Three-dimensional Superconductors Research Articles

Tricritical point in quantum phase transitions of the Coleman–Weinberg model at Higgs mass

The tricritical point, which separates first and second order phase transitions in three-dimensional superconductors, is studied in the four-dimensional Coleman–Weinberg model, and the similarities as well as the differences with respect to the three-dimensional result are exhibited. The position of the tricritical point in the Coleman–Weinberg model is derived and found to be in agreement with the Thomas–Fermi approximation in the three-dimensional Ginzburg–Landau theory. From this we deduce a special role of the tricritical point for the Standard Model Higgs sector in the scope of the latest experimental results, which suggests the unexpected relevance of tricritical behavior in the electroweak interactions. • The predictions for the tricritical point in the Ginzburg–Landau theory and the Coleman–Weinberg model are compared. • We prove the tricritical point in the Coleman–Weinberg is in agreement with the Thomas–Fermi approximation. • The recent discovery of the Higgs boson suggests the presence of tricritical behavior in the electroweak interactions.

Electromagnetic and thermal responses in topological matter: Topological terms, quantum anomalies and D-branes

We discuss the thermal (or gravitational) responses in topological superconductors and in topological phases in general. Such thermal responses (as well as electromagnetic responses for conserved charge) provide a definition of topological insulators and superconductors beyond the single-particle picture. In two-dimensional topological phases, the Str\v{e}da formula for the electric Hall conductivity is generalized to the thermal Hall conductivity. Applying this formula to the Majorana surface states of three-dimensional topological superconductors predicts cross-correlated responses between the angular momentum and thermal polarization (entropy polarization). We also discuss a use of D-branes in string theory as a systematic tool to derive all such topological terms and topological responses. In particular, we relate the $\mathbb{Z}_2$ index of topological insulators introduced by Kane and Mele (and its generalization to other symmetry classes and to arbitrary dimensions) to the K-theory charge of non-BPS D-branes, and vice versa. We thus establish a link between the stability of non-BPS D-branes and the topological stability of topological insulators.

Axion topological field theory of topological superconductors

Topological superconductors are gapped superconductors with gapless and topologically robust quasiparticles propagating on the boundary. In this paper, we present a topological field theory description of three-dimensional time-reversal invariant topological superconductors. In our theory the topological superconductor is characterized by a topological coupling between the electromagnetic field and the superconducting phase fluctuation, which has the same form as the coupling of ``axions'' with an Abelian gauge field. As a physical consequence of our theory, we predict the level crossing induced by the crossing of special ``chiral'' vortex lines, which can be realized by considering $s$-wave superconductors in proximity with the topological superconductor. Our theory can also be generalized to the coupling with a gravitational field.

Anomalous metallic state above the upper critical field of the conventional three-dimensional superconductor AgSnSe2with strong intrinsic disorder

We report superconducting properties of AgSnSe2 which is a conventional type-II superconductor in the very dirty limit due to intrinsically strong electron scatterings. While this material is an isotropic three-dimensional (3D) superconductor with a not-so-short coherence length where strong vortex fluctuations are NOT expected, we found that the magnetic-field-induced resistive transition at fixed temperatures becomes increasingly broader toward zero temperature and, surprisingly, that this broadened transition is taking place largely ABOVE the upper critical field determined thermodynamically from the specific heat. This result points to the existence of an anomalous metallic state possibly caused by quantum phase fluctuations in a strongly-disordered 3D superconductor.

Interaction-Mediated Surface-State Instability in Disordered Three-Dimensional Topological Superconductors with Spin SU(2) Symmetry

We show that arbitrarily weak interparticle interactions destabilize the surface states of 3D topological superconductors with spin SU(2) invariance (symmetry class CI) in the presence of nonmagnetic disorder. The conduit for the instability is disorder-induced wave function multifractality. We argue that time-reversal symmetry breaks spontaneously at the surface, so that topologically protected states do not exist for this class. The interaction-stabilized surface phase is expected to exhibit ferromagnetic order, or to reside in an insulating plateau of the spin quantum Hall effect.

