Sensitivity of the superconducting state in thin films

Broadened quantum critical ground state in a disordered superconducting thin film

A superconductor-insulator transition (SIT) in two dimensions is a prototypical quantum phase transition (QPT) with a clear quantum critical point (QCP) at zero temperature (T = 0). The SIT is induced by a field B and observed in disordered thin films. In some of weakly disordered or crystalline thin films, however, an anomalous metallic (AM) ground state emerges over a wide B range between the superconducting and insulating phases. It remains a fundamental open question how the QPT picture of the SIT is modified when the AM state appears. Here we present measurements of the Nernst effect N, which has great sensitivity to the fluctuations of the superconducting order parameter. From a thorough contour map of N in the B-T plane, we found a thermal-to-quantum crossover line of the superconducting fluctuations, a so-called ghost-temperature line associated with the QPT, as well as a ghost-field line associated with a thermal transition. The QCP is identified as a T = 0 intercept of the ghost-temperature line inside the AM state, which verifies that the AM state is a broadened critical state of the SIT.

Quantum phase transitions in two-dimensional superconductors: a review on recent experimental progress

Superconductor-insulator/metal transition (SMT) as a paradigm of quantum phase transition has been a research highlight over the last three decades. Benefit from recent developments in the fabrication and measurements of two-dimensional (2D) superconducting films and nanodevices, unprecedented quantum phenomena have been revealed in the quantum phase transitions of 2D superconductors. In this review, we introduce the recent progress on quantum phase transitions in 2D superconductors, focusing on the quantum Griffiths singularity (QGS) and anomalous metal state. Characterized by a divergent critical exponent when approaching zero temperature, QGS of SMT is discovered in ultrathin crystalline Ga films and subsequently detected in various 2D superconductors. The universality of QGS indicates the profound influence of quenched disorder on quantum phase transitions. Besides, in a 2D superconducting system, whether a metallic ground state can exist is a long-sought mystery. Early experimental studies indicate an intermediate metallic state in the quantum phase transition of 2D superconductors. Recently, in high-temperature superconducting films with patterned nanopores, a robust anomalous metal state (i.e. quantum metal or Bose metal) has been detected, featured as the saturated resistance in the low temperature regime. Moreover, the charge-2equantum oscillations are observed in nanopatterned films, indicating the bosonic nature of the anomalous metal state and ending the debate on whether bosons can exist as a metal. The evidences of the anomalous metal states have also been reported in crystalline epitaxial thin films and exfoliated nanoflakes, as well as granular composite films. High quality filters are used in these works to exclude the influence of external high frequency noises in ultralow temperature measurements. The observations of QGS and metallic ground states in 2D superconductors not only reveal the prominent role of quantum fluctuations and dissipations but also provide new perspective to explore quantum phase transitions in superconducting systems.

Study of Elastic and Structural Properties of BaFe2As2 Ultrathin Film Using Picosecond Ultrasonics

We obtain the through-thickness elastic stiffness coefficient (C33) in nominal 9 nm and 60 nm BaFe2As2 (Ba-122) thin films by using picosecond ultrasonics. Particularly, we reveal the increase in elastic stiffness as film thickness decreases from bulk value down to 9 nm, which we attribute to the increase in intrinsic strain near the film-substrate interface. Our density functional theory (DFT) calculations reproduce the observed acoustic oscillation frequencies well. In addition, temperature dependence of longitudinal acoustic (LA) phonon mode frequency for 9 nm Ba-122 thin film is reported. The frequency change is attributed to the change in Ba-122 orthorhombicity (a-b)/(a+b). This conclusion can be corroborated by our previous ultrafast ellipticity measurements in 9 nm Ba-122 thin film, which exhibit strong temperature dependence and indicate the structural phase transition temperature Ts.

Sharpness of the Berezinskii-Kosterlitz-Thouless Transition in Disordered NbN Films

We present a comprehensive investigation of the Berezinskii-Kosterlitz-Thouless transition in ultrathin strongly disordered NbN films. Measurements of resistance, current-voltage characteristics, and kinetic inductance on the very same device reveal a consistent picture of a sharp unbinding transition of vortex-antivortex pairs that fit standard renormalization group theory without extra assumptions in terms of inhomogeneity. Our experiments demonstrate that the previously observed broadening of the transition is not an intrinsic feature of strongly disordered superconductors and provide a clean starting point for the study of dynamical effects at the Berezinskii-Kosterlitz-Thouless transition.

