Localized Cooper Pairs Research Articles

Suppression of superconductivity dominated by proximity effect in amorphous MoSi nanobelts

A traditional concept proposes that the suppression of the transition temperature ${T}_{c}$ in an amorphous nanobelt is driven by enhanced disorder, which accounts for localized Cooper pairs. However, in this paper, we observe ${T}_{c}$ suppression in an amorphous molybdenum-silicide (MoSi) nanobelt, which scales as the inverse square of the width but contradicts disorder theory. Instead, the transition regime can be well described by Cooper pair diffusion in the proximity effect. Both the nonlinear reduction of the switching current density and the abnormal increase of the effective retrapping current density with the reduction of the width further verify the proximity-induced relation. Therefore, we attribute the main size dependence of the suppressed superconducting properties in the MoSi nanobelt to the proximity effect rather than disorder. We speculate that the competition between superconductivity and disorder only appears at the two narrow edge bands rather than the entire nanobelt. Subsequently, the reduction in width does not produce a significant impact on superconductivity for disorder, and only the proximity effect plays an overwhelming role in the MoSi nanobelt.

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.

Pressure tuning of superconductivity in Mo8Ga41 single crystals

We report on pressure tuning of superconductivity in a strongly coupled superconductor ${\mathrm{Mo}}_{8}{\mathrm{Ga}}_{41}$ with a critical temperature ${T}_{c}\ensuremath{\sim}9.8\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. Resistance measurements show that ${T}_{c}$ is suppressed to 3.6 K at 19 GPa followed by a nonmonotonic variation at higher pressures. Synchrotron x-ray diffraction experiments reveal an amorphization taking place at the critical pressure ${P}_{c}\ensuremath{\sim}19\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$. As comparing with $\mathrm{Mg}{\mathrm{B}}_{2}$, the ${\mathrm{Mo}}_{8}{\mathrm{Ga}}_{41}$ shows a relative low decreasing rate of ${T}_{c}$, which might be attributed to its unique vertex-sharing type of cluster architecture. Survival of superconductivity across the crystalline to amorphous transition indicates that, although long-range structural order of endohedral Ga clusters is destroyed, short-range-ordered intracluster structure still exists and allows for local Cooper pairing. Due to presence of disorders in the amorphous phase, establishment of Cooper pair coherence is shifted to lower temperatures, which causes unusual transport behaviors near ${T}_{c}$, e.g., the anomalous resistance peak and dip. The amorphous superconducting phase is able to be retained to ambient pressure and therefore provides an ideal platform to study disorder effects on superconductivity.

Bosonic Confinement and Coherence in Disordered Nanodiamond Arrays.

In the presence of disorder, superconductivity exhibits short-range characteristics linked to localized Cooper pairs which are responsible for anomalous phase transitions and the emergence of quantum states such as the bosonic insulating state. Complementary to well-studied homogeneously disordered superconductors, superconductor-normal hybrid arrays provide tunable realizations of the degree of granular disorder for studying anomalous quantum phase transitions. Here, we investigate the superconductor-bosonic dirty metal transition in disordered nanodiamond arrays as a function of the dispersion of intergrain spacing, which ranges from angstroms to micrometers. By monitoring the evolved superconducting gaps and diminished coherence peaks in the single-quasiparticle density of states, we link the destruction of the superconducting state and the emergence of bosonic dirty metallic state to breaking of the global phase coherence and persistence of the localized Cooper pairs. The observed resistive bosonic phase transitions are well modeled using a series-parallel circuit in the framework of bosonic confinement and coherence.

Large magnetoresistance of insulating silicon films with superconducting nanoprecipitates

We report on large negative and positive magnetoresistance in inhomogeneous, insulating Si:Ga films below a critical temperature of about 7 K. The magnetoresistance effect exceeds 300 % at temperatures below 3 K and fields of 8 T. The comparison of the transport properties of superconducting samples with that of insulating ones reveals that the large magnetoresistance is associated with the appearance of local superconductivity. A simple phenomenological model based on localized Cooper pairs and hopping quasiparticles is able to describe the temperature and magnetic field dependence of the sheet resistance of such films.

