The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, an unusual superconducting state, defies high magnetic fields beyond the Pauli paramagnetic limit. It exhibits a spatial modulation of the superconducting order parameter in real space and is exceptionally rare. Recently, an even more exotic variant - the orbital FFLO state - was predicted and identified in the transition metal dichalcogenide superconductor 2H-NbSe2. This state emerges in thin samples with thicknesses below ~40 nm, at the boundary between two and three dimensions. The complex interplay between Ising spin orbit coupling and the Pauli paramagnetic effect can lead to a stabilization of the FFLO state in a relatively large range of the magnetic phase diagram, even well below the Pauli limit. In this study, we present experimental evidence of the formation of this orbital FFLO state in bulk 2H-NbSe2 samples. This evidence was obtained using high-resolution DC magnetization and magnetic torque experiments in magnetic fields applied strictly parallel to the NbSe2 basal plane. Both quantities display a crossover to a discontinuous first-order superconducting transition at the normal state boundary in magnetic fields of 4 T and above. This is usually seen as a sign that Pauli paramagnetic pair breaking effects affect the superconducting state. The magnetic torque reveals a small step-like reversible anomaly, indicating a magnetic field-induced thermodynamic phase transition within the superconducting state. This anomaly bears many similarities to the FFLO transitions in other FFLO superconductors, suggesting the potential existence of an orbital FFLO state in bulk 2H-NbSe2 samples. Additionally, we observe a pronounced in-plane 6-fold symmetry of the upper critical field in the field range above this phase transition, which has previously been interpreted as a hallmark of the orbital FFLO state in thin 2H-NbSe2.
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state has received renewed interest recently due to the experimental indication of its presence in CeCoIn$_5$, a quasi 2-dimensional (2D) d-wave superconductor. However direct evidence of the spatial variation of the superconducting order parameter, which is the hallmark of the FFLO state, does not yet exist. In this work we explore the possibility of detecting the phase structure of the order parameter directly using conductance spectroscopy through micro-constrictions, which probes the phase sensitive surface Andreev bound states of d-wave supercon…
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state can be found in layered d-wave superconductors such as high $T_c$ cuprates and $κ$-(ET)$_2$ salts in a planar magnetic field. We show the superconducting order parameter forms two dimensional crystalline lattice in the FFLO state for d-wave superconductors. Also the quasiparticle density of states and the thermodynamics of FFLO state are constructed. Therefore STM or NMR will provide a definitive test for the existence of the FFLO state.
We study the superconducting order parameter fluctuations near the phase transition into the Larkin-Ovchinnikov-Fulde-Ferrell state in the clean limit at zero temperature. In contrast to the usual normal metal-to-uniform superconductor phase transition, the fluctuation corrections are dominated by the modes with the wave vectors away from the origin. We find that the superconducting fluctuations lead to a divergent spin susceptibility and a breakdown of the Fermi-liquid behavior at the quantum critical point.
We find theoretically that the vortex core in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is quite different from the ordinary core by a simple topological reason. The intersection point of a vortex and nodal plane of the FFLO state empties the excess spins. This leads to observable consequences in the spatial structure of the spontaneous magnetization. We analyze this topological structure based on the low lying excitation spectrum by solving microscopic Bogoliubov-de Gennes equation to clarify its physical origin.
In nonuniform Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) superconductors, both the gauge symmetry and the continuous translational symmetry of the normal state are spontaneously broken. This leads to additional bosonic excitations, or Goldstone modes, corresponding to the deformations of the order parameter amplitude modulation in real space. We derive general expressions for the energy of the phase and elastic Goldstone modes. As an example, the superfluid density and the elastic modulus of a one-dimensional LOFF superconductor are calculated at low temperatures.
