oxygen doping provides an effective and more direct way to tune the electronic properties of correlated oxides. Although several approaches, such as thermal annealing and oxygen migration, have been introduced to change the oxygen content, a continuous and reversible solution that can be integrated with modern electronic technology is much in demand. Here, we report a novel ionic field-effect transistor using solid Gd-doped CeO2 as the gate dielectric, which shows a remarkable carrier-density-tuning ability via electric-field-controlled oxygen concentration at room temperature. In Bi2Sr2CaCu2O8+δ (Bi-2212) thin flakes, we achieve a reversible superconductor-insulator transition by driving oxygen ions in and out of the samples with electric fields, and map out the phase diagram all the way from the insulating regime to the over-doped superconducting regime by continuously changing the oxygen doping level. Scaling analysis indicates that the reversible superconductor-insulator transition for the Bi-2212 thin flakes follows the theoretical description of a two-dimensional quantum phase transition. Our work provides a route for realizing electric-field control of phase transition in correlated oxides. Moreover, the configuration of this type of transistor makes heterostructure/interface engineering possible, thus having the potential to serve as the next-generation all-solid-state field-effect transistor.

Pressure induced superconductivity in nonlinear optical crystal ZnGeP2 and its capture at ambient pressure

An insulator could be driven into an emergent superconducting state when it is put in the extreme high-pressure condition, however, it is challenging to retain the obtained superconductivity to ambient pressure. Here we report on the creation and preservation of the superconductivity in chalcopyrite ZnGeP2, a commercial nonlinear optical crystal. Electrical transport measurements reveal that the superconductivity, induced at a critical pressure ∼17 GPa, is robust not only upon further compression to 52.9 GPa, but also in the process when the pressure is gradually released to ambient pressure. Synchrotron X-ray diffraction and Raman measurements document a structural origin of the unusual evolution of the superconductivity. The insulator-superconductor transition around 17 GPa is correlated with a structural transition from tetragonal to cubic phase, while the preserved superconductivity is consisitent with the irreversibility of the tetragonal-cubic phase transition and the presence of amorphization in the depressurized sample. These findings demonstrate a strategy to capture the high-pressure phase with emerging physical properties and will shed light on exploring novel superconductors by means of pressure treatment.

Hysteresis and jumps in the I−V curves of disordered two-dimensional materials

The superconductor-insulator transition (SIT) in thin-film disordered superconductors is a hallmark example of a quantum phase transition. Despite being observed more than 30 years ago, its nature is still under a vivid debate. One intriguing observations concerns the insulating side of the transition, which exhibits some unusual properties. Among them is its current-voltage relation ($I-V$ curve), which includes (1) a conductance that changes abruptly by several orders of magnitude with increasing voltage, (2) hysteretic behavior, and (3) multiple (sometimes more than a hundred) smaller current jumps near the transition. Some models have been suggested before, but no model has been successful in accounting for the observed behavior in full. One commonly used approach is to model the disordered sample as a two-dimensional array of conducting islands, where charge carriers tunnel from one island to its neighbors. In those models, fast relaxation is assumed, and the system is treated as always being in electrostatic and thermal equilibrium. Those models are successful in explaining some measurement results, including the phase transition itself, but fail to reproduce hysteresis in their predicted $I-V$ curves. Here, we suggest incorporating finite relaxation time into an array model. We show that, in the slow relaxation limit, our model can reproduce hysteresis and multiple jumps in the $I-V$ curve. Based on our results we argue that a similar behavior should be also observed in two-dimensional normal (non-superconducting) arrays. This claim is supported by past observations. We analyse the role of different parameters in our model, determine the range of relevant time scale in the problem, and compare our results with selected measurements.

FFLO state driven by quasiperiodic Zeeman field and its transition to localized states

We numerically study the ground-state properties of a one-dimensional lattice model in the presence of a quasiperiodic Zeeman field, by means of the density matrix renormalization group algorithm. We map out a global phase diagram, which encloses a Bardeen-Cooper-Schrieffer (BCS) phase, a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase where the Cooper pairs obtain a finite center-of-mass momentum, and a localized phase. The FFLO phase is promoted by the quasiperiodic Zeeman field, which demonstrates a power-law pairing correlation with a critical exponent ${\ensuremath{\eta}}_{\mathrm{FFLO}}<1$ decaying much slower than the charge density and spin density correlations. By tuning the interaction and the filling factor, we find the FFLO phase is suppressed in the strong interaction and low filling regions. A large Zeeman field destroys the FFLO state and drives a superconductor-insulator transition. Furthermore, we propose this FFLO phase and the superconductor-insulator transition could be observed in the optical lattice experiment.