Tunneling Spectroscopy of Two-Dimensional Materials Based on Via Contacts

We introduce a novel planar tunneling architecture for van der Waals heterostructures based on via contacts, namely, metallic contacts embedded into through-holes in hexagonal boron nitride (hBN). We use the via-based tunneling method to study the single-particle density of states of two different two-dimensional (2D) materials, NbSe₂ and graphene. In NbSe₂ devices, we characterize the barrier strength and interface disorder for barrier thicknesses of 0, 1, and 2 layers of hBN and study the dependence on the tunnel-contact area down to (44 ± 14)² nm². For 0-layer hBN devices, we demonstrate a crossover from diffusive to point contacts in the small-contact-area limit. In graphene, we show that reducing the tunnel barrier thickness and area can suppress effects due to phonon-assisted tunneling and defects in the hBN barrier. This via-based architecture overcomes limitations of other planar tunneling designs and produces high-quality, ultraclean tunneling structures from a variety of 2D materials.

Multivalley Superconductivity in Monolayer Transition Metal Dichalcogenides

In transition metal dichalcogenides (TMDs), Ising superconductivity with an antisymmetric spin texture on the Fermi surface has attracted wide interest due to the exotic pairing and topological properties. However, it is not clear whether the Q valley with a giant spin splitting is involved in the superconductivity of heavily doped semiconducting 2H-TMDs. Here by taking advantage of a high-quality monolayer WS₂ on hexagonal boron nitride flakes, we report an ionic-gating induced superconducting dome with a record high critical temperature of ∼6 K, accompanied by an emergent nonlinear Hall effect. The nonlinearity indicates the development of an additional high-mobility channel, which (corroborated by first principle calculations) can be ascribed to the population of Q valleys. Thus, multivalley population at K and Q is suggested to be a prerequisite for developing superconductivity. The involvement of Q valleys also provides insights to the spin textured Fermi surface of Ising superconductivity in the large family of transition metal dichalcogenides.

Anomalous metals: From "failed superconductor" to "failed insulator"

Resistivity saturation is found on both superconducting and insulating sides of an "avoided" magnetic-field-tuned superconductor-to-insulator transition (H-SIT) in a two-dimensional In/InOx composite, where the anomalous metallic behavior cuts off conductivity or resistivity divergence in the zero-temperature limit. The granular morphology of the material implies a system of Josephson junctions (JJs) with a broad distribution of Josephson coupling EJ and charging energy EC, with an H-SIT determined by the competition between EJ and EC. By virtue of self-duality across the true H-SIT, we invoke macroscopic quantum tunneling effects to explain the temperature-independent resistance where the "failed superconductor" side is a consequence of phase fluctuations and the "failed insulator" side results from charge fluctuations. While true self-duality is lost in the avoided transition, its vestiges are argued to persist, owing to the incipient duality of the percolative nature of the dissipative path in the underlying random JJ system.

Phase fluctuations in conventional superconductors

Within the Bardeen-Cooper-Schrieffer (BCS) theory, superconductivity is entirely governed by the pairing energy scale, which gives rise to the superconducting energy gap, Δ. However, another important energy scale, the superfluid phase stiffness,J, which determines the resilience of the superconductor to phase-fluctuations is normally ignored. The spectacular success of BCS theory owes to the fact that in conventional superconductorsJis normally several orders of magnitude larger than Δ and thus an irrelevant energy scale. However, in certain situations such as in the presence of low carrier density, strong disorder, at low-dimensions or in granular superconductors,Jcan drastically come down and even become smaller than Δ. In such situations, the temperature and magnetic field evolution of superconducting properties is governed by phase fluctuations, which gives rise to novel electronic states where signatures of electronic pairing continue to exist even when the zero resistance state is destroyed. In this article, we will review the recent experimental developments on the study of phase fluctuations in conventional superconductors.