The crystal structure determines both the Fermi surface and pairing symmetry of the superconducting metals. It is demonstrated in the framework of the general phenomenological approach that this is of the primary importance for the determination of the structure of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in the magnetic field. The FFLO modulation of the superconducting order parameter may be revealed in the form of the higher Landau level states or/and modulation along the magnetic field. The transition between different FFLO states could occur with the temperature variation or with …
We develop the Ginzburg-Landau theory of the vortex lattice in clean isotropic three-dimensional superconductors at large Maki parameter, when inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov state is favored. We show that diamagnetic superfluid currents mainly come from paramagnetic interaction of electron spins with local magnetic field, and not from kinetic energy response to the external field as usual. We find that the stable vortex lattice keeps its triangular structure as in usual Abrikosov mixed state, while the internal magnetic field acquires components perpendicular to applied magneti…
We show that the behaviour of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductors near a surface is considerably different from the usual case. The order parameter of the FF state is strongly deformed near the surface, which leads to a number of unusual features in the linear magnetic response, such as "anti-screening" or "over-screening" of the applied field. In a fully isotropic FF case, the Meissner effect is still present, despite the vanishing of the transverse superfluid density in the bulk. We also calculate the surface critical field Hc3, which exhibits a peculiar temperature d…
We studied the phase diagram for a two-dimensional d-wave superconducting system under an in-plane magnetic field or an exchange field. According to the spatial configuration of the order parameter, we show that there exists quantum phase transitions in which the uniform phase transforms to the one-dimensional Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, and then to two-dimensional FFLO state upon increasing the exchange field. The local density of states are calculated and suggested to be signatures to distinguish these phases.
Due to the difference in the momenta of the superconducting order parameters, the Josephson current in a Josephson junction between a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductor and a conventional BCS superconductor is suppressed. We show that the Josephson current may be recovered by applying a magnetic field in the junction. The field strength and direction at which the supercurrent recovery occurs depend upon the momentum and structure of the order parameter in the FFLO state. Thus the Josephson effect provides an unambiguous way to detect the existence of an FFLO state, and to m…
We derive the fluctuational magnetization and the paraconductivity of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductors in their normal state. The FFLO superconducting fluctuations induce oscillations of the magnetization between diamagnetism and unusual paramagnetism which originates from the competition between paramagnetic and orbital effects. We also predict a strong anisotropy of the paraconductivity when the FFLO transition is approached in contrast with the case of a uniform BCS state. Finally building a Ginzburg-Levanyuk argument, we demonstrate that these fluctuation effects can…
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state of a two-dimensional (2D) orthorhombic lattice superconductor is studied based on the Bogoliubov-de-Gennes equations. It is illustrated that the 2D FFLO state is suppressed and only one-dimensional (1D) stripe state is stable. The stripe changes its orientation with the increasing Zeeman field. There exists a crossover region where the gap structure has some local 2D features. These results are significantly different from those of the tetragonal lattice system. The local density of states is also studied which can be checked and compared with …
Vortex tilt response in Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) vortex lattice is theoretically examined as a probe reflecting the spatial structure of this state. In the FFLO state with nodal planes perpendicular to the magnetic field in a quasi 2D material under a parallel field, the tilt modulus E_{2} {\it of the nodal planes} decreases as the paramagnetic effect is effectively enhanced, and this reduction of E_{2} in turn reduces the vortex tilt modulus. This reduction of vortex tilt modulus, more remarkable in more anisotropic systems, accompanying the FFLO transition may be an origin of …
Motivated by recent NMR data suggesting the presence of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) vortex lattice in magnetic fields perpendicular to the superconducting plane in the heavy-fermion superconductor CeCoIn5, we examine here the stability of FFLO states in quasi two-dimensional (2D) superconductors under a perpendicular field. It is found that a 3D-like portion of Fermi surfaces peculiar to CeCoIn5 stabilizes a FFLO vortex state modulating along the field parallel to the c-axis and that the direction of modulation in a FFLO vortex lattice is related to the characters of the normal t…
Recent study on doping effects in the heavy fermion superconductor CeCoIn$_5$ has shown that a small amount of doping induces unexpectedly large broadening of the second order transition into the high field and low temperature (HFLT) phase of this material. Motivated by this observation, effects of quenched disorder on the second order transition into a longitudinal Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state are examined. The observed large broadening of the transition is naturally explained as a consequence of softness of each FFLO nodal plane. The present results strongly support the scen…
