Inhomogeneous Superconducting State Research Articles

Enhanced weak superconductivity in trigonal γ-PtBi2

Electrical resistivity experiments show superconductivity at Tc=1.1 K in a high-quality single crystal of trigonal γ-PtBi2, with an enhanced critical magnetic field μ0Hc2(0)≳1.5 Tesla and a low critical current-density Jc(0)≈40 A cm−2 at H = 0. Both Tc and Hc2(0) are the highest reported values for stoichiometric bulk samples at ambient pressure. We found a weak Hc2 anisotropy with Γ=Hc2ab/Hc2c<1 , which is unusual among superconductors. Under a magnetic field, the superconducting transition becomes broader and asymmetric. Along with the low critical currents, this observation suggests an inhomogeneous superconducting state. In fact, no trace of superconductivity is observed through field-cooling–zero-field-cooling magnetization experiments.

Strong increase in ultrasound attenuation below Tc in Sr2RuO4 : Possible evidence for domains

Recent experiments suggest that the superconducting order parameter of Sr$_2$RuO$_4$ has two components. A two-component order parameter has multiple degrees of freedom in the superconducting state that can result in low-energy collective modes or the formation of domain walls -- a possibility that would explain a number of experimental observations including the smallness of the time reversal symmetry breaking signal at T$_\mathrm{c}$ and telegraph noise in critical current experiments. We perform ultrasound attenuation measurements across the superconducting transition of Sr$_2$RuO$_4$ using resonant ultrasound spectroscopy (RUS). We find that the attenuation for compressional sound increases by a factor of seven immediately below T$_\mathrm{c}$, in sharp contrast with what is found in both conventional ($s$-wave) and high-T$_\mathrm{c}$ ($d$-wave) superconductors. We find our observations to be most consistent with the presence of domain walls between different configurations of the superconducting state. The fact that we observe an increase in sound attenuation for compressional strains, and not for shear strains, suggests an inhomogeneous superconducting state formed of two distinct, accidentally-degenerate superconducting order parameters that are not related to each other by symmetry. Whatever the mechanism, a factor of seven increase in sound attenuation is a singular characteristic with which any potential theory of the superconductivity in Sr$_2$RuO$_4$ must be reconciled.

Nematic superconductivity in magic-angle twisted bilayer graphene from atomistic modeling

Twisted bilayer graphene (TBG) develops large moiré patterns at small twist angles with flat energy bands hosting domes of superconductivity. The large system size and intricate band structure have however hampered investigations into the superconducting state. Here, using full-scale atomistic modelling with local electronic interactions, we find at and above experimentally relevant temperatures a highly inhomogeneous superconducting state with nematic ordering on both atomic and moiré length scales. The nematic state has a locally anisotropic real-valued d-wave pairing, with a nematic vector winding throughout the moiré pattern, and is three-fold degenerate. Although d-wave symmetric, the superconducting state has a full energy gap, which we tie to a π-phase interlayer coupling. The superconducting nematicity is further directly detectable in the local density of states. Our results show that atomistic modeling is essential and also that very similar local interactions produce very different superconducting states in TBG and the high-temperature cuprate superconductors.

Current–voltage characteristics of strained, highly underdoped LaSr x CuO4 thin films

The temperature dependence of resistance and of current–voltage characteristics are studied for two underdoped La1.952Sr0.048CuO4 films with different thickness and different degrees of built-in compressive strain. Strain induces an inhomogeneous superconducting (SC) state in the films, with two-step SC transition, consistent with the presence of SC islands coupled by the proximity effect. On further cooling, superfluid density is suppressed and global phase coherence is never reached. Instead, a reentrant increase of resistance appears, reaching several orders of magnitude in the thinner, more strongly strained film, and saturating at lowest temperatures. The saturation is accompanied by Coulomb blockade, which resembles the blockade reported for Josephson junction (JJ) arrays. However, increasing magnetic field quickly diminishes the influence of Coulomb blockade on transport, which is distinct from the behavior observed for JJ arrays. The observation of Coulomb blockade indicates that Cooper pairs survive in the insulating state, suggesting the local character of pairing.