Extrinsic and Intrinsic Anomalous Metallic States in Transition Metal Dichalcogenide Ising Superconductors

The metallic ground state in two-dimensional (2D) superconductors has attracted much attention but is still under intense scrutiny. Especially, the measurements in the ultralow temperature region are challenging for 2D superconductors due to the sensitivity to external perturbations. In this work, the resistance saturation induced by external noise, named as the "extrinsic anomalous metallic state", is observed in 2D transition metal dichalcogenide (TMD) superconductor 4Ha-TaSe₂ nanodevices. However, with further decreasing temperature, credible evidence of the intrinsic anomalous metallic state is obtained by adequately filtering external radiation. Our work indicates that, at ultralow temperatures, the anomalous metallic state can be experimentally revealed as the quantum ground state in 2D crystalline TMD superconductors. Besides, Ising superconductivity revealed by ultrahigh in-plane critical field (B_c2∥) going beyond the Pauli paramagnetic limit (B_p) is detected in 4Ha-TaSe₂, from the one-unit-cell device to the bulk situation, which might be due to the weak coupling between the TaSe₂ submonolayers.

Coexistence of resistance oscillations and the anomalous metal phase in a lithium intercalated TiSe2 superconductor

Superconductivity and charge density wave (CDW) appear in the phase diagram of a variety of materials including the high-T_c cuprate family and many transition metal dichalcogenides (TMDs). Their interplay may give rise to exotic quantum phenomena. Here, we show that superconducting arrays can spontaneously form in TiSe₂–a TMD with coexisting superconductivity and CDW—after lithium ion intercalation. We induce a superconducting dome in the phase diagram of Li_xTiSe₂ by using the ionic solid-state gating technique. Around optimal doping, we observe magnetoresistance oscillations, indicating the emergence of periodically arranged domains. In the same temperature, magnetic field and carrier density regime where the resistance oscillations occur, we observe signatures for the anomalous metal—a state with a resistance plateau across a wide temperature range below the superconducting transition. Our study not only sheds further insight into the mechanism for the periodic electronic structure, but also reveals the interplay between the anomalous metal and superconducting fluctuations.

The interplay between superconductivity and charge density wave (CDW) gives rise to exotic quantum phenomena. Here, the authors observe magnetoresistance oscillations and an anomalous metal state due to the coexistence of superconductivity and CDW in lithium intercalated TiSe₂.

Electric field control of superconductivity at the LaAlO3/KTaO3(111) interface

The oxide interface between LaAlO₃ and KTaO₃(111) can harbor a superconducting state. We report that by applying a gate voltage (V _G) across KTaO₃, the interface can be continuously tuned from superconducting into insulating states, yielding a dome-shaped T _c-V _G dependence, where T _c is the transition temperature. The electric gating has only a minor effect on carrier density but a strong one on mobility. We interpret the tuning of mobility in terms of change in the spatial profile of the carriers in the interface and hence, effective disorder. As the temperature is decreased, the resistance saturates at the lowest temperature on both superconducting and insulating sides, suggesting the emergence of a quantum metallic state associated with a failed superconductor and/or fragile insulator.

Recent Advances in 2D Superconductors

The emergence of superconductivity in 2D materials has attracted much attention and there has been rapid development in recent years because of their fruitful physical properties, such as high transition temperature (T_c ), continuous phase transition, and enhanced parallel critical magnetic field (B_c ). Tremendous efforts have been devoted to exploring different physical parameters to figure out the mechanisms behind the unexpected superconductivity phenomena, including adjusting the thickness of samples, fabricating various heterostructures, tuning the carrier density by electric field and chemical doping, and so on. Here, different types of 2D superconductivity with their unique characteristics are introduced, including the conventional Bardeen-Cooper-Schrieffer superconductivity in ultrathin films, high-T_c superconductivity in Fe-based and Cu-based 2D superconductors, unconventional superconductivity in newly discovered twist-angle bilayer graphene, superconductivity with enhanced B_c , and topological superconductivity. A perspective toward this field is then proposed based on academic knowledge from the recently reported literature. The aim is to provide researchers with a clear and comprehensive understanding about the newly developed 2D superconductivity and promote the development of this field much further.

