Nonuniform Superconducting State Research Articles

Nonuniform superconducting state in an antiferromagnetic superconductor

We consider the superconducting state in a clean crystal with antiferromagnetic (AF) structure of localized magnetic moments taking into account the exchange interaction between magnetic moments and conduction electrons. We assume that the localized moments order at the Neel temperature ${T}_{N}$ due to the RKKY interaction predominantly. In such crystals, the periodic exchange field acting on conducting electrons results in the formation of an insulating gap on the Fermi surface for electrons moving in directions that depend on the orientation of the wave vector of AF ordering. We assume a scenario in which the Cooper pairing occurs in the open parts of the Fermi surface at the temperature ${T}_{c}$. We show that at high amplitudes of exchange field ${h}_{e}g{T}_{c}/{\ensuremath{\mu}}_{B}$, the structure of superconducting state just below the temperature ${T}_{c}$ depends on the relation between ${T}_{c}$ and ${T}_{N}$. At low ratio ${T}_{c}/{T}_{N}$, a nonuniform superconducting state, like the Fulde-Farrell-Larkin-Ovchinnikov high-field phase, should exist, while at bigger ratio superconducting order parameter is uniform. The nonuniform structure of superconducting state may be probed by tunneling measurements.

Theory of Unusual Superconducting Phase Transitions in Heavy Fermion Metals at High Magnetic Fields

We present a non-perturbative theory of paramagnetically-driven superconducting (SC) phase transitions in heavy-fermion metals, which reliably determines their stable SC phases, treats properly the corresponding finite jumps of the order parameter, and can account for unusual features reported recently for this type of materials. It is found that for quasi-2D heavy-fermion metals, such as CeCoIn5, at high magnetic fields oriented perpendicular to the highly conducting planes, the effect of the Fulde-Ferrel (FF) modulation is too weak to prevent a direct first-order phase transition from the normal to the uniform SC state. For 3D heavy-fermion metals, such as URu2Si2, the FF modulation stabilizes, under a decreasing magnetic field, a non-uniform SC state via a second-order phase transition from the normal state. However, at a slightly lower field the modulated phase becomes unstable, transforming to a uniform SC state via a first-order transition.

Anomalous ( H, T) phase diagram in bilayered superconducting systems

We demonstrate that in a superconducting multilayered system with alternating interlayer coupling a new type of nonuniform superconducting state can be realized under in-plane magnetic field. The Zeeman effect in this state is compensated by the energy splitting between bonding and antibonding levels. At low temperature such compensation mechanism leads to the field-induced superconductivity. We discuss the choice of the optimal coupling between the layers in order to observe the predicted phenomena in experiments.

Nonuniform Spin Triplet Superconductivity due to Antisymmetric Spin–Orbit-Coupling in Noncentrosymmetric Superconductor CePt3Si

We show that the nonuniform state [Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state] of the spin triplet superconductivity in noncentrosymmetric systems is stabilized by antisymmetric spin–orbit coupling even if the magnetic field is absent. The transition temperature of the spin triplet superconductivity is reduced by the antisymmetric spin–orbit coupling in general. This pair breaking effect is shown to be similar to the Pauli pair breaking effect due to magnetic field for the spin singlet superconductivity, in which FFLO state is stabilized near the Pauli limit (or Chandrasekhar–Clogston limit) of external magnetic field. Since there are gapless excitations in nonuniform superconducting state, some physical quantities such as specific heat and penetration depth should obey different temperature-dependences from those in the uniform superconductivity. We discuss the possibility of the realization of nonuniform state in CePt 3 Si.

Field-Induced Superconductivity with an Enhanced and Tunable Paramagnetic Limit

We demonstrate that in a superconducting multilayered system with alternating interlayer coupling a new type of nonuniform superconducting state can be realized under an in-plane magnetic field. The Zeeman effect in this state is compensated by the energy splitting between bonding and antibonding levels. At low temperature such a compensation mechanism leads to field-induced superconductivity. We discuss the conditions for the experimental observation of the predicted phenomena.

