Generalized Ginzburg-Landau Theory Research Articles

The supercurrent diode effect and nonreciprocal paraconductivity due to the chiral structure of nanotubes

The phenomenon that critical supercurrents along opposite directions become unequal is called the supercurrent diode effect (SDE). It has been observed in various systems and can often be understood by combining spin-orbit coupling and Zeeman field, which break the spatial-inversion and time-reversal symmetries, respectively. Here, we theoretically investigate another mechanism of breaking these symmetries and predict the existence of the SDE in chiral nanotubes without spin-orbit coupling. The symmetries are broken by the chiral structure and a magnetic flux through the tube. With a generalized Ginzburg-Landau theory, we obtain the main features of the SDE in its dependence on system parameters. We further show that the same Ginzburg-Landau free energy leads to another important manifestation of the nonreciprocity in superconducting systems, i.e., the nonreciprocal paraconductivity (NPC) slightly above the transition temperature. Our study suggests a new class of realistic platforms to investigate nonreciprocal properties of superconducting materials. It also provides a theoretical link between the SDE and the NPC, which were often studied separately.

Symmetry analysis of odd- and even-frequency superconducting gap symmetries for time-reversal symmetric interactions

Odd-frequency superconductivity describes a class of superconducting states where the superconducting gap is an odd function in relative time and Matsubara frequency. We present a group theoretical analysis based on the linearized gap equation in terms of Shubnikov groups of the second kind. By discussing systems with spin-orbit coupling and an interaction kernel which is symmetric under the reversal of relative time, we show that both even- and odd-frequency gaps are allowed to occur. Specific examples are discussed for the square lattice, the octahedral lattice, and the tetragonal lattice. For irreducible representations that are even under reversal of relative time the common combinations of $s$- and d-wave spin singlet and p-wave spin triplet gaps are revealed, irreducible representations that are odd under reversal of relative time give rise to $s$- and d-wave spin triplet and p-wave spin singlet gaps. Furthermore, we discuss the construction of a generalized Ginzburg-Landau theory in terms of the associated irreducible representations. The result complements the established classification of superconducting states of matter.

Novel Lifshitz point for chiral transition in the magnetic field

Based on the generalized Ginzburg–Landau theory, chiral phase transition is discussed in the presence of magnetic field. Considering the chiral density wave we show that chiral anomaly gives rise to an inhomogeneous chiral phase for nonzero quark-number chemical potential. Novel Lifshitz point appears on the vanishing chemical potential line, which may be directly explored by the lattice QCD simulation.

Sharp existence theorems for multiple vortices induced from magnetic impurities

In a recent work Tong and Wong derived self-dual equations governing multiple vortices in a product Abelian Higgs model which may be regarded as a generalized Ginzburg–Landau theory. The purpose of this paper is to establish some sharp existence and uniqueness theorems for these multiple vortex solutions in a doubly periodic domain and on the full plane using the methods of calculus of variations.

Temperature dependence of the anisotropy parameter of the LiFeAs upper critical field in the two-band Ginzburg-Landau theory

An analytical formula is obtained for the temperature dependence of the anisotropy parameter of the upper critical field of a two-band superconductor in the context of the generalized Ginzburg-Landau theory for layered superconductors. The theoretical results are compared with the experimental data for new superconductor LiFeAs.

Role of electronic nematicity in the interplay between s- and d-wave broken-symmetry states

To understand the role of electronic nematic order in the interplay between s- and d-wave particle–particle or particle–hole condensate states, relations between various s- and d-wave order parameters are studied. We find that the nematic operator transforms two independent six-dimensional vectors. The d-wave superconducting, d-density wave, and antiferromagnetic orders are organized into one vector, and the s-wave superconducting, charge density wave, and spin-triplet d-density wave orders into the other vector. Each vector acts as a superspin and transforms under the action of SO(6) where charge, spin, η- and π-pairing, spin-triplet nematic operators satisfy the SO(6) Lie algebra. Electronic nematic order is not a part of the SO(6) group. It commutes with all 15 generators. Our findings imply that nematic order does not affect the competition among the order parameters within the same superspin, while it strongly interferes the interplay between two order parameters that belong to different superspins. For example, nematicity allows a linear coupling between d- and s-wave superconducting order parameters which modifies the superconducting transition temperature. A generalized Ginzburg-Landau theory and further physical implications are discussed.