Tuning electron correlation in magic-angle twisted bilayer graphene using Coulomb screening

Controlling the strength of interactions is essential for studying quantum phenomena emerging in systems of correlated fermions. We introduce a device geometry whereby magic-angle twisted bilayer graphene is placed in close proximity to a Bernal bilayer graphene, separated by a 3-nanometer-thick barrier. By using charge screening from the Bernal bilayer, the strength of electron-electron Coulomb interaction within the twisted bilayer can be continuously tuned. Transport measurements show that tuning Coulomb screening has opposite effects on the insulating and superconducting states: As Coulomb interaction is weakened by screening, the insulating states become less robust, whereas the stability of superconductivity at the optimal doping is enhanced. The results provide important constraints on theoretical models for understanding the mechanism of superconductivity in magic-angle twisted bilayer graphene.

Nonmonotonic Temperature-Dependent Dissipation at Nonequilibrium in Atomically Thin Clean-Limit Superconductors

Resistance in superconductors arises from the motion of vortices driven by flowing supercurrents or external electromagnetic fields and may be strongly affected by thermal or quantum fluctuations. The common expectation is that as the temperature is lowered, vortex motion is suppressed, leading to a decreased resistance. We show experimentally that in clean-limit atomically thin 2H-NbSe₂ the resistance below the superconducting transition temperature may be nonmonotonic, passing through a minimum before increasing again as the temperature is decreased further. The effect is most pronounced in monolayer devices and cannot be understood in terms of known mechanisms. We propose a qualitative two-fluid vortex model in which thermal fluctuations of pinned vortices control the mobility of the free vortices. The findings provide a new perspective on fundamental questions of vortex mobility and dissipation in superconductors.

Quantum Criticality inside the Anomalous Metallic State of a Disordered Superconducting Thin Film

The field-induced superconductor-insulator transition (SIT) in two-dimensional (2D) systems is a famous example of a quantum phase transition. However, an emergence of an anomalous metallic state induced by field has been a long-standing problem in 2D superconductors. While theories predicted that the emergence is attributed to strong phase fluctuations of the superconducting order parameter due to quantum fluctuations, usual resistance measurements have not probed them directly. Here, using Nernst effect measurements, we uncover superconducting fluctuations in the vicinity of the field-induced metallic state in an amorphous Mo_{x}Ge_{1-x} thin film. The field range where the vortex Nernst signals are detectable remains nonzero toward zero temperature, and it locates inside the metallic state defined by the magnetoresistance, indicating that the metallic state results from quantum vortex liquid (QVL) with phase fluctuations due to quantum fluctuations. Slow decay of transport entropy of vortices in the QVL with decreasing temperature suggests that the metallic state originates from broadening of a quantum critical point in SIT.

Conductivity Extraction Using a 180 GHz Quasi-Optical Resonator for Conductive Thin Film Deposited on Conductive Substrate

Measurement of electrical conductivity of conductive thin film deposited on a conductive substrate is important and challenging. An effective conductivity model was constructed for a bilayer structure to extract thin film conductivity from the measured Q-factor of a quasi-optical resonator. As a demonstration, aluminium films with thickness of 100 nm were evaporated on four silicon wafers whose conductivity ranges from ~10¹ to ~10⁵ S/m (thus, the proposed method can be verified for a substrate with a wide range of conductivity). Measurement results at ~180 GHz show that average conductivities are 1.66 × 10⁷ S/m (which agrees well with direct current measurements) with 6% standard deviation. The proposed method provides a contactless conductivity evaluation method for conductive thin film deposited on conductive substrate which cannot be achieved by the existing microwave resonant method.

Nonreciprocal superconducting NbSe2 antenna

The rise of two-dimensional (2D) crystalline superconductors has opened a new frontier of investigating unconventional quantum phenomena in low dimensions. However, despite the enormous advances achieved towards understanding the underlying physics, practical device applications like sensors and detectors using 2D superconductors are still lacking. Here, we demonstrate nonreciprocal antenna devices based on atomically thin NbSe₂. Reversible nonreciprocal charge transport is unveiled in 2D NbSe₂ through multi-reversal antisymmetric second harmonic magnetoresistance isotherms. Based on this nonreciprocity, our NbSe₂ antenna devices exhibit a reversible nonreciprocal sensitivity to externally alternating current (AC) electromagnetic waves, which is attributed to the vortex flow in asymmetric pinning potentials driven by the AC driving force. More importantly, a successful control of the nonreciprocal sensitivity of the antenna devices has been achieved by applying electromagnetic waves with different frequencies and amplitudes. The device’s response increases with increasing electromagnetic wave amplitude and exhibits prominent broadband sensing from 5 to 900 MHz.

