The mixed state of superconducting (SC) and normal (N) phases in one dimensional systems are characterized by several phase slips and localization of the order parameter of the SC phase. The phenomenon is explained on the basis of a complex Ginzburg Landau (CGL) model. We present a simple analysis of the system on multiple scales to capture localization and phase slips when phases coexist.
Superconducting Nb3Sn films can be synthesized by controlling the atomic concentration of Sn. Multilayer sequential sputtering of Nb and Sn thin films followed by high temperature annealing is considered as a method to fabricate Nb3Sn films, where the Sn composition of the deposited films can be controlled by the thickness of alternating Nb and Sn layers. We report on the structural, morphological and superconducting properties of Nb3Sn films fabricated by multilayer sequential sputtering of Nb and Sn films on sapphire substrates followed by annealing at 950 °C for 3 h. We have investigated th…
The competition between the singlet superconducting states with $s$- and d-wave symmetry of the order parameter is studied within a single-band model with nearest-neighbor attractive interaction. The zero- and finite-temperature ground state phase diagrams are constructed for different ratios between the nearest- and next-nearest-neighbor electron transfer integrals. The mixed $s+id$ pairing state is shown to form in the intermediate region between $s$- and d-waves. The temperature phase transitions between the pure and the mixed pairing state are found.
Motivated by recent experimental findings, we have developed a theory of the superconducting state for 2D metals without inversion symmetry modeling the geometry of a surface superconducting layer in a field-effect-transistor or near the boundary doped by adsorbed ions. In such systems the two-fold spin degeneracy is lifted by spin-orbit interaction, and singlet and triplet pairings are mixed in the wave function of the Cooper pairs. As a result, spin magnetic susceptibility becomes anisotropic and Knight shift retains finite and rather high value at T=0.
We studied the quantum oscillations in superconducting vortex mixed states with d-wave pairing. We showed that the Onsager relation does not always apply. Furthermore, at mean field level the quantum oscillations from electron pockets are suppressed by the pairing. We conclude that an interpretation of the experimental results asccoming from the four hole pockets created by a $(π,π)$ folding cannot be ruled out.
The temperature dependence of the magnetic field distribution in the mixed superconducting phase of randomly oriented MgB$_2$ powder was probed by $% ^{11}$B NMR spectroscopy. Below the temperature of the second critical ($B_{% {c2}}$) field, $T_{c2}\approx 27$K, our spectra reveal two NMR signal components, one mapping the magnetic field distribution in the mixed superconducting state and the other one arising from the normal state. The complementary use of bulk magnetization and NMR measurements reveals that MgB$_2$ is an anisotropic superconductor with a $B_{c2}^c<2.35$ Tesla anisotropy par…
We report on measurements of the magnetic moment in superconducting MgB2 single crystals. We find μ_0H_{c2}^c(0) = 3.2 T, μ_0H_{c2}^{ab}(0) = 14.5 T, γ= 4.6, μ_0H_c(0) = 0.28 T, and κ(T_c) = 4.7. The standard Ginzburg-Landau and London model relations lead to a consistent data set and indicate that MgB2 is a clean limit superconductor of intermediate coupling strength with very pronounced anisotropy effects.
We report the results of a zero-field muon spin relaxation (ZF-muSR) study of superconducting Ba1-xKxFe2As2 (0.5 < x < 0.9) in search of weak spontaneous internal magnetic fields associated with proposed time-reversal-symmetry breaking mixed pairing states. The measurements were performed on polycrystalline samples, which do not exhibit the mesoscopic phase separation previously observed in single crystals of Ba1-xKxFe2As2. No evidence of spontaneous internal magnetic fields is found in any of the samples at temperatures down to T ~ 0.02 K.
Small-angle neutron scattering is used in combination with transport measurements to investigate the current-induced effects on the morphology of the intermediate mixed state domains in the intertype superconductor niobium. We report the robust self-organisation of the vortex lattice domains to elongated parallel stripes perpendicular to the applied current in a steady-state. The experimental results for the formation of the superstructure are supported by theoretical calculations, which highlight important details of the vortex matter evolution. The investigation demonstrates a mechanism of a…
A systematic study of irreversible magnetization was performed in bulk Niobium after different surface treatments. Starting with smooth surfaces and abrading them, a strong increase of the critical current is observed up an apparent limiting value. An impressive change of the critical current is also observed in the surface superconductivity (SSC) state, reaching values of the same order of magnitude as in the mixed state. We explain also the observation of strong SSC for magnetic field perpendicular to larges facets in terms of nucleation of SC along bumps of a corrugated surface.