Tip-Pressure-Induced Incoherent Energy Gap in CaFe2As2**Supported by the National Natural Science Foundation of China under Grant No 11227903, the National Basic Research Program of China under Grant Nos 2015CB921300 and 2012CB933000, the State of Texas through TcSUH, and the Strategic Priority Research Program B of Chinese Academy of Sciences under Grant Nos XDB07030000, XDB04040300 and Y4VX092X81.

In CaFe2As2, superconductivity can be achieved by applying a modest c-axis pressure of several kbar. Here we use scanning tunneling microscopy/spectroscopy (STM/S) to explore the STM tip pressure effect on single crystals of CaFe2As2. When performing STM/S measurements, the tip-sample interaction can be controlled to act repulsive with reduction of the junction resistance, thus to apply a tip pressure on the sample. We find that an incoherent energy gap emerges at the Fermi level in the differential conductance spectrum when the tip pressure is increased. This energy gap is of the similar order of magnitude as the superconducting gap in the chemical doped compound Ca0.4Na0.6Fe2As2 and disappears at the temperature well below that of the bulk magnetic ordering. Moreover, we also observe the rhombic distortion of the As lattice, which agrees with the orthorhombic distortion of the underlying Fe lattice. These findings suggest that the STM tip pressure can induce the local Cooper pairing in the orthorhombic phase of CaFe2As2.

Nonequilibrium Second-Order Phase Transition in a Cooper-Pair Insulator.

In certain disordered superconductors, upon increasing the magnetic field, superconductivity terminates with a direct transition into an insulating phase. This phase is comprised of localized Cooper pairs and is termed a Cooper-pair insulator. The current-voltage characteristics measured in this insulating phase are highly nonlinear and, at low temperatures, exhibit abrupt current jumps. Increasing the temperature diminishes the jumps until the current-voltage characteristics become continuous. We show that a direct correspondence exists between our system and systems that undergo an equilibrium, second-order, phase transition. We illustrate this correspondence by comparing our results to the van der Waals equation of state for the liquid-gas mixture. We use the similarities to identify a critical point where an out of equilibrium second-order-like phase transition occurs in our system. Approaching the critical point, we find a power-law behavior with critical exponents that characterizes the transition.

Disorder driven superconductor-insulator transition in inhomogenous d-wave superconductor

We study the effect of disorder on the superconductor-insulator transition in an inhomogeneous d -wave superconductor using the kernel polynomial method. As the Bogoliubov-de Gennes equations of the two-dimensional square lattice are solved self-consistently for the cases with more than 100000 unit cells, it is possible to observe the spatial fluctuations of the superconducting order parameters at the nanoscale. We find that strong spatial fluctuation of the superconducting order parameters can be introduced by disorder, and some superconducting specific order parameters are even enhanced. Moreover, we find that some isolated superconducting “islands” can survive the strong disorder, giving a boson insulator with some localized Cooper pairs. Our numerical calculations predict the existence of two sequential transitions with the increasing disorder strength: a d -wave to s -wave superconductor transition, and then an s -wave superconductor to insulator transition. The possibility of the appearance of a metallic phase between the superconducting and insulating phases is excluded by performing the lattice-size scaling of the generalized inverse participation ratio. In addition, we also discuss the effect of disorder on the optical conductivity of the d -wave superconductors.