Asymptotic local moment formation in the Kondo lattice

A generalized Ginzburg-Landau theory is applied to the Kondo lattice model, taking account of all the modes of static thermal fluctuations of Kondo bosons in the mean mode-mode coupling approximation. The high-temperature asymptotic behaviors of thermodynamic quantities are determined. The result of magnetic susceptibility suggests that the local moments in the Kondo lattice are asymptotically free at high temperatures, similarly to the impurity Kondo system. We also discuss the possible smooth crossover to the low-temperature heavy-fermion state.

Lower pseudogap phase of Mott insulators: A spin/vortex liquid state

The pseudogap phase is considered to be a new state of matter in the phase string model of the doped Mott insulator, which is composed of two distinct regimes known as the upper and lower pseudogap phases, respectively. The former corresponds to the formation of spin-singlet pairing, the magnetic characterizations of which have been recently studied [Phys. Rev. B 72, 104520 (2005)]. The latter, as a low-temperature regime of the pseudogap phase, is systematically explored in this work, which is characterized by the formation of the Cooper pair amplitude and described by a generalized Ginzburg-Landau theory. Elementary excitation in this phase is a charge-neutral object carrying spin-$1∕2$ and locking with a supercurrent vortex, known as a spinon-vortex composite. Such a lower pseudogap phase can be regarded as a vortex liquid state due to the presence of free spinon vortices. Here thermally excited spinon vortices destroy the phase coherence and are responsible for the nontrivial Nernst effect and diamagnetism. The transport entropy and core energy associated with a spinon vortex are determined by the spin degrees of freedom. Such a spontaneous vortex liquid phase can be also considered as a spin liquid with a finite correlation length and gaped $S=1∕2$ excitations, where a resonancelike nonpropagating spin mode emerges at the antiferromagnetic wavevector $(\ensuremath{\pi},\ensuremath{\pi})$ with a doping-dependent characteristic energy. The superconducting phase is closely related to the lower pseudogap phase by a topological transition with spinon vortices and antivortices forming bound pairs and the emergence of fermionic quasiparticles as holon-spinon-vortex bound objects. A quantitative phase diagram in the parameter space of doping, temperature, and magnetic field is determined. Comparisons with experiments are also made.

Nearly ferromagnetic superconductors: Electromagnetic properties studied by a generalized Ginzburg-Landau theory

The electromagnetic properties of superconductors near a ferromagnetic instability are investigated by means of a generalized Ginzburg-Landau theory. It is found that the magnetic flux expulsion capability of the superconductor gets stronger, in a well-defined sense, as the normal-state magnetic susceptibility increases. The temperature dependencies of the London penetration depth, the critical fields, and the critical current are all strongly affected by ferromagnetic fluctuations. In particular, for the critical current we find a temperature exponent alpha ~ 2 over an appreciable temperature range. The extent to which proximity to magnetic criticality may be a viable explanation for recent observations in MgCNi microfibers, which find alpha ~ 2, is discussed.

Spontaneous Hall effect in a chiralp-wave superconductor

In a chiral superconductor with broken time-reversal symmetry a ``spontaneous Hall effect'' may be observed. We analyze this phenomenon by taking into account the surface properties of a chiral superconductor. We identify two main contributions to the spontaneous Hall effect. One contribution originates from the Bernoulli (or Lorentz) force due to spontaneous currents running along the surfaces of the superconductor. The other contribution has a topological origin and is related to the intrinsic angular momentum of Cooper pairs. The latter can be described in terms of a Chern-Simons-like term in the low-energy field theory of the superconductor and has some similarities with the quantum Hall effect. The spontaneous Hall effect in a chiral superconductor is, however, nonuniversal. Our analysis is based on three approaches to the problem: a self-consistent solution of the Bogoliubov--de Gennes equation, a generalized Ginzburg-Landau theory, and a hydrodynamic formulation. All three methods consistently lead to the same conclusion that the spontaneous Hall resistance of a two-dimensional superconducting Hall bar is of order ${h/(ek}_{F}\ensuremath{\lambda}{)}^{2},$ where ${k}_{F}$ is the Fermi wave vector and $\ensuremath{\lambda}$ is the London penetration depth; the Hall resistance is substantially suppressed from a quantum unit of resistance. Experimental issues in measuring this effect are briefly discussed.