The electronic nematic phase is characterized as an ordered state of matter with rotational symmetry breaking, and has been well studied in the quantum Hall system and the high-$T_c$ superconductors, regardless of cuprate or pnictide family. The nematic state in high-$T_c$ systems often relates to the structural transition or electronic instability in the normal phase. Nevertheless, the electronic states below the superconducting transition temperature is still an open question. With high-resolution scanning tunneling microscope measurements, direct observation of vortex core in FeSe thin film…
Starting from a random matrix model, we construct the low-energy effective field theory for the noninteracting gas of quasiparticles of a disordered superconductor in the mixed state. The theory is a nonlinear sigma model, with the order parameter field being a supermatrix whose form is determined solely on symmetry grounds. The weak localization correction to the field-axis thermal conductivity is computed for a dilute array of s-wave vortices near the lower critical field H_c1. We propose that weak localization effects, cut off at low temperatures by the Zeeman splitting, are responsible for…
The type II Dirac semimetal PdTe$_2$ is unique in the family of topological parent materials because it displays a superconducting ground state below 1.7 K. Despite wide speculations on the possibility of an unconventional topological superconducting phase, tunneling and heat capacity measurements revealed that the superconducting phase of PdTe$_2$ follows predictions of the microscopic theory of Bardeen, Cooper and Shriefer (BCS) for conventional superconductors. The superconducting phase in PdTe$_2$ is further interesting because it also displays properties that are characteristics of type-I…
A superconducting (SC) mixed state occurs in type-II superconductors where the upper critical field Hc2 is higher than the thermodynamic critical field Hc. When an applied field is in between these fields, the free energy depends weakly on the order parameter which therefore can be small (SC state) or zero (normal state) at different parts of the sample. In this paper we demonstrate how a normal state along a line traversing a superconductor can be turned on and off externally in zero field. The concept is based on a long, current-carrying excitation coil, piercing a ringshaped superconductor.…
The Landau expansion for the free energy of the superconducting mixed state near the upper critical field in powers of the square modulus of the order parameter averaged over Abrikosov lattice is derived. The analytical calculations has been carried out in frame of Gor'kov formalism for 3-dimensional isotropic BCS model beyond the limits of quasiclassical approximation, another words with Landau quantization of the quasiparticle energy levels taken into consideration. The derivation is performed at low temperature and high enough but finite crystal's purity. The effect of Pauli paramagnetic te…
The unusual superconducting state in Sr$_2$RuO$_4$ has long been viewed as being analogous to a superfluid state in liquid $^3$He. Nevertheless, calculations based on this odd-parity state are presently unable to completely reconcile the properties of Sr$_2$RuO$_4$. Using a self-consistent quantum many-body scheme that employs realistic parameters, we are able to model several signature properties of the normal and superconducting states of Sr$_2$RuO$_4$. We find that the dominant component of the model superconducting state is of even parity and closely related to superconducting state for th…
The Hall resistivity rho_{xy} of LuNi_2B_2C is negative in the normal as well as in the mixed state and has no sign reversal typical for high-T_c superconductors. A distinct nonlinearity in the rho_{xy} dependence on field H was found in the normal state for T < 40K, accompanied by a large magnetoresistance reaching +90% for mu_0H=16T at T=20K. The scaling relation rho_{xy} ~ ρ_{xx}^β(ρ_{xx} is the longitudinal resistivity) was found in the mixed state, the value of βbeing dependent on the degree of disorder.
