Field dependence of the ground state in the exotic superconductor CeCoIn5: a nuclear magnetic resonance investigation

We report 115In nuclear magnetic resonance (NMR) measurements in CeCoIn5 at low temperature (T approximately 70 mK) as a function of the magnetic field (H0) from 2 to 13.5 T applied perpendicular to the c axis. A NMR line shift reveals that below 10 T the spin susceptibility increases as sqrt[H0]. We associate this with an increase of the density of states due to the Zeeman and Doppler-shifted quasiparticles extended outside the vortex cores in a d-wave superconductor. Above 10 T a new superconducting state is stabilized, possibly the modulated phase predicted by Fulde, Ferrell, Larkin, and Ovchinnikov. This phase is clearly identified by a strong and linear increase of the NMR shift with the field, before a jump at the first order transition to the normal state.     

Calorimetric evidence for a Fulde-Ferrell-Larkin-Ovchinnikov superconducting state in the layered organic superconductor kappa-(BEDT-TTF)2Cu(NCS)2

The specific heat of the layered organic superconductor kappa-(BEDT-TTF)(2)Cu(NCS)(2), where BEDT-TTF is bisethylenedithio-tetrathiafulvalene, has been studied in magnetic fields up to 28 T applied perpendicular and parallel to the superconducting layers. In parallel fields above 21 T, the superconducting transition becomes first order, which signals that the Pauli-limiting field is reached. Instead of saturating at this field value, the upper-critical-field increases sharply and a second first-order transition line appears within the superconducting phase. Our results give strong evidence that the phase, which separates the homogeneous superconducting state from the normal state is a realization of a Fulde-Ferrell-Larkin-Ovchinnikov state.     

Two-phase regime in the magnetic field–temperature phase diagram of a type-II superconductor

The magnetic field and temperature dependencies of the magnetic moments of superconducting crystals of V₃Si have been studied. In a constant magnetic field and at temperatures somewhat below the superconducting transition temperature, the moments are hysteretic in temperature. However, the magnetic moment–magnetic field isotherms are reversible and exhibit features that formally resemble the pressure–volume isotherms of the liquid–gas transition. This suggests the existence of a first-order phase transition, a two-phase regime, and a critical point in the superconducting phase diagram. The two phases are disordered vortex configurations with the same magnetization, but with different vortex densities. The entropy change, determined from the data using the Clausius–Clapeyron equation, is consistent with estimates based on the difference in the vortex densities of the two phases.     

Composite to tilted vortex lattice transition in Bi2Sr2CaCu2O8+delta in oblique fields

Precision measurements of the vortex phase diagram in single crystals of the layered superconductor Bi2Sr2CaCu2O8+delta in oblique magnetic fields confirm the existence of a second phase transition, in addition to the usual first-order vortex-lattice melting line Hm(T). The transition has a strong first-order character, is accompanied by strong hysteresis, and intersects the melting line in a tricritical point (Hm perpendicular, Hcr parallel). Its field dependence and the changing character of the melting line at the tricritical point strongly suggest that the ground state for magnetic fields closely aligned with the superconducting layers is a lattice of uniformly tilted vortex lines.     

First-order phase transition from the vortex liquid to an amorphous solid

We present a systematic study of the topology of the vortex solid phase in superconducting Bi2Sr2CaCu2O8 samples with low doses of columnar defects. A new state of vortex matter imposed by the presence of geometrical contours associated with the random distribution of columns is found. The results show that the first-order liquid-solid transition in this vortex matter does not require a structural symmetry change.     

Temperature dependence of the magnetic penetration depth in the vortex state of the pyrochlore superconductor,Cd2Re2O7

We report transverse-field and zero-field muon spin rotation and relaxation studies of the superconducting rhenium oxide pyrochlore, Cd2Re2O7. Transverse-field measurements (H=0.007 T) show line broadening below T(c), which is characteristic of a vortex state, demonstrating conclusively the type-II nature of this superconductor. The penetration depth is seen to level off below about 400 mK (T/T(c) approximately 0.4), with a rather large value of lambda(T=0) approximately 7500 A. The temperature independent behavior below approximately 400 mK is consistent with a nodeless superconducting energy gap. Zero-field measurements indicate no static magnetic fields developing below the transition temperature.     

Observation of spin susceptibility enhancement in the possible Fulde-Ferrell-Larkin-Ovchinnikov state of CeCoIn(5)

We report (115)In nuclear magnetic resonance measurements of the heavy-fermion superconductor CeCoIn(5) in the vicinity of the superconducting critical field H(c2) for a magnetic field applied perpendicular to the ? axis. A possible inhomogeneous superconducting state, the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, is stabilized in this part of the phase diagram. In an 11 T applied magnetic field, we observe clear signatures of the two phase transitions: the higher temperature one to the homogeneous superconducting state and the lower temperature phase transition to a FFLO state. We find that the spin susceptibility in the putative FFLO state is significantly enhanced as compared to the value in a homogeneous superconducting state. The implications of this finding for the nature of the low temperature phase are discussed.     

