Pressure dependence of the Fulde-Ferrell-Larkin-Ovchinnikov state in CeCoIn5

Superconductivity beyond the Conventional Pauli Limit in High-Pressure CeSb_{2}

We report the discovery of superconductivity at a pressure-induced magnetic quantum phase transition in the Kondo lattice system CeSb_{2}, sustained up to magnetic fields that exceed the conventional Pauli limit eightfold. Like CeRh_{2}As_{2}, CeSb_{2} is locally noncentrosymmetric around the Ce site, but the evolution of critical fields and normal state properties as CeSb_{2} is tuned through the quantum phase transition motivates a fundamentally different explanation for its resilience to applied field.

Multiple phase transitions in Pauli-limited iron-based superconductors

Specific heat measurements have been successfully used to probe unconventional superconducting phases in one-band heavy-fermion and organic superconductors. We extend the method to study successive phase transitions in multi-band materials such as iron-based superconductors. The signatures are multiple peaks in the specific heat, at low temperatures and high magnetic field, which can lead to the experimental verification of unconventional superconducting states with non-zero total momentum.

Quasiparticle entropy in the high-field superconducting phase of CeCoIn(5)

The heavy-fermion superconductor CeCoIn(5) displays an additional transition within its superconducting (SC) state, whose nature is characterized by high-precision studies of the isothermal field dependence of the entropy, derived from combined specific heat and magnetocaloric effect measurements at temperatures T≥100  mK and fields H≤12  T aligned along different directions. For any of these conditions, we do not observe an additional entropy contribution upon tuning at constant temperature by magnetic field from the homogeneous SC into the presumed Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) SC state. By contrast, for H∥[100] a reduction of entropy was found that quantitatively agrees with the expectation for spin-density-wave order without FFLO superconductivity. Our data exclude the formation of a FFLO state in CeCoIn(5) for out-of-plane field directions, where no spin-density-wave order exists.

Antiferromagnetic order in Pauli-limited unconventional superconductors

We develop a theory of the coexistence of superconductivity (SC) and antiferromagnetism (AFM) in CeCoIn(5). We show that in Pauli-limited nodal superconductors the nesting of the quasiparticle pockets induced by Zeeman pair breaking leads to incommensurate AFM with the magnetic moment normal to the field. We compute the phase diagram and find a first order transition to the normal state at low temperatures, the absence of normal state AFM, and the coexistence of SC and AFM at high fields, in agreement with experiments. We also predict the existence of a new double-Q magnetic phase.

Determination of gap symmetry from angle-dependent H(c2) measurements on CeCu₂Si₂

The tetragonal heavy-fermion compound CeCu₂Si₂ exhibits a superconducting ground state (S type, T(c) = 0.67 K) close to a magnetic instability. Here, we present angle-resolved resistivity measurements of the upper critical field H(c2). In-plane rotation of S-type CeCu₂Si₂ single crystals reveals a fourfold oscillation of H(c2). An extended weak-coupling BCS model for a d-wave symmetry including strong Pauli-limiting effects confirms the aforementioned angular dependence and points towards d(xy) symmetry of the order parameter.

Evolution of paramagnetic quasiparticle excitations emerged in the high-field superconducting phase of CeCoIn5

We present (115)In NMR measurements in a novel thermodynamic phase of CeCoIn(5) in a high magnetic field, where exotic superconductivity exists with the incommensurate spin-density wave order. We show that the NMR spectra in this phase provide direct evidence for the emergence of the spatially distributed normal quasiparticle regions. The quantitative analysis for the field evolution of the paramagnetic magnetization and newly emerged low-energy quasiparticle density of states is consistent with the nodal plane formation, which is characterized by an order parameter in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. The NMR spectra also suggest that the spatially uniform spin-density wave is induced in the FFLO phase.