Applied electric field instead of pressure in H-based superconductors

In our desire to give a new suggestion for H-based superconductors experiments we present a theoretical framework for understanding the impact of an applied electric field on pressured hydride superconductors. We study a material at pressure $p$, when it possesses insulator-superconductor transition, at the respective superconducting critical temperature $T_{cr}$. The theory shows the applied electric field penetrates the material and forces the Cooper pairs to Bose condensate. If one applies an electric field and then increases the temperature, the theory predicts novel critical temperature $T^{el}_{cr}$ higher than $T_{cr}$. Therefore, the system has a higher superconducting critical temperature if we apply an electric field instead of increasing the pressure. The result shows that in the case of carbonaceous sulfur hydride at $234Gpa$ and near but below critical temperature $T_c=283K$, applying a sufficiently strong electric field, we can bring the superconducting critical temperature close to 300K.

Superconductor–insulator transitions in three-dimensional indium-oxide at high pressures

Experiments investigating magnetic-field-tuned superconductor–insulator transition (HSIT) mostly focus on two-dimensional material systems where the transition and its proximate ground-state phases, often exhibit features that are seemingly at odds with the expected behavior. Here we present a complementary study of a three-dimensional pressure-packed amorphous indium-oxide (InOx) powder where granularity controls the HSIT. Above a low threshold pressure of ∼0.2 GPa, vestiges of superconductivity are detected, although neither a true superconducting transition nor insulating behavior are observed. Instead, a saturation at very high resistivity at low pressure is followed by saturation at very low resistivity at higher pressure. We identify both as different manifestations of anomalous metallic phases dominated by superconducting fluctuations. By analogy with previous identification of the low resistance saturation as a ‘failed superconductor’, our data suggests that the very high resistance saturation is a manifestation of a ‘failed insulator’. Above a threshold pressure of ∼6 GPa, the sample becomes fully packed, and superconductivity is robust, with T C tunable with pressure. A quantum critical point at P C ∼ 25 GPa marks the complete suppression of superconductivity. For a finite pressure below P C, a magnetic field is shown to induce a HSIT from a true zero-resistance superconducting state to a weakly insulating behavior. Determining the critical field, H C, we show that similar to the 2D behavior, the insulating-like state maintains a superconducting character, which is quenched at higher field, above which the magnetoresistance decreases to its fermionic normal state value.

Onset of a superconductor-insulator transition in an ultrathin NbN film under in-plane magnetic field studied by terahertz spectroscopy

Optical conductivity of a moderately disordered superconducting NbN film was investigated by terahertz time-domain spectroscopy in external magnetic field applied along the film plane. The film thickness of about 5 nm was comparable with the coherence length, so vortices should not form. This was confirmed by the fact that no marked difference between the spectra with terahertz electric field set perpendicular and parallel to the external magnetic field was observed. Simultaneous use of Maxwell-Garnett effective medium theory and the model of optical conductivity by Herman and Hlubina proved to correctly reproduce the terahertz spectra obtained experimentally in a magnetic field of up to 7 T. This let us conclude that the magnetic field tends to suppress the superconductivity, resulting in an inhomogeneous state where superconducting domains are enclosed within a normal-state matrix. The scattering rate due to pair-breaking effects was found to linearly increase with magnetic field.