A weak-coupling formalism for superconducting states possessing both singlet (even parity) and triplet (odd parity) components of the order parameter in centrosymmetric crystals is developed. It is shown that the quasiparticle energy spectrum may be non-degenerate even if the triplet component is unitary. The superconducting gap of a mixed-parity state may have line nodes in the strong spin-orbit coupling limit. The pseudospin carried by the superconducting electrons is calculated, from which follows a prediction of a kink anomaly in the temperature dependence of muon spin relaxation rate. The…
Muon spin rotation (μ+SR) measurements of square-root second moments of local magnetic fields σ in superconducting mixed states, as published for oriented crystals and powder samples of YBa2Cu3O7-δ (δ {\approx} 0.05), YBa2Cu4O8 and La2-xSrxCuO4 (x ~ 0.15-0.17), are subjected to comparative analysis for superconducting gap symmetry. For oriented crystals it is shown that anomalous dependences of σ on temperature T and applied field H, as-measured and extracted a- and b-axial components, are attributable to fluxon depinning and disorder that obscure the intrinsic character of the superconducting…
We have probed the Landau levels of nodal quasi-particles by tunneling along a nodal direction of (110) oriented YBa$_2$Cu$_3$O$_{7-x}$ thin films with a magnetic field applied perpendicular to the $CuO_2$ planes, and parallel to the film's surface. In optimally doped films and at low temperature, finite energy nodal states are clearly observed in films thinner than the London penetration depth. Above a well defined temperature the order parameter reverts to a pure \emph{d}-wave symmetry.
Equilibrium magnetic properties of the mixed state in type-II superconductors were measured with high purity bulk and film niobium samples in parallel and perpendicular magnetic fields using dc magnetometry and scanning Hall-probe microscopy. Equilibrium magnetization data for the perpendicular geometry were obtained for the first time. It was found that none of the existing theories is consistent with these new data. To address this problem, a theoretical model is developed and experimentally validated. The new model describes the mixed state in an averaged limit, i.e. %without detailing the …
The large flux-flow velocity behavior of the high temperature superconductor BSCCO in the mixed state is studied by measurement of the current-voltage characteristic as a function of temperature and magnetic field direction. We find strong evidence for vortex-antivortex pairs that are excited by quantum fluctuations and contribute to the dissipation when dissociated by a large current.
Evidence of nematic effects in the mixed superconducting phase of slightly underdoped $\text{Ba}(\text{Fe}_{1-x}\text{Co}_x)_2\text{As}_2$ is reported. We have found strong in-plane resistivity anisotropy for crystals in different strain conditions. For these compositions, there is no magnetic long range order, so the description may be ascribed to the interplay between the superconducting and nematic order parameters. A piezoelectric-based apparatus is used to apply tensile or compressive strain to tune nematic domain orientation in order to examine intrinsic nematicity. Measurements are done…
Monolayer NbSe$_2$ is a nodal topological Ising superconductor at magnetic in-plane fields exceeding the Pauli limit, with nodal points strictly on high symmetry lines in the Brillouin zone. Here, we use a combined numerical and group-theoretical approach in real-space to characterize the unconventional superconducting state in monolayer transition metal dichalcogenides. Even with a conventional pairing interaction, the superconducting state is intrinsically parity-mixed and robust against on-site disorder. The interplay between the Zeeman magnetic field, strong spin-orbit interaction, and ele…
The thermal conductivity κin the basal plane of single-crystalline hexagonal NbSe2 has been measured as a function of magnetic field H, oriented both along and perpendicular to the c-axis, at several temperatures below T_c. With the magnetic field in the basal plane and oriented parallel to the heat flux we observed, in fields well below H_c2, an unexpected hysteretic behavior of κ(H) with all the generic features of a first order phase transition. The transition is not manifest in the κ(H) curves, if H is still in the basal plane but oriented perpendicularly to the heat-flux direction. The or…
It is shown that transition from the mixed state without the phase coherence to the mixed state with the long-range phase coherence (i.e. to the Abrikosov state) of superconductors without disorder must be first order phase transition. The phase coherence appearance in thin superconducting film with strong disorder is considered. The observed smooth transition is explained by increasing of the effective fluctuation dimensionality (from zero to one) in superconductors with strong disorder. Mendelssohn model is used for the explanation of the resistive properties of film with strong disorder.