Nearly flat Andreev bound states in superconductor-topological insulator hybrid structures

Exotic excitations arise at the interface between a three-dimensional topological insulator (TI) and superconductors. For example, Majorana fermions with a linear dispersion, $E\sim k$, exist in a short $\pi$ Josephson junction on the TI surface. We show that in these systems, the Andreev bound states spectrum becomes nearly flat at zero energy when the chemical potential is sufficiently away from the Dirac point. The flat dispersion is well approximated by $E\sim k^N$, where $N$ scales with the chemical potential. Similar evolution from linear to flat dispersion also occurs for the subgap spectrum of a periodic superconducting proximity structure, such as a TI surface in contact with a stripe superconductor.

Convergence of Ginzburg–Landau Functionals in Three-Dimensional Superconductivity

In this paper we consider the asymptotic behavior of the Ginzburg- Landau model for superconductivity in 3-d, in various energy regimes. We rigorously derive, through an analysis via {\Gamma}-convergence, a reduced model for the vortex density, and we deduce a curvature equation for the vortex lines. In a companion paper, we describe further applications to superconductivity and superfluidity, such as general expressions for the first critical magnetic field H_{c1}, and the critical angular velocity of rotating Bose-Einstein condensates.

Disorder-induced quantum phase transitions in three-dimensional topological insulators and superconductors

We discuss the effects of disorder in time-reversal invariant topological insulators and superconductors in three spatial dimensions. For three-dimensional topological insulator in symplectic (AII) symmetry class, the phase diagram in the presence of disorder and a mass term, which drives a transition between trivial and topological insulator phases, is computed numerically by the transfer matrix method. The numerics is supplemented by a field theory analysis (the large-$N_f$ expansion where $N_f$ is the number of valleys or Dirac cones), from which we obtain the correlation length exponent, and several anomalous dimensions at a non-trivial critical point separating a metallic phase and a Dirac semi-metal. A similar field theory approach is developed for disorder-driven transitions in symmetry class AIII, CI, and DIII. For these three symmetry classes, where topological superconductors are characterized by integer topological invariant, a complementary description is given in terms of the non-linear sigma model supplemented with a topological term which is a three-dimensional analogue of the Pruisken term in the integer quantum Hall effect.

Transport properties of stripe-ordered high Tc cuprates

Transport measurements provide important characterizations of the nature of stripe order in the cuprates. Initial studies of systems such as La(1.6-x)Nd(0.4)Sr(x)CuO(4) demonstrated the strong anisotropy between in-plane and c-axis resistivities, but also suggested that stripe order results in a tendency towards insulating behavior within the planes at low temperature. More recent work on La(2-x)Ba(x)CuO(4) with x=1/8 has revealed the occurrence of quasi-two-dimensional superconductivity that onsets with spin-stripe order. The suppression of three-dimensional superconductivity indicates a frustration of the interlayer Josephson coupling, motivating a proposal that superconductivity and stripe order are intertwined in a pair-density-wave state. Complementary characterizations of the low-energy states near the Fermi level are provided by measurements of the Hall and Nernst effects, each revealing intriguing signatures of stripe correlations and ordering. We review and discuss this work.

Anisotropy of Upper Critical Field in a One-Dimensional Organic System, (TMTTF)2PF6 under High Pressure

We have measured the temperature-dependent resistivity of (TMTTF) 2 PF 6 up to 7 GPa using a turnbuckle-type diamond anvil cell (DAC) and at magnetic fields of up to 5 T. Unlike previous reports on organic compounds, a zero resistance was observed in the superconducting state even at high pressures. Superconductivity was observed in the range of P = 4.18 to 6.03 GPa and showed a peak T c of 2.25 K at 4.58 GPa. The temperature dependence of the upper critical magnetic field H c2 ( T ) was determined via resistivity at P = 4.58 GPa, for the intrachain ( a ), interchain ( b '), and interlayer ( c * ) configurations, and H c2 ( T ) displays a positive curvature without saturation. This could be related to the wide pressure range of the coexistence between the spin density wave (SDW) and superconductivity (SC) ground state, and may be caused by an FFLO state, for a magnetic field along the a - and b '-axes with T ≥0.5 K for P = 4.48 GPa. This feature is suppressed with increasing pressure when the orbital pair breaking mechanism becomes dominant. The Ginzburg–Landau coherence lengths for three different axes obtained from this work show that (TMTTF) 2 PF 6 is an anisotropic three-dimensional superconductor.