A generalized Ginzburg-Landau approach to second harmonic generation

We develop a generalized Ginzburg-Landau theory for second harmonic generation (SHG) in magnets by expanding the free energy in terms of the order parameter in the magnetic phase and the susceptibility tensor in the corresponding high-temperature phase. The non-zero components of the SHG susceptibility in the ordered phase are derived from the symmetries of the susceptibility tensor in the high-temperature phase and the symmetry of the order parameter. In this derivation, the dependence of the SHG susceptibility on the order parameter follows naturally, and therefore its nonreciprocal optical properties. We examine this phenomenology for the magnetoelectric compound Cr$_2$O$_3$ as well as for the ferroelectromagnet YMnO$_3$.

The Competition between the 0- and -Phase Shift in the Pb-Sr2RuO4-Pb Junction

Recent measurements of the Josephson effect between two Ph-films via Sr2Ru04 show a very anomalous temperature dependence of the maximal supercurrent. In this article we show that this result is consistent with the assumption of (spin-triplet) odd-parity pairing. Using a generalized Ginzburg-Landau theory for the specific geometry of the experimental device, it is shown that there are two contributions to the Josephson current. One is due to a proximity-induced s-wave component in Sr2 Ru04, and the other is due to the intrinsic odd­ parity order parameter. These two components have opposite sign and lead to a competition below the onset of superconductivity in Sr2Ru04 yielding the anomalous properties. Two possible test experiments for this kind of scenario are proposed. 53

Phase Fluctuations and Kosterlitz-Thouless Transition in Two-Dimensional Fulde-Ferrell-Larkin-Ovchinnikov Superconductors

Effects of the phase fluctuations of the order parameter on the stability of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states are examined in exactly two-dimensional (2D) type-II superconductors with cylindrically symmetric Fermi surface on the basis of a generalized Ginzburg-Landau theory. It is found that for the FFLO states with oscillations in a single direction, not only the long-range order but also quasi-long-range order (QLRO), which is characterized by a power law decay of the order parameter correlation function, is suppressed by the phase fluctuations at any finite temperatures. On the other hand, for the FFLO states with order parameter structures such as triangular and square lattices, it is shown that the QLRO is possible as the uniform BCS state. Systems with anisotropy in the Fermi surface and pairing are also discussed.

Time-Reversal Symmetry Breaking at Grain Boundaries in d-Wave Superconductors

Crystal lattice distortion can generate a superconducting state which breaks locally time-reversal symmetry by yielding a coupling between order parameters of different symmetry. The problem of a twist in the crystal lattice at a boundary between differently oriented grains is investigated by means of a generalized Ginzburg–Landau theory. It is shown that under certain conditions a time-reversal breaking state appears at the grain boundary. This state leads to a nontrivial phase shift in the Josephson effect across the grain boundary. This phase shift can be observed through a modified flux quantization (fractional fluxes) and phase slip effects.

About the local Curie temperature distribution of Invar alloys

Strongly disordered ferromagnetic alloys which exhibit magnetic inhomogeneities are described in the frame of a generalized Ginzburg-Landau theory by averaging the Ginzburg-Landau energy of a subsystem with a definite Curie temperature over the Curie temperature of all subsystems of the inhomogeneous magnetic system. It is shown that this leads to the rough scaling of a smooth phase transition. Furthermore the distribution function of the Curie temperature is derived from the experimental data of the specific heat, the volume thermal expansion coefficient and the compressibility.