Magnetic structure of the antiferromagnetic Fulde-Ferrell-Larkin-Ovchinnikov state

The properties of incommensurate antiferromagnetic (AFM) order in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state are studied by solving the Bogoliubov-de Gennes (BdG) equations. The relationship between the electronic structure and the magnetic structure is clarified. We find that the magnetic structure in the AFM-FFLO state includes three cases. (I) In the strongly localized case, the AFM staggered moment is confined into the FFLO nodal planes where the superconducting order parameter vanishes. (II) In the weakly localized case, the AFM staggered moment appears in the whole spatial region, and its magnitude is enhanced around the FFLO nodal planes. (III) In the extended case, the AFM staggered moment is nearly homogeneous and slightly suppressed in the vicinity of the FFLO nodal planes. The structure of Bragg peaks in the momentum resolved structure factor is studied in each case. We discuss the possibility of an AFM-FFLO state in the heavy fermion superconductor CeCoIn5 by comparing these results with the neutron scattering data of CeCoIn5. Experimentally the magnetic structure and its dependence on the magnetic field orientation in the high-field superconducting phase of CeCoIn5 are consistent with case (II).

Towards the identification of a quantum critical line in the (p, B) phase diagram of CeCoIn5 with thermal-expansion measurements

The low-temperature thermal expansion of CeCoIn(5) single crystals measured parallel and perpendicular to magnetic fields B oriented along the c axis yields the volume thermal-expansion coefficient β. Considerable deviations of β(T) from Fermi-liquid behavior occur already within the superconducting region of the (B, T) phase diagram and become maximal at the upper critical field B(c2)(0). However, β(T) and the Grüneisen parameter Γ are incompatible with a quantum critical point at B(c2)(0), but allow for a quantum criticality shielded by superconductivity and extending to negative pressures for B<B(c2)(0). We construct a tentative (p, B, T) phase diagram of CeCoIn(5) suggesting a quantum critical line in the (p, B) plane.

Magnetic-field-induced pattern of coexisting condensates in the superconducting state of CeCoIn5

CeCoIn5 is an anomalous superconductor which exhibits a high-magnetic-field phase that consists of a modulated magnetic coupling together with persistent superconducting order. Here we use a generic microscopic model to argue that this state is a pattern of coexisting condensates: a d-wave singlet superconducting (SC) state, a staggered π-triplet SC state, and a spin density wave (SDW). Our microscopic picture allows a calculation of the phase diagram, and physical consequences including NMR. We interpret the appearance of the SDW order in the Q phase as being induced by odd-triplet pairing.

Imbalanced superfluid state in an annular disk

The imbalanced superfluid state of spin- 1/2 fermions with s-wave pairing is numerically studied by solving the Bogoliubov-de Gennes equation at zero temperature in an annular disk geometry with narrow radial width. Two distinct types of systems are considered. The first case may be relevant to heavy fermion superconductors, where magnetic field causes spin imbalance via Zeeman interaction and the system is studied in a grand canonical ensemble. As the magnetic field increases, the system is transformed from the uniform superfluid state to the Fulde-Ferrell-Larkin-Ovchinnikov state, and finally to the spin polarized normal state. The second case may be relevant to cold fermionic systems, where the number of fermions of each species is fixed as in a canonical ensemble. In this case, the ground state depends on the pairing strength. For weak pairing, the order parameter exhibits a periodic domain wall lattice pattern with a localized spin distribution at low spin imbalance, and a sinusoidally modulated pattern with extended spin distribution at high spin imbalance. For strong pairing, the phase separation between the superfluid state and polarized normal state is found to be preferable, while the increase of spin imbalance simply changes the ratio between them.

Unitary Fermi supersolid: the Larkin-Ovchinnikov phase

We present strong theoretical evidence that a Larkin-Ovchinnikov (LOFF/FFLO) pairing phase is favored over the homogeneous superfluid and normal phases in three-dimensional unitary Fermi systems. Using a density functional theory (DFT) based on the latest quantum Monte Carlo calculations and experimental results, we show that this phase is competitive over a large region of the phase diagram. The oscillations in the number densities and pairing field have a substantial amplitude, and a period some 3 to 10 times the average interparticle separation. Within the DFT, the transition to a normal polarized Fermi liquid at large polarizations is smooth, while the transition to a fully paired superfluid is abrupt.

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.

Multigap superconductivity in the heavy-Fermion system CeCoIn5

New thermal conductivity experiments on the heavy-fermion superconductor CeCoIn5 down to 10 mK rule out the suggested existence of unpaired electrons. Moreover, they reveal strong multigap effects with a remarkably low "critical" field Hc2S for the small gap band, showing that the complexity of heavy-fermion band structure has a direct impact on their response under magnetic field.