Here, the authors observe reversible nonreciprocal charge transport in two-dimensional NbSe₂, and demonstrate antenna devices exhibiting strong sensitivity to driving AC electromagnetic waves in the superconducting regime.

Upper critical field and superconductor-metal transition in ultrathin niobium films

Recent studies suggest that in disordered ultrathin films superconducting (SC) state may be intrinsically inhomogeneous. Here we investigate the nature of SC state in ultrathin Nb films, of thickness d ranging from 1.2 to 20 nm, which undergo a transition from amorphous to polycrystalline structure at the thickness [Formula: see text] nm. We show that the properties of SC state are very different in polycrystalline and amorphous films. The upper critical field ([Formula: see text]) is orbitally limited in the first case, and paramagnetically limited in the latter. The magnetic field induced superconductor-metal transition is observed, with the critical field approximately constant or decreasing as a power-law with the film conductance in polycrystalline or amorphous films, respectively. The scaling analysis indicates distinct scaling exponents in these two types of films. Negative contribution of the SC fluctuations to conductivity exists above [Formula: see text], particularly pronounced in amorphous films, signaling the presence of fluctuating Cooper pairs. These observations suggest the development of local inhomogeneities in the amorphous films, in the form of proximity-coupled SC islands. An usual evolution of SC correlations on cooling is observed in amorphous films, likely related to the effect of quantum fluctuations on the proximity-induced phase coherence.

Disorder-Induced Quantum Griffiths Singularity Revealed in an Artificial 2D Superconducting System

Disorder-induced Griffiths singularity of quantum phase transition (QPT) is a crucial issue in 2D superconductors (2DSC). In a superconducting system, the strength of disorder is found to be associated with the vortex pinning energy, which is closely related to the quantum Griffiths singularity; however, a direct study to elucidate the role of vortex pinning energy on the quantum Griffiths singularity in 2DSC remains to be undertaken. Here, an artificial 2DSC system is designed by randomly depositing superconducting nanoislands on 2Delectron gas (2DEG). Quantum Griffiths singularity is present in a graphene/Pb-islands-array hybrid, where the superconducting behavior transits to weakly localized metallic behavior induced by the vertical magnetic field and exhibits critical behavior with a diverging dynamical critical exponent approaching zero temperature. Compared to the study of graphene/Sn-islands-array hybrid where the sharp QPT is observed, the vortex pinning energy acquired from the Arrhenius plot analysis is greater in graphene/Pb-islands-array hybrid, which may contribute to the presence of the quantum Griffiths singularity. This work may provide a comprehensive interpretation of the QPT in 2DSC.

AC measurement of the Nernst effect of thin films at low temperatures

We describe an alternating current method to measure the Nernst effect in superconducting thin films at low temperatures. The Nernst effect is an important tool in the understanding of superconducting fluctuations and, in particular, vortex motion near critical points. However, in most materials, the Nernst signal in a typical experimental setup rarely exceeds a few μV, in some cases being as low as a few nV. DC measurements of such small signals require extensive signal processing and protection against stray pickups and offsets, limiting the sensitivity of such measurements to >1 nV. Here, we describe a method utilizing a one-heater-two-thermometer setup with the heating element and thermometers fabricated on-chip with the sample, which helped to reduce the thermal load and temperature lag between the substrate and the thermometer. Using AC heating power and 2ω measurement, we are able to achieve sub-nanovolt sensitivity in 20 nm-30 nm thin superconducting films on a glass substrate, compared to a sensitivity of ∼10 nV using DC techniques on the same setup.