Generalized Ginzburg-Landau theory for nonuniform FFLO superconductors

We derive a generalized Ginzburg-Landau (GL) functional near the tricritical point in the ( T, H)-phase diagram for the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting state, in one, two, and three dimensions. We find that the transition from the normal to the FFLO state is of second order in one and two dimensions, and the order parameter with one-coordinate sine modulation corresponds to the lowest energy near the transition line. We also compute the jump of the specific heat and describe in the one-dimensional case the transformation of the sine modulation into the soliton-lattice state as the magnetic field decreases. In three dimensions however, we find that the transition into an FFLO state is of first order, and it is impossible to obtain an analytic expression for the critical temperature. In this case the generalized GL functional proposed here provides a suitable basis for a numerical study of the properties of the FFLO state, and in particular for computing the critical temperature, and for describing the transition into a uniform state.

DEFORMABLE SUPERCONDUCTORS: A RENORMALIZATION GROUP APPROACH

Deformable superconductors, i.e., superconductors with structural instabilities are considered as a model for high T c , superconductors. A generalized Ginzburg-Landau theory is studied by renormalization group theory. The fixed points and their stability properties are discussed using the ∊ analysis.

Generalized Ginzburg-Landau theory for a spin glass superconductor

A generalized Ginzburg-Landau theory for a spin glass superconductor, based on a free energy functional depending on superconducting and spin glass order parameters, is presented. It is found that the coupling between the superconducting and spin glass order assists in freezing of spins by enhancing the spin glass order parameter but acts as pair breaking effect for superconducting order by decreasing the superconducting order parameter. Analytical expressions for several thermodynamic and electromagnetic quantities are obtained. All these quantities show either cusps or discontinuities at the superconducting and /or spin glass transition temperatures.

Effective Hamiltonian and generalized Ginzburg–Landau theory

We propose an effective Hamiltonian for the Ginzburg–Landau theory of a superconductor at rest. This yields the ordinary, and a time-dependent generalized Ginzburg–Landau theory. Then we generalize the Hamiltonian and derive a generalized Ginzburg–Landau theory for non-uniformly moving superconductors. We show that the fluxoid in a singly connected rotating superconductor is quantized.

Phenomenological theory of unconventional superconductivity

This article is a review of recent developments in the phenomenological description of unconventional superconductivity. Starting with the BCS theory of superconductivity with anisotropic Cooper pairing, the authors explain the group-theoretical derivation of the generalized Ginzburg-Landau theory for unconventional superconductivity. This is used to classify the possible superconducting states in a system with given crystal symmetry, including strong-coupling effects and spin-orbit interaction. On the basis of the BCS theory the unusual low-temperature properties and the (resonant) impurity scattering effects are discussed for superconductors with anisotropic pairing. Using the Ginzburg-Landau theory, the authors study several bulk properties of such superconductors: spontaneous lattice distortion, upper critical magnetic field, splitting of a phase transition due to uniaxial stress. Two possible mechanisms for ultrasound absorption are discussed: collective modes and damping by domain-wall motion. The boundary conditions for the Ginzburg-Landau theory are derived from a correlation function formulation and by group-theoretical methods. They are applied to a study of the Josephson and proximity effects if unconventional superconductors are involved there. The magnetic properties of superconductors that break time-reversal symmetry are analyzed. Examples of current and magnetic-field distributions close to inhomogeneities of the superconducting order parameter are given and their physical origin is discussed. Vortices in a superconductor with a multicomponent order parameter can exhibit various topological structures. As examples the authors show fractional vortices on domain walls and nonaxial vortices in the bulk. Furthermore, the problem of the possible coexistence of a superconducting and a magnetically ordered phase in an unconventional superconductor is analyzed. The combination of two order parameters that are almost degenerate in their critical temperature is considered with respect to the phase-transition behavior and effects on the lower and upper critical fields. Because heavy-fermion superconductors---which are possible realizations of unconventional superconductivity---have been the main motivation for the phenomenological studies presented here, the authors compare the theoretical results with the experimental facts and data. In particular, they emphasize the intriguing features of the compound U${\mathrm{Pt}}_{3}$ and consider in detail the alloy ${\mathrm{U}}_{1\ensuremath{-}x}{\mathrm{Th}}_{x}{\mathrm{Be}}_{13}$.