Superconducting interstitial MoReRuCx medium-entropy alloys with a hexagonal structure

We report the results of structural and physical studies on the MoReRuCx medium-entropy alloys (MEAs) with x varying from 0 to 0.20. In the whole x range, a single hexagonal phase is formed. The variation of lattice parameters indicates that carbon atoms are located at the interstitial site for x ≤ 0.10 while occupy both the interstitial and substitutional sites at higher x values, which is corroborated by the x-ray photonelectron spectroscopy (XPS) results. Moreover, the resistivity, magnetic and thermodynamic measurements evidence that these MEAs are bulk fully gapped superconductors. In particular, the transition temperature Tc displays a dome-like dependence on carbon content with a maximum of 9.62 K at x = 0.05, whereas a maximal zero-temperature upper critical field Bc2(0) of 10.5 T is achieved at x = 0.10. For all MEAs, the specific heat data reveal the existence of an inhomogeneous superconducting state, which is discussed in relation to the chemical inhomogeneity and strong atomic disorder. In addition, we show that the key factors that control superconductivity are essentially the same for both MoReRuCx and ReCx, despite their very different Tc values. Our work not only provides the first series of interstitial MEAs with a hexagonal structure, but also demonstrates a feasible way to tune the superconductivity in multicomponent alloys.

Inhomogeneous Superconducting State Probed by 125Te NMR on UTe2

UTe$_2$ is a recently discovered promising candidate for a spin-triplet superconductor. In contrast to conventional spin-singlet superconductivity, spin-triplet superconductivity possesses spin and angular momentum degrees of freedom. To detect these degrees of freedom and obtain the solid evidence of spin-triplet superconductivity in UTe$_2$, we performed $^{125}$Te-NMR measurement. We previously reported that the shoulder signal appears in NMR spectra below the superconducting (SC) transition temperature $T_{\rm c}$ in $H \parallel b$, and that a slight decrease in the Knight shift along the $b$ and $c$ axes ($K_b$ and $K_c$, respectively) below $T_{\rm c}$ at a low magnetic field $H$. To clarify the origin of the shoulder signal and the trace of the decrease in $K_b$, we compared the $^{125}$Te-NMR spectra obtained when $H~\parallel~b$ and $H~\parallel~c$ and measured the $^{125}$Te-NMR spectra for $H~\parallel~b$ up to 14.5~T. The intensity of the shoulder signal observed for $H~\parallel~b$ has a maximum at $\sim 6$~T and vanishes above 10~T, although the superconductivity is confirmed by the $\chi_{\rm AC}$ measurements, which can survive up to 14.5~T (maximum $H$ in the present measurement). Moreover, the decrease in $K_b$ in the SC state starts to be small around 7~T and almost zero at 12.5~T. This indicates that the SC spin state gradually changes with the application of $H$. Meanwhile, in $H~\parallel~c$, unexpected broadening without the shoulder signals was observed below $T_{\rm c}$ at 1~T, and this broadening was quickly suppressed with increasing $H$. We construct the $H$--$T$ phase diagram for $H~\parallel~b$ and $H~\parallel~c$ based on the NMR measurements and discuss possible SC states with the theoretical consideration. We suggest that the inhomogeneous SC state characterized by the broadening of the NMR spectrum originates from the spin degrees of freedom.

Above-gap differential conductance dips in superconducting point contacts

Point-contact Andreev spectroscopy is one of the most powerful techniques for obtaining quantitative energy and momentum-resolved information on the electronic properties of a superconductor. However, appropriate measurements often reveal unexpected conductance features that cannot be adequately modeled using conventional theory. In particular, these include conductance dips at voltage biases slightly exceeding the expected energy gap value for a superconductor. Guided by recent point-contact measurements of proximity-induced superconductivity in topological materials, we explain these features by inhomogeneous superconducting state in the studied material, conditionally divided into two parts with different gap values and a semitransparent potential barrier between them. To test this assumption, we designed a model experiment that mimics the main features of the model. The heterostructure under study is formed by an almost ideal point contact, formed using a new technology of self-textured nanofilaments based on the resistive-switching effect in a TiO2 film, a Pt counter-electrode, and a proximized Al/Ni0.5Cu0.5/NbN system, where superconducting correlations from the NbN superconductor are penetrating into a weak ferromagnetic Ni0.5Cu0.5 alloy in contact with an Al film. For a quantitative description of the conductance dips observed in all such devices and their evolution with temperature, we propose an extension of the conventional theory, the main element of which is a non-equilibrium-driven superconducting-to-normal transition and a crossover from coherent to sequential transmission in the Al/NiCu bilayer. Understanding the origin of the conductance dips imposes some restrictions on the explanation of induced superconductivity and paves the way for discovering novel superconducting materials with advanced properties.