Type-II Ising Superconductivity and Anomalous Metallic State in Macro-Size Ambient-Stable Ultrathin Crystalline Films

Recent emergence of two-dimensional (2D) crystalline superconductors has provided a promising platform to investigate novel quantum physics and potential applications. To reveal essential quantum phenomena therein, ultralow temperature transport investigation on high-quality ultrathin superconducting films is critically required, although it has been quite challenging experimentally. Here, we report a systematic transport study on the ultrathin crystalline PdTe₂ films grown by molecular beam epitaxy (MBE). Interestingly, a new type of Ising superconductivity in 2D centrosymmetric materials is revealed by the detection of large in-plane critical field more than 7 times the Pauli limit. Remarkably, in a perpendicular magnetic field, we provide solid evidence of an anomalous metallic state characterized by the resistance saturation at low temperatures with high-quality filters. The robust superconductivity with intriguing quantum phenomena in the macro-size ambient-stable ultrathin PdTe₂ films remains almost the same for 20 months, showing great potentials in electronic and spintronic applications.

Type-II Ising pairing in few-layer stanene

Spin-orbit coupling has proven indispensable in the realization of topological materials and, more recently, Ising pairing in two-dimensional superconductors. This pairing mechanism relies on inversion symmetry–breaking and sustains anomalously large in-plane polarizing magnetic fields whose upper limit is predicted to diverge at low temperatures. Here, we show that the recently discovered superconductor few-layer stanene, epitaxially strained gray tin (α-Sn), exhibits a distinct type of Ising pairing between carriers residing in bands with different orbital indices near the Γ-point. The bands are split as a result of spin-orbit locking without the participation of inversion symmetry–breaking. The in-plane upper critical field is strongly enhanced at ultralow temperature and reveals the predicted upturn.

Superconducting phase transitions in disordered NbTiN films

Suppression of superconductivity in disordered systems is a fundamental problem of condensed matter physics. Here we investigate superconducting niobium-titanium-nitride (Nb_1-xTi_xN) thin films grown by the atomic layer deposition (ALD) with slightly different growth process parameters. We observe a smooth crossover from the disorder-driven superconductor-normal metal transition (SMT) to the superconductor-insulator transition (SIT) via the intermediate Bose metal state detected by the low-temperature saturation of the temperature dependence of the sheet resistance. We demonstrate that the SIT via the intervening Bose metal state occurs if the sheet resistance of the film in the maximum, R_max prior to the superconducting drop of R(T), exceeds R_q = h/4e².

Intermediate bosonic metallic state in the superconductor-insulator transition

Whether a metallic ground state exists in a two-dimensional system beyond Anderson localization remains an unresolved question. We studied how quantum phase coherence evolves across superconductor–metal–insulator transitions through magnetoconductance quantum oscillations in nanopatterned high-temperature superconducting films. We tuned the degree of phase coherence by varying the etching time of our films. Between the superconducting and insulating regimes, we detected a robust intervening anomalous metallic state characterized by saturating resistance and oscillation amplitude at low temperatures. Our measurements suggest that the anomalous metallic state is bosonic and that the saturation of phase coherence plays a prominent role in its formation.

Anomalous Quantum Metal in a 2D Crystalline Superconductor with Electronic Phase Nonuniformity

The details of the superconducting to quantum metal transition (SQMT) at T = 0 are an open problem that invokes great interest in the nature of this exotic and unexpected ground state (Ephron et al., 1996; Mason and Kapitulnik, 1999; Chervenak and Valles, 2000). However, the SQMT was not yet investigated in a crystalline 2D superconductor with coexisting and fluctuating quantum orders. Here, we report the observation of a SQMT in 2D ion-gel-gated 1T-TiSe₂ (Li et al., 2016) driven by a magnetic field. A field-induced crossover between Bose quantum metal and vortex quantum creeping with an increasing field is observed. We discuss the interplay between superconducting and CDW fluctuations (discommensurations) and their relation to the anomalous quantum metal (AQM) phase. From our findings, gate-tunable 1T-TiSe₂ emerges as a privileged platform to scrutinize, in a controlled way, the details of the SQMT, the role of coexisting fluctuating orders and, ultimately, to obtain a deeper understanding of the fate of superconductivity in strictly two-dimensional crystals near zero temperature.