Quantum oscillation phenomena in low-dimensional superconductors

<sec>Low-dimensional superconductor serves as an excellent platform for investigating emergent superconducting quantum oscillation phenomena. The low-dimensional natures of these materials, originating from the finite size which is comparable with the superconducting coherence length, indicate that the corresponding physical properties will be constrained by quantum confinement effects. Importantly, some of the frontiers and hot issues in low-dimensional superconductors, including the anomalous metal state during the superconductor-insulator transition, spin-triplet pairing mechanism in superconductors, thermal-excited and electrical current-excited vortex dynamics in superconductors, and the “charge-vortex duality” in quantum dot materials and superconducting nanowires, are strongly correlated with the superconducting quantum oscillation effects. In recent years, all the above-mentioned topics have achieved breakthroughs based on the studies of superconducting quantum oscillation effects in low-dimensional superconductors. Generally, the periodicity and amplitude of the oscillation can clearly demonstrate the relation between the geometric structure of superconductors and various superconducting mechanisms. In particular, superconducting quantum oscillation phenomena are always correlated with the quantization of magnetic fluxoids and their dynamics, the pairing mechanism of superconducting electrons, and the excitation and fluctuation of superconducting systems.</sec><sec>In this review article, three types of typical superconducting quantum oscillation effects observed in low-dimensional superconductors will be discussed from the aspects of research methods, theoretical expectations, and experimental results. a) The Little-Parks effect is the superconducting version of the Aharonov-Bohm effect, whose phase, amplitude and period are all helpful in studying superconductivity: the phase reflects the pairing mechanism in superconductors, the amplitude can be used for investigating the anomalous metal state, and the period provides the information about the sample geometry. b) The vortex motion effect is excited by thermal fluctuation or electrical current, and the corresponding oscillation phenomena show distinct temperature-dependent amplitudes compared with the Little-Parks effect. c) The Weber blockade effect originates from the magnetic flux moving across the superconducting nanowire, and such an effect provides a unique nonmonotonic critical current <inline-formula><tex-math id="M1">\begin{document}$ {I}_{\mathrm{C}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20212289_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20212289_M1.png"/></alternatives></inline-formula> under a magnetic field in <inline-formula><tex-math id="M2">\begin{document}$I\text{-}V$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20212289_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20212289_M2.png"/></alternatives></inline-formula> characteristics. The prospects of the above-mentioned quantum oscillation effects of low-dimensional superconductors for applications are also discussed at the end of this review, including quantum computing, device physics and low-temperature physics.</sec>

Infrared broadband photoresponse characteristics of nanoporous NbN film

Nanoporous superconducting films with superconductor-insulator transition characteristics have potential application in the field of infrared photoelectric detection, but their broadband optical response characteristics in infrared band have not been reported. Therefore, taking nanoporous niobium nitride (NbN) films as the main object, the optical response characteristics in the near and medium infrared wavelength range of 780–5000 nm are studied in this paper. Firstly, the Drude-model fitting accuracy of measured NbN permittivity is improved by about 17%, and the NbN optical parameters in mid-infrared band are obtained. Furthermore, the optical response characteristics of the back-illuminated device with nanoporous NbN film are analyzed by finite difference time domain method, and a Bruggeman equivalent model which can simplify the nanoporous film into a uniform film is given, thereby reducing the three-dimensional simulation of nanoporous NbN film into one dimensional simulation. Finally, based on the equivalent model and the transfer matrix method, the light absorption characteristics of the back-illuminated device in near-/mid-infrared wavelength ranges are optimized. The results indicate that, on the one hand, simplifying the design process by using Bruggeman equivalent model will not affect the correctness of the final optimization results, and, on the other hand, a relatively simple optical cavity can make the detector achieve polarization-independent film absorption greater than 82% for near-/mid-infrared broadband design and 93.7% for double-wavelength design.

Distribution of the order parameter in strongly disordered superconductors: An analytic theory

We developed an analytic theory of inhomogeneous superconducting pairing in strongly disordered materials, which are moderately close to superconducting-insulator transition. Single-electron eigenstates are assumed to be Anderson-localized, with a large localization volume. Superconductivity develops due to coherent delocalization of originally localized pre-formed Cooper pairs. The key assumption of the theory is that each such pair is coupled to a large number $Z\gg1$ of similar neighboring pairs. We derived integral equations for the probability distribution $P\left(\Delta\right)$ of local superconducting order parameter $\Delta\left(\boldsymbol{r}\right)$ and analyzed their solutions in the limit of small dimensionless Cooper coupling constant $\lambda\ll1$. The shape of the order-parameter distribution is found to depend crucially upon the effective number of nearest neighbors $Z_{\text{eff}}=2\nu_{0}\Delta_{0}Z$. The solution we provide is valid both at large and small $Z_{\text{eff}}$; the latter case is nontrivial as the function $P\left(\Delta\right)$ is heavily non-Gaussian. The discovery of a broad parameter range where the distribution function $P\left(\Delta\right)$ is non-Gaussian but also non-critical (in the sense of SIT criticality) is one of our key findings. The analytic results are supplemented by numerical data, and good agreement between them is observed.

Overactivated transport in the localized phase of the superconductor-insulator transition

Beyond a critical disorder, two-dimensional (2D) superconductors become insulating. In this Superconductor-Insulator Transition (SIT), the nature of the insulator is still controversial. Here, we present an extensive experimental study on insulating NbxSi1−x close to the SIT, as well as corresponding numerical simulations of the electrical conductivity. At low temperatures, we show that electronic transport is activated and dominated by charging energies. The sample thickness variation results in a large spread of activation temperatures, fine-tuned via disorder. We show numerically and experimentally that this originates from the localization length varying exponentially with thickness. At the lowest temperatures, there is an increase in activation energy related to the temperature at which this overactivated regime is observed. This relation, observed in many 2D systems shows that conduction is dominated by single charges that have to overcome the gap when entering superconducting grains.