The Effects of Chemical Doping on the Diamagnetic Thermodynamic Fluctuations of YBa2Cu2.97X0.03O7-δ (X = Au, Ni, Zn, and Mg) Single Crystals

In this article, we investigated the effects of chemical doping on the diamagnetic thermodynamic fluctuations (DTFs) of YBa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2.97</sub> X <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.03</sub> O <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{7-\delta}$ </tex-math></inline-formula> (X = Au, Ni, Zn, and Mg) single crystals. In-plane dc zero field cooled [ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M_{\mathrm {ZFC}}(T)$ </tex-math></inline-formula> ] and field cooled cooling [ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M_{\mathrm {FCC}}(T)$ </tex-math></inline-formula> ] magnetizations were measured with a superconducting quantum interference device (SQUID) magnetometer while magnetic fields ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H$ </tex-math></inline-formula> ) ranging from 0.01 up to 50 kOe were applied. The DTF contribution on the reversible <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M_{\mathrm {ZFC}}(T)$ </tex-math></inline-formula> magnetization was accounted by applying 3D-XY and 3-D lowest Landau level (3D-LLL) scaling functions. The results show that the DTF contribution on the reversible <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M_{\mathrm {ZFC}}(T)$ </tex-math></inline-formula> data of our samples is well described by the 3D-XY scaling function when <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H \le 1$ </tex-math></inline-formula> kOe (low-magnetic-field regime) is applied and by the 3D-LLL scaling function when <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H &gt; 10$ </tex-math></inline-formula> kOe (high-magnetic-field regime) is applied. The reversible <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M_{\mathrm {ZFC}}(T)$ </tex-math></inline-formula> data of the doped samples display in the low-magnetic-field regime a rounded of the DTF regime around <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{\mathrm {C}}$ </tex-math></inline-formula> and a temperature enlargement of the DTF regime range in the high-magnetic-field regime. We believe that these effects are connected to intensification of YBa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{7-\delta}$ </tex-math></inline-formula> inhomogeneous superconducting state caused by individual partial substitution of ≈1% of Cu for chemical dopants listed above.

Nonuniform superconductivity in wires with strong spin-orbit coupling

We study theoretically the onset of nonuniform superconductivity in a one-dimensional single wire in presence of Zeeman (or exchange field) and spin-orbit coupling. Using the Green's function formalism, we show that the spin-orbit coupling stabilizes modulated superconductivity in a broad range of temperatures and Zeeman fields. We investigate the anisotropy of the temperature-Zeeman field phase diagram, which is related to the orientation of the Zeeman field. In particular, the inhomogeneous superconducting state disappears if this latter field is aligned or perpendicular to the wire direction. We identify two regimes corresponding to weak and strong spin-orbit coupling respectively. The wave-vector of the modulated phase is evaluated in both regimes. The results also pertain for quasi-1D superconductors made of weakly coupled 1D chains.

Spatially inhomogeneous competition between superconductivity and the charge density wave in YBa2Cu3O6.67

The charge density wave in the high-temperature superconductor YBa2Cu3O7−x (YBCO) has two different ordering tendencies differentiated by their c-axis correlations. These correspond to ferro- (F-CDW) and antiferro- (AF-CDW) couplings between CDWs in neighbouring CuO2 bilayers. This discovery has prompted several fundamental questions: how does superconductivity adjust to two competing orders and are either of these orders responsible for the electronic reconstruction? Here we use x-ray diffraction to study YBa2Cu3O6.67 as a function of magnetic field and temperature. We show that regions with F-CDW correlations suppress superconductivity more strongly than those with AF-CDW correlations. This implies that an inhomogeneous superconducting state exists, in which some regions show a fragile form of superconductivity. By comparison of F-CDW and AF-CDW correlation lengths, it is concluded that F-CDW ordering is sufficiently long-range to modify the electronic structure. Our study thus suggests that F-CDW correlations impact both the superconducting and normal state properties of YBCO.

Enhancement of superconductivity by pressure-induced critical ferromagnetic fluctuations in UCoGe

A $^{59}$Co nuclear quadrupole resonance (NQR) was performed on a single-crystalline ferromagnetic (FM) superconductor UCoGe under pressure. The FM phase vanished at a critical pressure $P_c$, and the NQR spectrum just below $P_c$ showed phase separation of the FM and paramagnetic (PM) phases below Curie temperature $T_{\textrm{Curie}}$, suggesting first-order FM quantum phase transition (QPT). We found that the internal field was absent above $P_c$, but the superconductivity is almost unchanged. This result suggests the existence of the nonunitary to unitary transition of the superconductivity around $P_c$. Nuclear spin-lattice relaxation rate $1/T_1$ showed the FM critical fluctuations around $P_c$, which persist above $P_c$ and are clearly related to superconductivity in the PM phase. This FM QPT is understood to be a weak first order with critical fluctuations. $1/T_1$ sharply decreased in the superconducting (SC) state above $P_c$ with a single component, in contrast to the two-component $1/T_1$ in the FM SC state, indicating that the inhomogeneous SC state is a characteristic feature of the FM SC state in UCoGe.