Anisotropic effect of Cd and Hg doping on the Pauli limited superconductor CeCoIn5

We studied the effect of impurity on the first order superconducting (SC) transition and the high field-low temperature (HFLT) SC state of CeCoIn5 by measuring the specific heat of CeCo(In1-xCdx)_{5} with x=0.0011, 0.0022, and 0.0033 and CeCo(In1-xHgx)_{5} with x=0.000 16, 0.000 32, and 0.000 48 at temperatures down to 0.1 K and fields up to 14 T. Cd substitution rapidly suppresses the crossover temperature T0, where the SC transition changes from second to first order, to T=0 K with x=0.0022 for H parallel[100], while it remains roughly constant up to x=0.0033 for H parallel[001]. The associated anomaly of the proposed FFLO state in Hg-doped samples is washed out by x=0.000 48, while remaining at the same temperature, indicating high sensitivity of that state to impurities. We interpret these results as supporting the nonmagnetic, possibly FFLO, origin of the HFLT state in CeCoIn5.

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.

Extremely high upper critical magnetic field of the noncentrosymmetric heavy fermion superconductor CeRhSi3

We report an extremely high upper critical field B(c2) in the noncentrosymmetric heavy fermion superconductor CeRhSi3 for a magnetic field B along the tetragonal c axis. B(c2)(T=0) possibly reaching 30 T is much higher than B(c2)(0)=7 T for B perpendicular c and greatly exceeds the paramagnetic limiting field. The strong anisotropy of B(c2)(0) with extremely high B(c2)(0) for B || c is qualitatively explained by the paramagnetic pair-breaking mechanism specific to the noncentrosymmetric superconductor. However, an unusual B(c2)(T) curve with a positive curvature for B || c cannot be explained satisfactorily by conventional orbital pair-breaking models.

Magnetic-field-induced lattice anomaly inside the superconducting state of CeCoIn5: anisotropic evidence of the possible Fulde-Ferrell-Larkin-Ovchinnikov state

We report high magnetic field linear magnetostriction experiments on CeCoIn5 single crystals. Two features are remarkable: (i) a sharp discontinuity in all the crystallographic axes associated with the upper superconducting critical field B(c2) that becomes less pronounced as the temperature increases and (ii) a distinctive second orderlike feature observed only along the c axis in the high field (10 T < or approximately B< or = B(c2)) low temperature (T < or approximately 0.35 K) region. This second order transition is observed only when the magnetic field lies within 20 degrees of the ab planes and there is no signature of it above B(c2), which raises questions regarding its interpretation as a field induced magnetically ordered phase. Good agreement with previous results suggests that this anomaly is related to the transition to a possible Fulde-Ferrel-Larkin-Ovchinnikov superconducting state.

Visualization of vortex bound states in polarized fermi gases at unitarity

We theoretically analyze a single vortex in a spin polarized 3D trapped atomic Fermi gas near a broad Feshbach resonance. Above a critical polarization the Andreev-like bound states inside the core become occupied by the majority spin component. As a result, the local density difference at the core center suddenly rises at low temperatures. This provides a way to visualize the lowest bound state using phase-contrast imaging. As the polarization increases, the core expands gradually and the energy of the lowest bound state decreases.

Fulde-Ferrell-Larkin-Ovchinnikov state in a perpendicular field of quasi-two-dimensional CeCoIn5

A Fulde-Ferrell-Larkin-Ovchinnkov (FFLO) state was previously reported in the quasi-2D heavy fermion CeCoIn5 when a magnetic field was applied parallel to the ab plane. Here, we conduct 115In NMR studies of this material in a perpendicular field, and provide strong evidence for FFLO in this case as well. Although the topology of the phase transition lines in the H-T phase diagram is identical for both configurations, there are several remarkable differences between them. Compared to H parallelab, the FFLO phase for H perpendicularab is confined in a much narrower region at the low-T-high-H corner in the H-T plane, and the critical field separating the FFLO and non-FFLO superconducting states almost ceases to have a temperature dependence. Moreover, directing H perpendicularab results in a notable change in the quasiparticle excitation spectrum within the planar node associated with the FFLO transition.