Fluctuation-Driven First-Order Transition in Pauli-Limitedd-Wave Superconductors

We study the phase transition between the normal and nonuniform (Fulde-Ferrell-Larkin-Ovchinnikov) superconducting state in quasi-two-dimensional d-wave superconductors at finite temperature. We obtain an appropriate Ginzburg-Landau theory for this transition, in which the fluctuation spectrum of the order parameter has a set of minima at nonzero momenta. The momentum shell renormalization group procedure combined with epsilon expansion is then applied to analyze the phase structure of the theory. We find that all fixed points have more than one relevant direction, indicating the transition is of the fluctuation-driven first-order type for this universality class.

Huge metastability in high-Tcsuperconductors induced by parallel magnetic field

We present a study of the temperature-magnetic field phase diagram of homogeneous and inhomogeneous superconductivity in the case of a quasi-two-dimensional superconductor with an extended saddle point in the energy dispersion under a parallel magnetic field. At low temperature, a huge metastability region appears, limited above by a steep superheating critical field (H_sh) and below by a strongly reentrant supercooling field (H_sc). We show that the Pauli limit (H_p) for the upper critical magnetic field is strongly enhanced due to the presence of the Van Hove singularity in the density of states. The formation of a non-uniform superconducting state is predicted to be very unlikely.

Peculiar vortex structures in Fulde-Ferrell-Larkin-Ovchinnikov phase

A long time ago, it was predicted by Larkin and Ovchinnikov and Fulde and Ferrell that the non-uniform superconducting state (FFLO state) must appear in the magnetic field acting on the electron spins. Up to now, there have been no unambiguous experimental proofs in the favour of this state observation. We discuss the unusual properties of such a state, which can permit its identification. It is demonstrated that in 2D (or quasi 2D) superconductors the FFLO state leads to an appearance of a very special oscillatory - like dependence of the upper critical field versus the angle with the respect to the layers. The new solutions, corresponding to the higher Landau level functions are realized, and the vortex lattice structures are quite exotic. Corresponding vortex states reveal the zeros of superconducting order parameter with high winding numbers. The predicted quasi-oscillatory angular and temperature dependence of Bc2, as well as a cascade of first order transitions must permit the unambiguous identification of mysterious FFLO state. Very recently the magnetic-field-induced superconductivity has been observed in the quasi two-dimensional (2d) organic conductor (BETS)2FeCI4 which is an excellent candidate for the observation of the discussed effects.

Stationary-phase slip state in quasi-one-dimensional rings

The nonuniform superconducting state in a ring in which the order parameter vanishing at one point is studied. This state is characterized by a jump of the phase by $\pi$ at the point where the order parameter becomes zero. In uniform rings such a state is a saddle-point state and consequently unstable. However, for non-uniform rings with e.g. variations of geometrical or physical parameters or with attached wires this state can be stabilized and may be realized experimentally.

Influence of the nonuniform superconductivity on the upper critical field in the extended saddle-point model

The upper critical field is calculated in the framework of the extended saddle-point model, taking into account the formation of a nonuniform superconducting state. The temperature dependence of the upper critical field is characterized by a positive curvature at all temperatures. This peculiar behavior may be of some relevance to the experimental data on low-dimensional superconductors and overdoped ${\mathrm{Tl}}_{2}{\mathrm{Ba}}_{2}{\mathrm{CuO}}_{6}$ single crystals.

Possible pseudogap behavior of electron-doped high-temperature superconductors

We have measured the low-energy quasiparticle excitation spectrum of the electron doped high-temperature superconductors (HTS) Nd(1.85)Ce(0.15)CuO(4-y) and Pr(1.85)Ce(0.15)CuO(4-y) as a function of temperature and applied magnetic field using tunneling spectroscopy. At zero magnetic field, for these optimum doped samples no excitation gap is observed in the tunneling spectra above the transition temperature Tc. In contrast, below Tc for applied magnetic fields well above the resistively determined upper critical field, a clear excitation gap at the Fermi level is found which is comparable to the superconducting energy gap below Tc. Possible interpretations of this observation are the existence of a normal state pseudogap in the electron doped HTS or the existence of a spatially non-uniform superconducting state.