Cross-Correlated Responses of Topological Superconductors and Superfluids

We study nontrivial responses of topological superconductors and superfluids to the temperature gradient and rotation of the system. In two-dimensional gapped systems, the Strěda formula for the electric Hall conductivity is generalized to the thermal Hall conductivity. Applying this formula to the Majorana surface states of three-dimensional topological superconductors predicts cross-correlated responses between the orbital angular momentum and thermal polarization (entropy polarization). These results can be naturally related to the gravitoelectromagnetism description of three-dimensional topological superconductors and superfluids, analogous to the topological magnetoelectric effect in Z(2) topological insulators.

Self-consistent Ginzburg–Landau theory for transport currents in superconductors

We elaborate on boundary conditions for Ginzburg-Landau (GL) theory in the case of external currents. We implement a self-consistent theory within the finite element method (FEM) and present numerical results for a two-dimensional rectangular geometry. We emphasize that our approach can in principle also be used for general geometries in three-dimensional superconductors.

Topological phases and surface flat bands in superconductors without inversion symmetry

We examine different topological phases in three-dimensional non-centrosymmetric superconductors with time-reversal symmetry by using three different types of topological invariants. Due to the bulk boundary correspondence, a non-zero value of any of these topological numbers indicates the appearance of zero-energy Andreev surface states. We find that some of these boundary modes in nodal superconducting phases are dispersionless, i.e., they form a topologically protected flat band. The region where the zero-energy flat band appears in the surface Brillouin zone is determined by the projection of the nodal lines in the bulk onto the surface. These dispersionless Andreev surface bound states have many observable consequences, in particular, a zero-bias conductance peak in tunneling measurements. We also find that in the gapless phase there appear Majorana surface modes at time-reversal invariant momenta which are protected by a $\mathbb{Z}_2$ topological invariant.

Vortex states in layered mesoscopic superconductors

Within the Ginzburg-Landau theory, we study the vortex structures in three-dimensional anisotropic mesoscopic superconductors in the presence of a uniform magnetic field. Anisotropy is included through varied ${T}_{c}$ in different layers of the sample and leads to distinct differences in the vortex states and their free energy. Several unconventional states are found, some comprising vortex clusters or exhibiting asymmetry. In a tilted magnetic field, we found second-order transitions between different vortex states, although vortex entry is generally a first-order transition in mesoscopic samples. In multilayered samples the kinked vortex strings are formed owing to the competing interactions of vortices with Meissner currents and the weak-link boundaries. The length and deformation of vortex fragments are determined solely by the inclination and strength of applied magnetic field, and this lock-in does not depend on the degree of anisotropy between the superconducting layers.

Observation of anisotropic diamagnetism above the superconducting transition in iron pnictide Ba1−xKxFe2As2single crystals due to thermodynamic fluctuations

High-resolution magnetization measurements performed in a high-quality Ba${}_{1\ensuremath{-}x}$K${}_{x}$Fe${}_{2}$As${}_{2}$ single crystal allowed to determine the diamagnetism induced above the superconducting transition by thermally activated Cooper pairs. These data, obtained with magnetic fields applied along and transverse to the crystal $\mathit{ab}$ layers, demonstrate experimentally that the superconducting transition of iron pnictides may be explained at a phenomenological level in terms of the Gaussian Ginzburg-Landau approach for three-dimensional anisotropic superconductors.