Antiferromagnetic vortex core in Tl(2)Ba(2)CuO(6+delta) studied by nuclear magnetic resonance

Spatially resolved NMR is used to probe the magnetism in and around vortex cores of nearly optimally doped Tl(2)Ba(2)CuO(6+delta) (T(c)=85 K). The NMR relaxation rate T(-1)1 at the 205Tl site provides direct evidence that the antiferromagnetic (AF) spin correlation is significantly enhanced in the vortex core region. In the core region Cu spins show a local AF ordering with moments parallel to the layers at T(N)=20 K. Above T(N) the core region is in the paramagnetic state which is a reminiscence of the state above the pseudogap temperature (T(*) approximately 120 K), indicating that the pseudogap disappears within cores.     

Coexistence of magnetism and superconductivity in the iron-based compound Cs0.8(FeSe0.98)2

We report on muon-spin rotation and relaxation (μSR), electrical resistivity, magnetization and differential scanning calorimetry measurements performed on a high-quality single crystal of Cs(0.8)(FeSe(0.98))(2). Whereas our transport and magnetization data confirm the bulk character of the superconducting state below T(c)=29.6(2) K, the μSR data indicate that the system is magnetic below T(N)=478.5(3) K, where a first-order transition occurs. The first-order character of the magnetic transition is confirmed by differential scanning calorimetry data. Taken all together, these data indicate in Cs(0.8)(FeSe(0.98))(2) a microscopic coexistence between the superconducting phase and a strong magnetic phase. The observed T(N) is the highest reported to date for a magnetic superconductor.     

New superconducting phases in field-induced organic superconductor lambda-(BETS)2FeCl4

We derive the parallel upper critical field, Hc2, as a function of the temperature T in quasi-2D organic compound lambda-(BETS)2FeCl4, accounting for the formation of the nonuniform Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) state. To further check the 2D LOFF model, we propose to study the Hc2(T) curve at low T in tilted fields, where the vortex state is described by the high Landau level functions characterized by the index n. We predict a cascade of first-order transitions between vortex phases with different n, between phases with different types of the symmetry at given n and the change of the superconducting transition from the second order to the first order as FeCl4 ions are replaced partly by GaCl4 ions.     

Nodal d + id pairing and topological phases on the triangular lattice of Na(x)CoO(2).yH(2)O: evidence for an unconventional superconducting state

We show that finite angular momentum pairing chiral superconductors on the triangular lattice have point zeroes in the complex gap function. A topological quantum phase transition takes place through a nodal superconducting state at a specific carrier density x(c) where the normal state Fermi surface crosses the isolated zeros. For spin-singlet pairing, we show that the second-nearest-neighbor (d+id)-wave pairing can be the dominant pairing channel. The gapless critical state at x (c) approximately 0.25 has six Dirac points and is topologically nontrivial with a T3 spin relaxation rate below T(c). This picture provides a possible explanation for the unconventional superconducting state of Na(x)Co O(2). yH(2)O. Analyzing a pairing model with strong correlation using the Gutzwiller projection and symmetry arguments, we study these topological phases and phase transitions as a function of Na doping.     

Low-frequency spin dynamics in the CeMIn5 materials

We measure the spin lattice relaxation of the planar In(1) nuclei in the CeMIn5 materials, extract quantitative information about the low energy spin dynamics of the lattice of Ce moments in both CeRhIn5 and CeCoIn5, and identify a crossover in the normal state. Above a temperature T(*) the Ce lattice exhibits "Kondo gas" behavior characterized by local fluctuations of independently screened moments; below T(*) both systems exhibit a "Kondo liquid" regime in which interactions between the local moments contribute to the spin dynamics. Both the antiferromagnetic and superconducting ground states in these systems emerge from the Kondo liquid regime. Our analysis provides strong evidence for quantum criticality in CeCoIn5.     

LiVGe2O6, an anomalous quasi-1D, S = 1 system, as revealed by NMR

We report the results of 7Li nuclear magnetic resonance (NMR) studies of LiVGe2O6, a quasi-one-dimensional spin S = 1 model system, at low temperatures. Our data, including NMR spectra and the temperature dependence of the spin-lattice relaxation rate T-11, indicate that a first-order phase transition occurs at T(c) approximately 23 K. The NMR response of LiVGe2O6 below T(c) suggests that the ordered phase is antiferromagnetic and has unusual features. Possible reasons for this unexpected behavior are discussed.     