Triplet electron pairing and anisotropic spin susceptibility in organic superconductors(TMTSF)2X

We argue that (TMTSF)_2 PF_6 compound under pressure is likely a triplet superconductor with a vector order parameter d(k) \equiv (d_a(k) \neq 0, d_c(k) = ?, d_{b'}(k) = 0); |d_a(k)| > |d_c(k)|. It corresponds to an anisotropic spin susceptibility at T=0: \chi_{b'} = \chi_0, \chi_a \ll \chi_0, where \chi_0 is its value in a metallic phase. [The spin quantization axis, z, is parallel to a so-called b'-axis]. We show that the suggested order parameter explains why the upper critical field along the b'-axis exceeds all paramagnetic limiting fields, including that for a nonuniform superconducting state, whereas the upper critical field along the a-axis (a \perp b') is limited by the Pauli paramagnetic effects [I. J. Lee, M. J. Naughton, G. M. Danner and P. M. Chaikin, Phys. Rev. Lett. 78, 3555 (1997)]. The triplet order parameter is in agreement with the recent Knight shift measurements by I. J. Lee et al. as well as with the early results on a destruction of superconductivity by nonmagnetic impurities and on the absence of the Hebel-Slichter peak in the NMR relaxation rate.

Nonuniform superconductivity due to the orbital magnetic effect in a d-wave superconductor in a magnetic field.

A type-II superconductor with d-wave pairing interactions with anisotropy due to the crystal lattice is studied. A kind of nonuniform superconductivity due to the orbital magnetic effect with a spatially oscillating order parameter is found to occur under appropriate conditions on the coupling constants and the direction of the magnetic field. It is found that the state depends on the direction of the magnetic field strongly. The spin magnetic effect on this nonuniform superconducting state is also examined. The relevance to the recent experimental result in heavy fermion ${\mathrm{UPd}}_{2}$${\mathrm{Al}}_{3}$ system is discussed. \textcopyright{} 1996 The American Physical Society.

Strong coupling effects on the upper critical field of the heavy-fermion superconductor UBe13

The upper critical fieldH c2 (T) of a high quality single crystal of UBe13 is studied with very low noise resistivity measurements. It shows a large but finite slope of —45 T/K, an unusual temperature dependence with an inflexion point atT/T C ∼ 0.5 and a large saturated limit forT→ 0 ofH c2 (0) = 14 T. The complete temperature dependence ofH c2 (T) can be described by a simple model of strong coupling superconductor, assuming a full Pauli limitation and the occurence of a non-uniform superconducting state (FFLO state) at low temperature.

Recent issues in the physics of heavy fermion materials

The basic properties of heavy fermion materials are briefly summarized. Several recent issues in the physics of heavy fermion materials are discussed, including the unconventional superconductivity of UPt 3, non Fermi liquid behavior in strongly correlated f-electron systems, and the possible observation of the Fulde-Ferrel-Larkin-Ovchinnikov spatially nonuniform superconducting state.

Anisotropy of the upper critical field in URu 2Si 2 and FFLO state in antiferromagnetic superconductors

Experimental data of the upper critical field of the heavy-fermion superconductor URu 2Si 2 are analysed, in the clean limit, taking account of both orbital and Pauli limits. A discussion on the possible existence of a non-uniform superconducting state expected in clean Pauli-limited superconductors (FFLO state) follows. We also present calculations determining the influence of an AF ground state on the existence of such a non-uniform superconducting state.

Possible formation of a nonuniform superconducting state in the heavy-fermion compound UPd2Al3.

Thermal expansion and magnetostriction measurements on single crystalline ${\mathrm{UPd}}_{2}$${\mathrm{Al}}_{3}$, a very clean, strongly Pauli-limited, heavy-fermion superconductor (${\mathit{T}}_{\mathit{c}}$\ensuremath{\simeq}1.82 K), have been utilized to establish a first-order transition at T\ensuremath{\le}T\ifmmode \tilde{}\else \~{}\fi{}\ensuremath{\simeq}1.5 K and B${\mathit{B}}_{\mathit{c}2}$(T). This is ascribed to the hitherto unobserved formation of a nonuniform superconducting state, as pedicted theoretically in 1963.

Effects of impurities on the nonuniform state in layered superconductors

The possibility of the existence of a nonuniform state is investigated, and the nature of the phase transition is determined in layered superconductors with Josephson-like interlayer coupling as a function of sample purity and temperature for a field parallel to the layers. The dependence of the upper critical field HK2(‖) on temperature and electron mean free path within the layers is obtained. At temperatures T < 0.55 Tc, it is shown that depending on the purity of the superconductor and the temperature, either a second-order phase transition into a nonuniform superconducting state or a first-order transition into a uniform superconducting state is observed in layered superconductors with Josephson interlayer coupling for a field parallel to the layers.