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 grouptheoretical 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 topo1ogical 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 UPt3 and consider in detail the alloy U& Th Be/3.

Electronic and magnetic properties of ribbon-shaped nanographite systems with zigzag and armchair edges in a magnetic field are investigated by using a tight binding model. One of the most remarkable features of these systems is the appearance of edge states, strongly localized near zigzag edges. The edge state in magnetic field, generating a rational fraction of the magnetic flux (φ = p/q) in each hexagonal plaquette of the graphite plane, behaves like a zero-field edge state with q internal degrees of freedom. The orbital diamagnetic susceptibility strongly depends on the edge shapes. The reason is found in the analysis of the ring currents, which are very sensitive to the lattice topology near the edge. Moreover, the orbital diamagnetic susceptibility is scaled as a function of the temperature, Fermi energy and ribbon width. Because the edge states lead to a sharp peak in the density of states at the Fermi level, the graphite ribbons with zigzag edges show Curie-like temperature dependence of the Pauli paramagnetic susceptibility. Hence, it is shown that the crossover from high-temperature diamagnetic to low-temperature paramagnetic behavior of the magnetic susceptibility of nanographite ribbons with zigzag edges. 73.20At, 81.50.Tp,

In addition to its importance for existing and potential applications, superconductivity [1] is one of the most interesting phenomena in condensed matter physics.Although most superconducting materials are well-described in the context of the Bardeen Cooper and Schrieffer (BCS) theory [2], considerable effort has been devoted to the search for exotic systems whose novel properties cannot be described by the BCS theory. Conventional superconductors break only gauge symmetry by selecting a definite phase for the Cooper pair wavefunction; a signature of an unconventional superconducting state is the breaking of additional symmetries [3].Evidence for such broken symmetries include anisotropic pairing (such as d-wave in the high-T c cuprates) and the presence of multiple superconducting phases (UPt 3 and superfluid 3 He[4]). We have performed muon spin relaxation measurements of Sr 2 RuO 4 and observe a spontaneous internal magnetic field appearing below T c . Our measurements indicate that the superconducting state in Sr 2 RuO 4 is characterized by broken time reversal symmetry which, when combined with symmetry considerations indicate that its superconductivity is of p-wave (odd-parity) type, analagous to superfluid 3 He. Despite the structural similarity with the high T c cuprates, the origin of the unconventional superconductivity in Sr 2 RuO 4 is fundamentally different in nature.Sr 2 RuO 4 , which is isostructural to the high-T c cuprate La 1.85 Sr 0.15 CuO 4 , is to date the only known layered perovskite superconductor which does not contain copper. Although first synthesized in the 50's, [5] its superconductivity was only found in 1994[6]; T c 's of early samples were roughly 0.7 K but have increased to T c = 1.5 K in recent high quality single crystals [7]. Despite its low transition temperature, Sr 2 RuO 4 is of great interest as there is growing evidence for an unconventional superconducting state. In this system, strong correlation effects enhance the effective mass seen in quantum oscillation [8] and Pauli spin susceptibility measurements, in the same way as in 3 He [9]. Combining this feature with Sr 2 RuO 4 's expected tendency to display ferromagnetic spin fluctuations, Rice and Sigrist [10], and later Baskaran [11] argued that the pairing in Sr 2 RuO 4 could be of odd parity (spin triplet) type.The strong suppression of the superconducting T c by even non-magnetic impurities suggests non-s-wave pairing [7]. Specific heat [12] and NMR 1/T 1 [13] measurements indicate the presence of a large residual density of states (RDOS) at low temperatures (well within the superconducting state); in high quality samples, this RDOS as T→ 0 seems to approach half of the normal state value. Several authors [14,15] have proposed so-called non-unitary p-wave superconducting states for Sr 2 RuO 4 to account for this RDOS as well as the absence of a Hebel-Slichter peak in NMR measurements [13]. A finite RDOS is not a unique signature of unconventional superconductivity; for example it is observed in so-called gapless sup...

CePt3Si is a novel heavy fermion superconductor, crystallizing in the CePt3B structure as a tetragonally distorted low symmetry variant of the AuCu3 structure type. CePt3Si exhibits antiferromagnetic order at T(N) approximately 2.2 K and enters into a heavy fermion superconducting state at T(c) approximately 0.75 K. Large values of H(')(c2) approximately -8.5 T/K and H(c2)(0) approximately 5 T refer to heavy quasiparticles forming Cooper pairs. Hitherto, CePt3Si is the first heavy fermion superconductor without a center of symmetry.