The paper examines part of the ground state diagram of the extended Hubbard model, with the on-site attraction U<0 and intersite repulsion W>0 in the presence of charge density waves, superconducting and $η$-superconducting order parameters. We show the possibility of the stabilization of the mixed state, with all three nonzero order parameters, in the model with nearest neighbor interactions. The other result of the paper is application of the exact solution of the Schrodinger equation for the two electron bound state, as an additional bound for the phase diagram of the model, resulting in th…
We report measurements of the magnetic-field induced microwave complex resistivity in REBa$_{2}$Cu$_{3}$O$_{7-δ}$ thin films, with RE = Y, Sm. Measurements are performed at 48 GHz by means of a resonant cavity in the end-wall-replacement configuration. The magnetic field dependence is investigated by applying a moderate (0.8 T) magnetic field along the c-axis. The measured vortex state complex resistivity in YBa$_{2}$Cu$_{3}$O$_{7-δ}$ and SmBa$_{2}$Cu$_{3}$O$_{7-δ}$ is analyzed within the well-known models for vortex dynamics. It is shown that attributing the observed response to vortex motion…
We theoretically investigate the transport properties of a quasi one dimensional ferromagnet-superconductor junction where the superconductor consists of mixed singlet and triplet pairings. We show that the relative orientation of the stoner field ($\bf{\tilde{h}}$) in the ferromagnetic lead and the $\bf{d}$ vector of the superconductor acts like a on-off switch for the zero bias conductance of the device. In the regime, where triplet pairing amplitude dominates over the singlet counterpart (topological phase), a pair of Majorana zero modes appear at each end of the superconducting part of the…
Discontinuities in elastic constants are detected at the superconducting transition of layered organic conductors κ-(BEDT-TTF)_{2}X by longitudinal and transverse ultrasonic velocity measurements. Symmetry arguments show that discontinuities in shear elastic constants can be explained in the orthorhombic compound only if the superconducting order parameter has a mixed character that can be of two types, either A_{1g}+B_{1g} or B_{2g}+B_{3g} in the classification of irreducible representations of the orthorhombic point group D_{2h}. Consistency with other measurements suggests that the A_{1g}+B…
Superconductors that possess both broken spatial inversion symmetry and spin-orbit interactions exhibit a mix of spin singlet and triplet pairing. Here, we report on measurements of the superconducting properties of electron-doped, strained SrTiO3 films. These films have an enhanced superconducting transition temperature and were previously shown to undergo a transition to a polar phase prior to becoming superconducting. We show that some films show signatures of an unusual superconducting state, such as an in-plane critical field that is higher than both the paramagnetic and orbital pair brea…
We show that a two-dimensional semiconductor with Rashba spin-orbit coupling could be driven into the second-order topological superconducting phase when a mixed-pairing state is introduced. The superconducting order we consider involves only even-parity components and meanwhile breaks time-reversal symmetry. As a result, each corner of a square-shaped Rashba semiconductor would host one single Majorana zero mode in the second-order nontrivial phase. Starting from edge physics, we are able to determine the phase boundaries accurately. A simple criterion for the second-order phase is further es…
We describe a simple AC susceptometer built in-house that can be used to make high-resolution measurements of the magnetic susceptibility of high-temperature superconductors in an undergraduate physics lab. Our system, cooled using liquid nitrogen, can reach a base temperature of 77 K. Our apparatus does not require gas handling systems or PID temperature controllers. Instead, it makes use of a thermal circuit that is designed to allow the sample to cool on a time scale that is suitable for an undergraduate lab. Furthermore, the temperature drift rate at the superconducting transition temperat…
We construct a pair potential which in a scaling limit leads to a Hamiltonian that generates co-existing mean-field and superconducting phases. Depending on the relative values of the coupling constants, the superconducting phase may exist at arbitrarily high temperatures.