Multiband theory of superconductivity at theLaAlO3/SrTiO3interface

We present a multi-band model for superconductivity at the metallic interface between insulating oxides LaAlO$_3$ and SrTiO$_3$ (001). Using a self-consistent Bogoliubov-de Gennes theory, formulated with the realistic bands at the interface, we investigate the spin-singlet and spin-triplet pairings in intra-band and inter-band channels. We find that the Rashba and atomic spin-orbit interactions at the interface induce singlet pairing in the inter-band channel and triplet pairing in both the intra-band and inter-band channels when the pairing amplitude in the singlet intra-band channel is finite. The gate-voltage variation of superconductivity is resolved in different pairing channels, compared with experimental results and found to match quite well. Interestingly, an enhancement of the superconducting transition temperature by external in-plane magnetic field is found revealing the existence of a hidden superconducting state above the observed one. As the interface is known to possess high level of inhomogeneity, we explore the role of non-magnetic disorder incorporating thermal phase fluctuations by using a Monte-Carlo method. We show that even after the transition to the non-superconducting phase, driven by temperature or magnetic field, the interface possesses localized Cooper pairs whose signature was observed in previous experiments.

Signature of Cooper pairs in the non-superconducting phases of amorphous superconducting tantalum films

We have studied the magnetic field or disorder induced insulating and metallic phases in amorphous Ta superconducting thin films. The evolution of the nonlinear transport in the insulating phase exhibits a non-monotonic behavior as the magnetic field is increased. We suggest that this observation could be evidence of the presence of localized Cooper pairs in the insulating phase. As the metallic phase intervenes the superconducting and insulating states in Ta films, this result further reveals that Cooper pairs also exist in the metallic ground state.

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.

Global and Local Superconductivity in Boron‐Doped Granular Diamond

Strong granularity-correlated and intragrain modulations of the superconducting order parameter are demonstrated in heavily boron-doped diamond situated not yet in the vicinity of the metal-insulator transition. These modulations at the superconducting state (SC) and at the global normal state (NS) above the resistive superconducting transition, reveal that local Cooper pairing sets in prior to the global phase coherence.

Phase diagram of the strongly disordereds-wave superconductor NbN close to the metal-insulator transition

We present a phase diagram as a function of disorder in three-dimensional NbN thin films, as the system enters the critical disorder for the destruction of the superconducting state. The superconducting state is investigated using a combination of magnetotransport and tunneling spectroscopy measurements. Our studies reveal 3 different disorder regimes. At low disorder the (k_{F}l~10-4), the system follows the mean field Bardeen-Cooper-Schrieffer behavior where the superconducting energy gap vanishes at the temperature where electrical resistance appears. For stronger disorder (k_{F}l<4) a "pseudogap" state emerges where a gap in the electronic spectrum persists up to temperatures much higher than Tc, suggesting that Cooper pairs continue to exist in the system even after the zero resistance state is destroyed. Finally, very strongly disordered samples (k_{F}l<1) exhibit a pronounced magnetoresistance peak at low temperatures, suggesting that localized Cooper pairs continue to survive in the system even after the global superconducting ground state is completely destroyed.

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.

Level statistics of disordered spin-1/2 systems and materials with localized Cooper pairs

The origin of continuous energy spectra in large disordered interacting quantum systems is one of the key unsolved problems in quantum physics. Although small quantum systems with discrete energy levels are noiseless and stay coherent forever in the absence of any coupling to external world, most large-scale quantum systems are able to produce a thermal bath and excitation decay. This intrinsic decoherence is manifested by a broadening of energy levels, which aquire a finite width. The important question is: what is the driving force and the mechanism of transition(s) between these two types of many-body systems - with and without intrinsic decoherence? Here we address this question via the numerical study of energy-level statistics of a system of interacting spin-1/2 with random transverse fields. We present the first evidence for a well-defined quantum phase transition between domains of discrete and continous many-body spectra in such spin models, implying the appearance of novel insulating phases in the vicinity of the superconductor-insulator transition in InO(x) and similar materials.

Localization of preformed Cooper pairs in disordered superconductors

The most profound effect of disorder on electronic systems is the localization of the electrons transforming an otherwise metallic system into an insulator. If the metal is also a superconductor then, at low temperatures, disorder can induce a dramatic transition from a superconducting into an insulating state. An outstanding question is whether the route to insulating behavior proceeds via the direct localization of Cooper pairs or, alternatively, by a two-step process in which the Cooper pairing is first destroyed followed by the standard localization of single electrons. Here we address this question by studying the local superconducting gap of a highly disordered, amorphous, superconductor by means of scanning tunneling spectroscopy. Our measurements reveal that, in the vicinity of the superconductor-insulator transition, the coherence peaks in the one-particle density of states disappear while the superconducting gap remains intact indicating the presence of localized Cooper pairs. Our results provide the first direct evidence that the transition in our system is driven by Cooper pair localization.

