Phenomenological theory of unconventional superconductivity
TL;DR: In this paper, a review of recent developments in the phenomenological description of unconventional superconductivity is presented, starting with the BCS theory of superconductivities with anisotropic Cooper pairing, and the group-theoretical derivation of the generalized Ginzburg-Landau theory for unconventional supercondivity.
Abstract: 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 ${\mathrm{U}}_{1\ensuremath{-}x}{\mathrm{Th}}_{x}{\mathrm{Be}}_{13}$.
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TL;DR: In this paper, a summary and evaluation of the experimental properties of spin-triplet superconductivity in a quasi-two-dimensional Fermi liquid is presented. But the authors do not consider the effect of symmetry-breaking magnetic fields on the phase diagram.
Abstract: This review presents a summary and evaluation of the experimental properties of unconventional superconductivity in ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ as they were known in the spring of 2002. At the same time, the paper is intended to be useful as an introduction to the physics of spin-triplet superconductivity. First, the authors show how the normal-state properties of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ are quantitatively described in terms of a quasi-two-dimensional Fermi liquid. Then they summarize its phenomenological superconducting parameters in the framework of the Ginzburg-Landau model, and discuss the existing evidence for spin-triplet pairing. After a brief introduction to the vector order parameter, they examine the most likely symmetry of the triplet state. The structure of the superconducting energy gap is discussed, as is the effect of symmetry-breaking magnetic fields on the phase diagram. The article concludes with a discussion of some outstanding issues and desirable future work. Appendixes on additional details of the normal state, difficulty in observing the bulk Fermi surface by angle-resolved photoemission, and the enhancement of superconducting transition temperature in a two-phase ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}\ensuremath{-}\mathrm{Ru}$ system are included.
1,573 citations
TL;DR: A detailed review of the superconductivity of FePnictide and chalcogenide (FePn/Ch) superconductors can be found in this paper.
Abstract: Kamihara and coworkers' report of superconductivity at ${T}_{c}=26\text{ }\text{ }\mathrm{K}$ in fluorine-doped LaFeAsO inspired a worldwide effort to understand the nature of the superconductivity in this new class of compounds. These iron pnictide and chalcogenide (FePn/Ch) superconductors have Fe electrons at the Fermi surface, plus an unusual Fermiology that can change rapidly with doping, which lead to normal and superconducting state properties very different from those in standard electron-phonon coupled ``conventional'' superconductors. Clearly, superconductivity and magnetism or magnetic fluctuations are intimately related in the FePn/Ch, and even coexist in some. Open questions, including the superconducting nodal structure in a number of compounds, abound and are often dependent on improved sample quality for their solution. With ${T}_{c}$ values up to 56 K, the six distinct Fe-containing superconducting structures exhibit complex but often comparable behaviors. The search for correlations and explanations in this fascinating field of research would benefit from an organization of the large, seemingly disparate data set. This review provides an overview, using numerous references, with a focus on the materials and their superconductivity.
1,349 citations
TL;DR: In this paper, a review of the physics of spin liquid states is presented, including spin-singlet states, which may be viewed as an extension of Fermi liquid states to Mott insulators, and they are usually classified in the category of SU(2), U(1), or Z2.
Abstract: This is an introductory review of the physics of quantum spin liquid states. Quantum magnetism is a rapidly evolving field, and recent developments reveal that the ground states and low-energy physics of frustrated spin systems may develop many exotic behaviors once we leave the regime of semiclassical approaches. The purpose of this article is to introduce these developments. The article begins by explaining how semiclassical approaches fail once quantum mechanics become important and then describe the alternative approaches for addressing the problem. Mainly spin-1/2 systems are discussed, and most of the time is spent in this article on one particular set of plausible spin liquid states in which spins are represented by fermions. These states are spin-singlet states and may be viewed as an extension of Fermi liquid states to Mott insulators, and they are usually classified in the category of so-called SU(2), U(1), or Z2 spin liquid states. A review is given of the basic theory regarding these states and the extensions of these states to include the effect of spin-orbit coupling and to higher spin (S>1/2) systems. Two other important approaches with strong influences on the understanding of spin liquid states are also introduced: (i) matrix product states and projected entangled pair states and (ii) the Kitaev honeycomb model. Experimental progress concerning spin liquid states in realistic materials, including anisotropic triangular-lattice systems [κ-(ET)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2], kagome-lattice system [ZnCu3(OH)6Cl2], and hyperkagome lattice system (Na4Ir3O8), is reviewed and compared against the corresponding theories.
1,108 citations
Cites background from "Phenomenological theory of unconven..."
...To determine the pairing symmetry, Zhou et al. noted that a group theoretical analysis indicates that a spin-triplet pairing state on a cubic lattice can create only full or point nodal gaps (Sigrist and Ueda, 1991), which seems to imply singlet pairing....
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TL;DR: In this article, the authors provide a theoretical basis for understanding the current phase relation (CPhiR) for the stationary Josephson effect in various types of superconducting junctions.
Abstract: This review provides a theoretical basis for understanding the current-phase relation (CPhiR) for the stationary (dc) Josephson effect in various types of superconducting junctions The authors summarize recent theoretical developments with an emphasis on the fundamental physical mechanisms of the deviations of the CPhiR from the standard sinusoidal form A new experimental tool for measuring the CPhiR is described and its practical applications are discussed The method allows one to measure the electrical currents in Josephson junctions with a small coupling energy as compared to the thermal energy A number of examples illustrate the importance of the CPhiR measurements for both fundamental physics and applications
1,084 citations
TL;DR: In this paper, the relation between topological superconductivity and Majorana fermions is explained, and the difference between dispersive Majorana Fermions and a localized Majorana zero mode is emphasized.
Abstract: This review elaborates pedagogically on the fundamental concept, basic theory, expected properties, and materials realizations of topological superconductors. The relation between topological superconductivity and Majorana fermions are explained, and the difference between dispersive Majorana fermions and a localized Majorana zero mode is emphasized. A variety of routes to topological superconductivity are explained with an emphasis on the roles of spin-orbit coupling. Present experimental situations and possible signatures of topological superconductivity are summarized with an emphasis on intrinsic topological superconductors.
1,024 citations