We investigate the flux penetration patterns and matching fields of a long cylindrical wire of circular cross section in the presence of an external magnetic field. For this study we write the London theory for a long cylinder both for the mixed and Meissner state, with boundary conditions appropriate for this geometry. Using the Monte Carlo Simulated Annealing method, the free energy of the mixed state is minimized with respect to the vortex position and we obtain the ground state of the vortex lattice for N=3 up to 18 vortices. The free energy of the Meissner and mixed state provides express…
We investigate the potential existence of a superconducting phase in $5d$ Mott insulators with an eye to hole doped Sr$_2$IrO$_4$. Using a mean-field method, a mixed singlet-triplet superconductivity, $d + p$, is observed due to the antisymmetric exchange originating from a quasi-spin-orbit-coupling. Our calculation on ribbon geometry shows possible existence of the topologically protected edge states, because of nodal structure of the superconducting gap. These edge modes are spin polarized and emerge as zero-energy flat bands, supporting a symmetry protected Majorana states, verified by eval…
By use of ultrasound studies we resolved magneto-acoustic quantum oscillation deep into the mixed state of the multiband nonmagnetic superconductor YNi2B2C. Below the upper critical field, only a very weak additional damping appears that can be well explained by the field inhomogeneity caused by the flux-line lattice in the mixed state. This is clear evidence for no or a vanishingly small gap for one of the bands, namely, the spheroidal alpha band. This contrasts de Haas--van Alphen data obtained by use of torque magnetometry for the same sample, with a rapidly vanishing oscillation signal in …
We illuminate the superconducting phases in [001]-grown-noncentrosymmetric quantum wells with an anisotropic spin-orbit coupling in the presence of on-site Hubbard interaction. Within the random phase approximation, we investigate the spin-fluctuation-mediated pairing in the presence of Rashba/Dresselhaus antisymmetric spin-orbit couplings. Although the existence of spatial inversion symmetry desires a dominant d-wave pairing for all filling levels, a broken inversion symmetry generates antisymmetric spin-orbit coupling and mixes the even- and odd-parity in the superconducting gap. We study th…
We investigate parity-mixing superconductivity in the two-dimensional Hubbard model with Rashba spin-orbit coupling, using Cellular Dynamical Mean-Field Theory (CDMFT). A superconducting state with mixed singlet $d$-wave and triplet $p$-wave character is found in a wide range of doping. The singlet component decreases with the amplitude of the Rashba spin-orbit coupling, whereas the triplet component increases, but both disappear at about 20\% doping. The effect of a Zeeman field is also investigated; it tends to suppress both types of superconductivity, but induces nontrivial topological prop…
The Hall voltage in the mixed state close to the superconducting critical temperature is determined in the framework of the macroscopic approach. Only flux flow and macroscopic excitations motion are taken into account. The Hall anomaly can appear for rather low magnetic field values.
We report a combined theoretical and experimental investigation of the superconducting state in the quasi-two-dimensional organic superconductor $κ$-(ET)$_2$Cu[N(CN)$_2$]Br. Applying spin-fluctuation theory to a low-energy material-specific Hamiltonian derived from ab initio density functional theory we calculate the quasiparticle density of states in the superconducting state. We find a distinct three-peak structure that results from a strongly anisotropic mixed-symmetry superconducting gap with eight nodes and twofold rotational symmetry. This theoretical prediction is supported by low-tempe…
Superconducting crystals with lack of inversion symmetry can potentially host unconventional pairing. However, till date, no direct conclusive experimental evidence of such unconventional order parameters in non-centrosymmetric superconductors has been reported. In this paper, through direct measurement of the superconducting energy gap by scanning tunnelling spectroscopy, we report the existence of both $s$-wave (singlet) and $p$-wave (triplet) pairing symmetries in non-centrosymmetric Ru$_7$B$_3$. Our temperature and magnetic field dependent studies also indicate that the relative amplitudes…
Superconductors are considered in view of applications to atom chip devices. The main features of magnetic traps based on superconducting wires in the Meissner and mixed states are discussed. The former state may mainly be interesting for improved atom optics, while in the latter, cold atoms may provide a probe of superconductor phenomena. The properties of a magnetic side guide based on a single superconducting strip wire placed in an external magnetic field are calculated analytically and numerically. In the mixed state of type II superconductors, inhomogeneous trapped magnetic flux, relaxat…