Localized Superconductivity in the Quantum-Critical Region of the Disorder-Driven Superconductor-Insulator Transition in TiN Thin Films

We investigate low-temperature transport properties of thin TiN superconducting films in the vicinity of the disorder-driven superconductor-insulator transition. In a zero magnetic field, we find an extremely sharp separation between superconducting and insulating phases, evidencing a direct superconductor-insulator transition without an intermediate metallic phase. At moderate temperatures, in the insulating films we reveal thermally activated conductivity with the magnetic field-dependent activation energy. At very low temperatures, we observe a zero-conductivity state, which is destroyed at some depinning threshold voltage V{T}. These findings indicate the formation of a distinct collective state of the localized Cooper pairs in the critical region at both sides of the transition.

Survival of superconducting correlations across the two-dimensional superconductor-insulator transition: A finite-frequency study

The complex ac conductivity of thin highly disordered InOx films was studied as a function of magnetic field through the nominal two-dimensional superconductor-insulator transition. We have resolved a significant finite-frequency superfluid stiffness well into the insulating regime, giving direct evidence for quantum superconducting fluctuations around an insulating ground state and a state of matter with localized Cooper pairs. A phase diagram is established that includes the superconducting state, a transition to a "Bose" insulator, and an eventual crossover to a "Fermi" insulating state at high fields. We speculate on the consequences of these observations, their impact on our understanding of the insulating state, and its relevance as a prototype for other insulating states of matter that derive from superconductors.

Dissipation and quantum phase transitions of a pair of Josephson junctions

A model system consisting of a mesoscopic superconducting grain coupled by Josephson junctions to two macroscopic superconducting electrodes is studied. We focus on the effects of Ohmic dissipation caused by resistive shunts and superconducting-normal charge relaxation within the grain. As the temperature is lowered, the behavior crosses over from uncoupled Josephson junctions, similar to situations analyzed previously, to strongly interacting junctions. The crossover temperature is related to the energy-level spacing of the grain and is of the order of the inverse escape time from the grain. In the limit of zero temperature, the two-junction system exhibits five distinct quantum phases, including a novel superconducting state with localized Cooper pairs on the grain but phase coherence between the leads due to Cooper pair cotunneling processes. In contrast to a single junction, the transition from the fully superconducting to fully normal phases is found to be controlled by an intermediate-coupling fixed point whose critical exponents vary continuously as the resistances are changed. The model is analyzed via two-component sine-Gordon models and related Coulomb gases that provide effective low-temperature descriptions in both the weak and strong Josephson coupling limits. The complicated phase diagram is consistent with symmetries of the two component sine-Gordon models, which include weak- to strong-coupling duality and permutation triality. Experimental consequences of the results and potential implications for superconductor to normal transitions in thin wires and films are discussed briefly.

Vortex states at T=0 in disordered thin and thick films of a-Mo xSi 1− x

We measure the transport properties of highly disordered thin and thick films of amorphous (a-)Mo x Si 1− x at low temperatures T. For thin films we have observed an anomalous peak in the magnetoresistance in fields B higher than the critical field B C of the field-driven superconductor–insulator transition (SIT). This suggests the presence of localized Cooper pairs on the insulating side of the SIT. We present data supporting the view that this insulating regime may correspond to the quantum-vortex-liquid (QVL) phase. The metallic QVL phase in B< B C is not evident, most likely absent. On the other hand, for thick films the existence of the vortex-glass transition and the metallic QVL phase at T=0 has been demonstrated. Based on these data, we construct the T=0 phase diagram of disordered two-dimensional and three-dimensional superconductors.