Effects of point defects on the phase diagram of vortex states in high- T(c) superconductors in the B parallel to c axis

The phase diagram for the vortex states of high- T(c) superconductors with point defects in the B--> parallel to c axis is drawn by large-scale Monte Carlo simulations. The vortex slush (VS) phase is found between the vortex glass (VG) and vortex liquid (VL) phases. The first-order transition between this novel normal phase and the VL phase is characterized by a sharp jump of the density of dislocations. The first-order transition between the Bragg glass (BG) and VG or VS phases is also clarified. These two transitions are compared with the melting transition between the BG and VL phases.     

Two-dimensional superconducting fluctuations in stripe-ordered La1.875Ba0.125CuO4

Recent spectroscopic observations of a d-wave-like gap in stripe-ordered La(2-x)Ba(x)CuO(4) with x=1/8 have led us to critically analyze the anisotropic transport and magnetization properties of this material. The data suggest that concomitant with the spin ordering is an electronic decoupling of the CuO(2) planes. We observe a transition (or crossover) to a state of two-dimensional (2D) fluctuating superconductivity, which eventually reaches a 2D superconducting state below a Berezinskii-Kosterlitz-Thouless transition. Thus, it appears that the stripe order in La(2-x)Ba(x)CuO(4) frustrates three-dimensional superconducting phase order, but is fully compatible with 2D superconductivity and an enhanced T(c).     

Nuclear magnetic resonance studies of vortices in high temperature superconductors

The distinct distribution of local magnetic fields due to superconducting vortices can be detected with nuclear magnetic resonance (NMR) and used to investigate vortices and related physical properties of extreme type II superconductivity. This review summarizes work on high temperature superconductors (HTS) including cuprates and pnictide materials. Recent experimental results are presented which reveal the nature of vortex matter and novel electronic states. For example, the NMR spectrum has been found to provide a sharp indication of the vortex melting transition. In the vortex solid a frequency dependent spin–lattice relaxation has been reported in cuprates, including YBa₂Cu₃O_7-x, Bi₂SrCa₂Cu₂O_8+δ, and Tl₂Ba₂CuO_6+δ. These results have initiated a new spectroscopy via Doppler shifted nodal quasiparticles for the investigation of vortices. At very high magnetic fields this approach is a promising method for the study of vortex core excitations. These measurements have been used to quantify an induced spin density wave near the vortex cores in Bi₂SrCa₂Cu₂O_8+δ. Although the cuprates have a different superconducting order parameter than the iron arsenide superconductors there are, nonetheless, some striking similarities between them regarding vortex dynamics and frequency dependent relaxation.     

Fluctuation-driven first-order transition in Pauli-limited d-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.     

Spin Triplet Superconducting State due to Broken Inversion Symmetry in Li(2)Pt(3)B

We report (11)B and (195)Pt NMR measurements in noncentrosymmetric superconductor Li(2)Pt(3)B. We find that the spin susceptibility measured by the Knight shift remains unchanged across the superconducting transition temperature T(c). With decreasing temperature (T) below T(c), the spin-lattice relaxation rate 1/T(1) decreases with no coherence peak and is in proportion to T3. These results indicate that the Cooper pair is in the spin-triplet state and that there exist line nodes in the superconducting gap function. They are in sharp contrast to those in the isostructural Li(2)Pd(3)B which is a spin-singlet, s-wave superconductor, and are ascribed to the enhanced spin-orbit coupling due to the lack of spatial inversion symmetry. Our finding points to a new paradigm where exotic superconductivity arises in the absence of electron-electron correlations.     

On the two-parametric theory of superconductivity

The concept of spin fluctuations in the Hubbard model is used for deriving a closed system of equations for the superconducting order parameter Δ and spin susceptibility. The limiting cases of low temperatures and temperatures close to the superconducting transition temperature are considered. The temperature dependences of the parameter Δ and the Knight shift are obtained. The conditions under which the second-order phase transition turns to the first-order phase transition are established.     

Majorana modes at the ends of superconductor vortices in doped topological insulators

Recent experiments have observed bulk superconductivity in doped topological insulators. Here we ask whether vortex Majorana zero modes, previously predicted to occur when s-wave superconductivity is induced on the surface of topological insulators, survive in these doped systems with metallic normal states. Assuming inversion symmetry, we find that they do but only below a critical doping. The critical doping is tied to a topological phase transition of the vortex line, at which it supports gapless excitations along its length. The critical point depends only on the vortex orientation and a suitably defined SU(2) Berry phase of the normal state Fermi surface. By calculating this phase for available band structures we determine that superconducting p-doped Bi(2)Te(3), among others, supports vortex end Majorana modes. Surprisingly, superconductors derived from topologically trivial band structures can support Majorana modes too.