The large single crystals of SrSnP were prepared using Sn self-flux method. The superconductivity in the tetragonal SrSnP is observed with the critical temperature of ~2.3 K. The results of a crystallographic analysis, superconducting characterization, and theoretical assessment of tetragonal SrSnP are presented. The SrSnP crystallizes in the CaGaN structure type with space group P4/nmm (S.G.129, Pearson symbol tP6) according to the single crystal X-ray diffraction characterization. A combination of magnetic susceptibility, resistivity, and heat capacity measurements confirms the bulk supercon…
We have performed Ce $L_3$-edge x-ray absorption spectroscopy (XAS) and Ce $4d$-$4f$ resonant photoemission spectroscopy (PES) on single crystals of CeO$_{1-x}$F$_x$BiS$_2$ for $x=0.0$ and 0.5 in order to investigate the Ce $4f$ electronic states. In the Ce $L_3$-edge XAS, mixed valence of Ce was found in the $x=0.0$ sample and the F-doping suppresses it, which is consistent with the results on polycrystalline samples. As for the resonant PES, we found that the Ce $4f$ electrons in both $x=0.0$ and $0.5$ systems respectively form a flat band at 1.0 eV and 1.4 eV below the Fermi level and there…
We propose a model for a superconductor where both spin-singlet and chiral triplet pairing amplitudes can coexist. By solving the Bogoliubov-de Gennes equations with a general pair potential that accounts for both spin states we study experimental signatures of normal metal and superconductor hybrids. The interplay between the spin-singlet and triplet correlations manifests in the appearance of two effective gaps. When the amplitude of the spin-triplet component is stronger than that of the spin-singlet, a topological phase transition into a non-trivial regime occurs. As a result, the normal m…
The La2-xPrxCayBa2Cu4+yOz (LaPrCaBCO) mixed oxides have been studied for their structural and superconducting properties using X-ray diffraction (XRD), d. c. resistivity, d. c. susceptibility and iodometric double titration. All the LaPrCaBCO samples for x = 0.1 - 0.5, exhibit tetragonal crystalline structure with P 4/mmm space group as determined by Rietveld analysis of the X-ray diffraction data. With increasing x, enhancement in Tc is observed, which is quite interesting for Pr substituted high Tc oxides. Maximum Tc ~ 58 K has been observed for x = 0.5(La-2125 stoichiometry). The results of…
We study the superconducting pairing symmetry in twisted bilayer graphene by solving the Bogoliubov-de Gennes equation for all electrons in moiré supercells. With increasing the pairing potential, the system evolves from the mixed nontopological $d+id$ and $p+ip$ phase to the $s+p+d$ phase via the first-order phase transition. In the time-reversal symmetry breaking $d+id$ and $p+ip$ phase, vortex and antivortex lattices accompanying spontaneous supercurrent are induced by the twist. The superconducting order parameter is nonuniform in the moiré unit cell. Nevertheless, the superconducting gap …
The parity breaking gives rise to rich superconducting properties through the admixture of even and odd-parity Cooper pairs. A new light has been shed on parity-breaking superconductors by recent observations of nonreciprocal responses such as the nonlinear optical responses and the superconducting diode effect. In this Letter, we demonstrate that the nonreciprocal responses are characterized by a unidirectional correction to the superfluid density, which we call nonreciprocal superfluid density. This correction leads to the nonreciprocal Meissner effect, namely, asymmetric screening of magnet…
We examine the stability of mixed-symmetry superconducting states with broken time-reversal symmetry in spatial-symmetry-broken systems, including chiral states, on the basis of the free-energy functional derived in the weak-coupling theory. We consider a generic a_1 + i a_2 wave state, with a_1 and a_2 being different symmetry indices such as (a_1,a_2) = (d,s), (p_x,p_y), and (d,d').The time-reversal symmetry of the mixed-symmetry state with the a_1- and a_2-wave components is broken when the phases of these components differ, and such a state is called the time-reversal-symmetry breaking (TR…
Anomalous field evolution of the mixed-state linewidth in the second superconducting dome of LaFeAsO$_{1-x}M_x$ ($M={\rm F,H}$)
PSI Center for Neutron and Muon Sciences CNM（瑞士保罗谢尔研究所中子与μ子科学中心）；Université Grenoble Alpes, CEA, Grenoble INP, IRIG-PHELIQS（格勒诺布尔阿尔卑斯大学）；Dipartimento di Fisica e Astronomia “Augusto Righi”, Università di Bologna（博洛尼大学物理与天文学系）；CNR-SPIN（意大利国家研究委员会自旋物理研究所）；Dipartimento di Fisica, Università degli Studi di Pavia（帕维亚大学物理系）；Leibniz-Institute for Solid State and Materials Research, IFW-Dresden（德累斯顿莱布尼茨固体与材料研究所）；CrystMat Company（CrystMat公司）