The effect of low divalent chemical doping on the high field diamagnetic thermodynamic fluctuations of the YBa2Cu3O7-δ single crystals

Abstract We report on reversible dc magnetization data of the YBa2Cu3O7-δ, YBa2Cu2.97Zn0.03O7-δ, YBa2Cu2.97Mg0.03O7-δ and YBa2Cu2.97Ni0.03O7-δ single crystals with the aim of studying the contribution of the divalent chemical doping on the diamagnetic thermodynamic fluctuations (DTF) of the YBa2Cu3O7-δ. The dc zero field cooled [MZFC(T)] and field cooled cooling [MFCC(T)] diamagnetic magnetizations were measured with a SQUID magnetometer. The DTF behavior of our samples was interpreted in light of the 3D lowest Landau level formalism (3D-LLL). The results highlight that the amount of the Cu partially substituted individually for Zn, Mg or Ni in the YBa2Cu3O7-δ structure do not change the 3D character of its vortices dynamics. In addition, they show an increase in the temperature range dominated by 3D-DTF of ours doped single crystals. This increase could be connected to the intensification of their inhomogeneous superconducting state due to the chemical doping.

Spatially Inhomogeneous Superconducting State near Hc2 in UPd2Al3

We have performed $^{27}$Al-NMR measurements on single-crystalline UPd$_2$Al$_3$ with the field parallel to the $c$ axis to investigate the superconducting (SC) properties near the upper critical field of superconductivity $H_{\rm c2}$. The broadening of the NMR linewidth below 14~K indicates the appearance of the internal field at the Al site, which originates from the antiferromagnetically ordered moments of U 5$f$ electrons. In the SC state well below $\mu_0H_{\rm c2}$ = 3.4~T, the broadening of the NMR linewidth due to the SC diamagnetism and a decrease in the Knight shift are observed, which are well-understood by the framework of spin-singlet superconductivity. In contrast, the Knight shift does not change below $T_{\rm c}(H)$, and the NMR spectrum is broadened symmetrically in the SC state in the field range of 3~T $< \mu_0 H < \mu_0 H_{\rm c2}$. The unusual NMR spectrum near $H_{\rm c2}$ suggests that a spatially inhomogeneous SC state such as the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state would be realized.

Phase transitions in hybrid SFS structures with thin superconducting layers

Calculations of critical temperature T c of the phase transition to superconducting state of a superconductor/ ferromagnet/superconductor (SFS) hybrid structure with proximity effect is performed on the base of linearized Usadel equations. It is shown that the proximity effect between S and F metals and the exchange interaction can induce an inhomogeneous superconducting state with longitudinal to layers Δ ∝ exp(ipz) modulation of the superconductivity order parameter, which is characterized by nonzero value of the wave number p, describing the Larkin–Ovchinnikov–Fulde–Ferrell instability. Influence of this instability on transitions between 0- and π-states of the SFS structure is studied. It is shown that the 0–π transition is accompanied by a nonmonotonic dependence of both the critical temperature T c and the effective penetration depth Λ of the magnetic field into the hybrid structure on the characteristic size of the ferromagnetic region.

Screening properties of multiply connected ferromagnet–superconductor hybrid structures

Superconducting phase transition temperature T c of a ferromagnet/superconductor (SF) hybrid structure consisting of a hollow superconducting (S) cylinder (shell) with the central part (core) filled with a ferromagnetic (F) metal has been analyzed on the basis of linearized Usadel equations. It has been shown that the proximity effect between the S and F metals, as well as the exchange interaction, may induce an inhomogeneous superconducting state with Δ ~ exp(iLθ + ipz), which is characterized by nonzero circulation of phase L and wavenumber p describing the Larkin–Ovchinnikov–Fulde–Ferrell (LOFF) instability along the cylinder axis. The transitions between the states with different values of L and p, which are accompanied by a nonmonotonic dependence of superconducting transition temperature T c and effective magnetic field penetration depth Λ into the SF structure on the characteristic size of the ferromagnetic region, have been investigated.