Granular metallicity as a minimal normal state for superconductivity

We report the evolution of electrical transport properties in insulating FeSe films with electron doping induced by the ionic liquid gating technique. Superconductivity never emerges in the strong insulators with variable-range hopping behavior but is shown to arise once the resistance of the normal state varies as $ln(1/T)$, indicating that this behavior corresponds to the minimal conducting character for developing superconductivity. Our work points toward granular metallicity for the $ln(1/T)$ behavior, suggesting that the emergence of superconductivity requires at least an insulating state containing metallic granules. Moreover, it unravels an electronic segregation in proximity to superconductor-insulator transition, which calls for a comprehensive understanding of this segregated phase.

(Invited) Long Range Coherent Transport in Proteins via Electron Pairing

Recently, Lindsay et al. showed in a series of papers (summarized in Lindsay, S. Life 2020, 10, 72.) that single proteins coupled to metal electrodes have unexpectedly good conductance properties. It became clear that much of the resistance drop happens at the metallic contacts, and the internal conductivity of the protein itself can be very close to the quantum limit 2e^2/h for short proteins. The localization length can be as large as ten nanometers for longer ones. Cahen et al. showed that the conductance is temperature independent in the range of 30-300 Kelvins in a series of measurements. All this indicates that proteins support fast and at least partially coherent electron transport at room temperature. According to electronic structure calculations, proteins have significant HOMO-LUMO gaps surrounded by localized orbitals, a typical arrangement for insulators ruling out efficient single-electron quantum transport even in the presence of photon mediation. However, due to the repetitive nature of the basic peptide backbone of the proteins, there are states deeper below the HOMO energy, which are intermediary between extended states typical in metallic conductance bands and the localized ones. These so-called critical states (Vattay G. et al. 2015 J. Phys.: Conf. Ser. 626 012023) have fractal density distributions and show large electron density correlations between other orbitals in the same energy region. It has been shown that in the presence of electron-electron attraction, these states are especially suited for pair formation of electrons, and an insulator-superconductor transition can occur even at high temperatures. Here we argue that polarizable sidechains of amino acids can create an attractive force between electrons propagating along the backbone. We show that the typical size and polarization of amino acids make the proper magnitude of pairing energy to maintain superconducting patches even at room temperature. We calculate and display the geometry of the superconducting gap over the protein structure and propose this new mechanism as a possible explanation for the observed coherent transport.

Setup for pressurizing thin films through the superconductor-insulator transition.

We describe an experimental setup designed for transport measurement of thin disordered superconducting films as a function of pressure up to several GPa. We use a specially designed single screw diamond anvil cell that allows the gradual increase of high pressure at cryogenic temperatures. By depositing amorphous films of disordered superconducting indium oxide directly on the diamond, we avoid the effect of pressure-induced structural changes in the substrate. Using this technique, we are able to drive thin films through a pressure tuned superconductor-insulator transition.

Superinsulators: An Emergent Realisation of Confinement

Superinsulators (SI) are a new topological state of matter, predicted by our collaboration and experimentally observed in the critical vicinity of the superconductor-insulator transition (SIT). SI are dual to superconductors and realise electric-magnetic (S)-duality. The effective field theory that describes this topological phase of matter is governed by a compact Chern-Simons in (2+1) dimensions and a compact BF term in (3+1) dimensions. While in a superconductor the condensate of Cooper pairs generates the Meissner effect, which constricts the magnetic field lines penetrating a type II superconductor into Abrikosov vortices, in superinsulators Cooper pairs are linearly bound by electric fields squeezed into strings (dual Meissner effect) by a monopole condensate. Magnetic monopoles, while elusive as elementary particles, exist in certain materials in the form of emergent quasiparticle excitations. We demonstrate that at low temperatures magnetic monopoles can form a quantum Bose condensate (plasma in (2+1) dimensions) dual to the charge condensate in superconductors. The monopole Bose condensate manifests as a superinsulating state with infinite resistance, dual to superconductivity. The monopole supercurrents result in the electric analogue of the Meissner effect and lead to linear confinement of the Cooper pairs by Polyakov electric strings in analogy to quarks in hadrons. Superinsulators realise thus one of the mechanism proposed to explain confinement in QCD. Moreover, the string mechanism of confinement implies asymptotic freedom at the IR fixed point. We predict thus for superinsulators a metallic-like low temperature behaviour when samples are smaller than the string scale. This has been experimentally confirmed. We predict that an oblique version of SI is realised as the pseudogap state of high-TC superconductors.