Andreev spectroscopy and surface density of states for a three-dimensional time-reversal-invariant topological superconductor

A topological superconductor is a fully gapped superconductor that exhibits exotic zero-energy Andreev surface states at interfaces with a normal metal. In this paper we investigate the properties of a three-dimensional time reversal invariant topological superconductor by means of a two-band model with unconventional pairing in both the inter- and intraband channels. Due to the bulk-boundary correspondence the presence of Andreev surface states in this system is directly related to the topological structure of the bulk wavefunctions, which is characterized by a winding number. Using quasiclassical scattering theory we construct the spectrum of the Andreev bound states that appear near the surface and compute the surface density of states for various surface orientations. Furthermore, we consider the effects of band splitting, i.e., the breaking of an inversion-type symmetry, and demonstrate that in the absence of band splitting there is a direct transition between the fully gapped topologically trivial phase and the nontrivial phase, whereas in the presence of band splitting there exists a finite region of a gapless nodal superconducting phase between the fully gapped topologically trivial and nontrivial phases.

Three-dimensional simulation of quasi-particle structures in nano-scaled superconductors

Abstract We have developed numerical simulation method for quasi-particle structures in the three-dimensional nano-sized superconductors, using the three-dimensional finite element method and the Bogoliubov-de Gennes equation. Using this method, we analyzed the superconducting state in the nano-sized cubic superconductors. We found the spatial oscillations of order parameter because of the confinement of superconducting electrons, and also we found the quasi-particle bound states at the corners of the cubic superconductors because of suppression of superconductivity at the corners.

Three-dimensional superconductivity in nominal composition Fe1.03Se with Tczero up to 10.9 K induced by internal strain

Iron selenide with the nominal composition Fe1.03Se was synthesized by a self-flux solution method which shows a zero resistance temperature up to 10.9 K and a Tconset (90% ρn, ρn: normal state resistivity) up to 13.3 K. The residual resistivity ratio RRR=R(300 K)/R0=12. Scanning electron microscopy-EDX study shows that the composition of as grown sample is near stoichiometric FeSe. The decrease in superconducting transition temperature by heat treatment indicates that internal crystallographic strain which plays the same effect as external pressure is the origin of its high Tc. The fluctuation conductivity was studied which could be well described by three-dimensional (3D) Aslamazov–Larkin power law. The estimated value of coherence length ξc=9.2 Å is larger than the distance between conducting layers (∼6.0 Å), indicating the 3D nature of superconductivity in this compound.

Angular dependence of the upper critical field ofSr2RuO4

One of the remaining issues concerning the spin-triplet superconductivity of Sr2RuO4 is the strong limit of the in-plane upper critical field Hc2 at low temperatures. In this study, we clarified the dependence of Hc2 on the angle theta between the magnetic field and the ab plane at various temperatures, by precisely and accurately controlling the magnetic field direction. We revealed that, although the temperature dependence of Hc2 for |theta| > 5 is well explained by the orbital pair-breaking effect, Hc2(T) for |theta| < 5 is clearly limited at low temperatures. We also revealed that the Hc2 limit for |theta| < 5 is present not only at low temperatures, but also at temperatures close to Tc. These features may provide additional hints for clarifying the origin of the Hc2 limit. Interestingly, if the anisotropic ratio in Sr2RuO4 is assumed to depend on temperature, the observed angular dependence of Hc2 is reproduced better at lower temperature with an effective-mass model for an anisotropic three-dimensional superconductor. We discuss the observed behavior of Hc2 based on existing theories.

The fluctuation effect of BaFe1.8Co0.2As2 single crystals from reversible magnetization

We present reversible magnetization measurements for applied fields in therange from 0.5 to 7 T made while varying the temperature for optimally dopedBaFe1.8Co0.2As2 singlecrystals with Tc = 23.6 K. The rounding fluctuating magnetization was observed in the reversible range ofmagnetization for temperatures above 18 K. This fluctuation effect is quite small comparedwith that in high temperature cuprate superconductors, but is still large enough forobtaining the essence of the physical properties in this iron pnictide superconductor. Thisreversible magnetic fluctuation follows a three-dimensional scaling form in thecritical fluctuation region for fields above 0.5 T, which indicates that this ironpnictide superconductor belongs to the class of three-dimensional superconductors.