Strong dopant dependence of electric transport in ion-gated MoS2

We report modifications of the temperature-dependent transport properties of MoS2 thin flakes via field-driven ion intercalation in an electric double layer transistor. We find that intercalation with Li+ ions induces the onset of an inhomogeneous superconducting state. Intercalation with K+ leads instead to a disorder-induced incipient metal-to-insulator transition. These findings suggest that similar ionic species can provide access to different electronic phases in the same material.

Evidence for defect-induced superconductivity up to 49 K in(Ca1−xRx)Fe2As2

To explore the origin of the unusual non-bulk superconductivity with a Tc up to 49 K reported in the rare-earth-doped CaFe2As2 , the chemical composition, magnetization, specific heat, resistivity, and annealing effect are systematically investigated on nominal (Ca1-xRx)Fe2As2 single crystals with different x's and R = La, Ce, Pr, and Nd. All display a doping-independent Tc once superconductivity is induced, a doping-dependent low field superconducting volume fraction f, and a large magnetic anisotropy {\eta} in the superconducting state, suggesting a rather inhomogeneous superconducting state in an otherwise microscale-homogenous superconductor. The wavelength dispersive spectroscopy and specific heat show the presence of defects which are closely related to f, regardless of the R involved. The magnetism further reveals that the defects are mainly superparamagnetic clusters for R = Ce, Pr, and Nd with strong intercluster interactions, implying that defects are locally self-organized. Annealing at 500 {\deg}C, without varying the doping level x, suppresses f profoundly but not the Tc. The above observations provide evidence for the crucial role of defects in the occurrence of the unusually high Tc ~ 49 K in (Ca1-xRx)Fe2As2 and are consistent with the interface-enhanced superconductivity recently proposed.

Effect of Parallel Magnetic Field on Superconductivity of Ultrathin Metal Films Grown on a Cleaved GaAs Surface

The parallel-magnetic-field $H_\parallel$ dependence of the superconducting transition temperature $T_c$ is studied for ultrathin films of In, Bi, and Al grown on GaAs(110). In the case of In films in the monolayer regime, $T_c$ exhibits a quadratic-like $H_\parallel$ dependence, which is one order of magnitude stronger than that previously observed in monolayer Pb films by the present authors [Phys. Rev. Lett. 111, 057005 (2013)]. The results are well reproduced by a model developed for an inhomogeneous two-dimensional superconducting state in the presence of a moderate Rashba spin-orbit interaction. The Rashba spin splitting is estimated to be 0.04 eV, which is much smaller than that expected for monolayer Pb films. In a few-monolayer Bi film, the suppression of $T_c$ with increasing $H_\parallel$ is comparable to that in monolayer Pb films. On the other hand, much stronger suppression, which is attributed to the Pauli paramagnetic effect, was observed for the Al film.

Electronic Homogeneity in the Overdoped Regime of the Electron-Doped High-Tc Superconductors

In order to investigate the electronic homogeneity in electron-doped high-Tc cuprates, magnetization and specific heat measurements have been performed for Pr1-xLaCexCuO4 single crystals with x = 0.13 – 0.17. It has been found from the magnetization curve that the hysteresis is relatively small and that the so-called second magnetization peak is absent for every x. Moreover, the Sommerfeld constant in the ground state has shown HlnH dependence on magnetic field H for every x, suggesting that the superconductivity is not pure but dirty. These results are in contrast to those observed in the overdoped regime of hole-doped La2-xSrxCuO4 where an inhomogeneous superconducting state is formed in spite of the superconductivity being pure. Therefore, it has been concluded that a rather homogeneous electronic state is realized in the electron-doped cuprates, suggesting different electronic states between hole- and electron-doped cuprates.

Magneto-resistance study of AFe&lt;SUB align="right"&gt;2As&lt;SUB align="right"&gt;2 (A = Sr, Ba) iron-based compounds

We have investigated the magneto-resistance (MR) from the two main A Fe 2 As 2 compounds (with A = Sr and Ba) and a low energy Ca ion implanted SrFe 2 As 2 crystal up to 8 T. We show that MR from BaFe 2 As 2 and SrFe 2 As 2 single crystals are similar and a quantum linear MR model favoured by some authors is probably not appropriate especially since the MR is not linear. The SrFe 2 As 2 sample with a near surface Ca concentration of 0.8 at.% has a larger MR at low temperatures that is probably due to current transport in the near surface region and in an inhomogeneous normal and superconducting state.