SnRuOa is a supercanductor with a similar structure to a high-l; cuprate superconductor. Nevertheless. the superconducting state may have diffemt symmetry than that of cuprate superconductors. Strong Hund's rule coupling favours triplet over singlet pairing, similar to A strong candidate is the odd-parity pairing state which is the two-dimensional analogue of the Baliai-Werthamer state of 3He. Various experimental consequences and tests a x analysed.Recently Cava er a1 [l], while looking for a 4d analogue of the high-T, cuprates, explored the localized to itinerant transition in an alloy series, Sr2Irt,Ru,04, with the same layered perovskite structure as the La~-,Sr,Cu04 compounds. Shortly thereafter Maeno er a1 [2] discovered superconductivity in high-quality crystals of SrzRu04 but with a low value of T, =~0.93 K and contrasted this material with the high-T, cuprates. At present, not much is known in detail about the superconducting state of SrzRu04 and any possible relation to the cuprates. The purpose of this letter is to raise an alternative possibility, namely a close analogy of the electronic superconductor Sr2Ru04 to the triplet superfluid phases of 3He.A lot is known about the electronic bandstructure of Sr~Ru04. Quantum oscillations in high magnetic fields in the normal phase at low temperatures were observed in an elegant series of experiments by Mackenzie et al 131. The Fermi surface consists of three approximately cylindrical pieces in agreement with bandstructure calculations [4]. The oxidation state Rue has four 4d electrons which partially fill the non-bonding tzs subband. Taking z to be parallel to the c axis, we can identify the relevant orbitals as an x y orbital dispersing strongly along k, and ky, ,and ( x z , y z } orbitals which are degenerate at the r point but do not disperse along k, and kr7 respectively. All three bands are occupied at

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The band theory of solids is arguably the most successful theory of condensed matter physics, providing the description of the electronic energy levels in a variety of materials. Electronic wavefunctions obtained from the band theory allow for a topological characterization of the system and the electronic spectrum may host robust, topologically protected fermionic quasiparticles. Many of these quasiparticles are analogs of the elementary particles of the Standard Model, but others do not have a counterpart in relativistic high-energy theories. A full list of possible quasiparticles in solids is still unknown, even in the non-interacting case. Here, we report on a new type of fermionic excitation that appears in metals. This excitation forms a nodal chain -a chain of connected loops in momentum space -along which conduction and valence band touch. We prove that the nodal chain is topologically distinct from any other excitation reported before. We discuss the symmetry requirements for the appearance of this novel excitation and predict that it is realized in an existing material IrF4, as well as in other compounds of this material class. Using IrF4 as an example, we provide a detailed discussion of the topological surface states associated with the nodal chain. Furthermore, we argue that the presence of the novel quasiparticles results in anomalous magnetotransport properties, distinct from those of the known materials.In metallic band structures valence and conduction bands overlap, and a degeneracy can occur between them at points, lines or planes in the Brillouin zone (BZ). In some cases, the degeneracies are stable against perturbations because their existence is protected by a topological invariant. If such degeneracies occur close to the Fermi level, also the low energy excitations of the metal are topologically protected [1]. This is the case in Weyl (Dirac) metals [2][3][4][5][6][7][8][9][10][11][12], where a topologically protected degeneracy of two (four) bands occurs at isolated points in the BZ [13][14][15][16][17][18][19]. Remarkably, these materials exhibit the chiral anomaly [20][21][22][23][24] and topological surface Fermi arcs [10, 11, 14, 25, 26], while their low energy quasiparticle excitations correspond to Weyl (Dirac) fermions of the quantum field theory.Topological metals can also host elementary excitations that do not have a direct analog in relativistic field theories [27][28][29][30][31][32][33][34][35][36][37][38][39]. For example, in Weyl nodal line (NL) metals [29][30][31][32], two bands are degenerate along a line in the BZ. In the presence of spin-orbit coupling, this NL, referred to as an accidental NL (ANL) in the following, occurs on mirror-symmetric planes and is formed by crossing bands of opposite mirror-symmetry eigenvalue. The ANL materials are predicted to host flat topological drumhead states [30,40], which were argued to provide a route to higher-temperature superconductivity [41]. Given the variety of striking physical phenomena emerging from topological excitations i...