We investigate the vortex state with Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) modulations suggested for a high field phase of CeCoIn_5. On the basis of the quasiclassical Eilenberger theory, we calculate the three dimensional structure of pair potentials, internal magnetic fields, paramagnetic moments, and electronic states, for the s-wave and the d-wave pairings comparatively. The π-phase shift of the pair potential at the FFLO nodal plane or at the vortex core induces sharp peak states in the local density of states, and enhances the local paramagnetic moment. We also discuss the NMR spectrum…
In superconductors with singlet pairing, the inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is expected to be stabilized by a large Zeeman splitting. We develop an efficient method to evaluate the Landau-Ginzburg free energies of FFLO-state vortex lattices and use it to simplify the considerations that determine the optimal vortex configuration at different points in the phasediagram. We demonstrate that the order parameter spatial profile is completely determined, up to a uniform translation, by its Landau level index n and the vortex Lattice structure and derive an explicit expr…
We propose that in a system with pocket Fermi surfaces, a pairing state with a finite total momentum q_tot like the Fulde-Ferrell-Larkin-Ovchinnikov state can be stabilized even without a magnetic field. When a pair is composed of electrons on a pocket Fermi surface whose center is not located at Gamma point, the pair inevitably has finite q_tot. To investigate this possibility, we consider a two-orbital model on a square lattice that can realize pocket Fermi surfaces and we apply fluctuation exchange approximation. Then, by changing the electron number n per site, we indeed find that such sup…
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in the vortex lattice state is quantitatively studied using the selfconsistent Eilenberger theory in three-dimensional (3D) space. We estimate free energy to determine the FFLO phase diagram in the H-T plane and stable FFLO wave number in the isotropic system with the 3D Fermi sphere and s-wave pairing. To facilitate the experimental identification of the FFLO state, we investigate the field evolution of NMR spectra and flux line lattice form factors obtained in neutron scattering in the FFLO vortex states. Possible applications of our results …
Clean superconductors with weakly coupled conducting planes have been suggested as promising candidates for observing the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. We consider here a layered superconductor in a magnetic field of arbitrary orientation with respect to the conducting plane. In this case there is competition of spin-pair-breaking and orbital-pair-breaking effects. In previous work, phase boundaries characterized by Landau quantum numbers n > 0 have been predicted. Here, we calculate the actual structure of the stable states below Hc2 by minimizing the free energy. We find sev…
We theoretically study the orbital destructive effect against superconductivity in a parallel magnetic field in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO or LOFF) phase at zero temperature in a quasi-two-dimensional (Q2D) conductor. We demonstrate that at zero temperature a special parameter, $λ= l_{\perp}(H)/d$, is responsible for strength of the orbital effect, where $l_{\perp}(H)$ is a typical "size" of the quasi-classical electron orbit in a magnetic field and $d$ is the inter-plane distance. We discuss applications of our results to the existing experiments on the FFLO phase in the organ…
We measure the heat capacity of UBe13 with an unusually low Tc for a polycrystal. We find an upturn in the upper critical field Hc2(T) below about Tc/2, much as for higher-Tc samples. Comparing the critical fields in our sample and in samples with higher Tc's shows that the low-temperature limit of Hc2 is proportional to Tc(H=0), as expected if the upturn comes from an FFLO phase and strong coupling.
We consider a formation of the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase in a quasi-one-dimensional (Q1D) conductor in a magnetic field, parallel to its conducting chains, where we take into account both the paramagnetic spin-splitting and orbital destructive effects against superconductivity. We show that, due to a relative weakness of the orbital effects in a Q1D case, the LOFF phase appears in (TMTSF)$_2$ClO$_4$ superconductor for real values of its Q1D band parameters. We compare our theoretical calculations with the recent experimental data by Y. Maeno's group [S. Yonezawa et al., Phy…
We study exotic superconducting states in SrTiO$_3$ heterostructures on the basis of the three-orbital model, which reproduces the band structure of two-dimensional electron gases. We show various Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states induced by the broken inversion symmetry and orbital degree of freedom. In particular, a novel orbital-dependent FFLO state is stabilized in a magnetic field along the [110]-axis. The field angle dependence of the FFLO state is clarified on the basis of the spin and orbital texture in the momentum space. It is shown that the orbital degree of freedom in …
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is a superconducting state stabilized by a large Zeeman splitting between up- and down-spin electrons in a singlet superconductor. In the absence of disorder, the superconducting order parameter has a periodic spatial structure, with periodicity determined by the Zeeman splitting. Using the Bogoliubov-de Gennes (BdG) approach, we investigate the spatial profiles of the order parameters of FFLO states in a two-dimensional s-wave superconductors with nonmagnetic impurities. The FFLO state is found to survive under moderate disorder strength, and …
The effect of a nonmagnetic impurity on the subgap electronic spectrum in a d-wave superconductor in the Fulde-Ferrell-Larkin-Ovchinnikov state is investigated. In a pure system, the spatial variation of the order parameter (OP) of the FFLO state forms a two-dimensional lattice, and there exist two types of sub-gap quasi-particle states. Our numerical iterations indicate that an OP saddle point, and slightly less so energetically, an OP extremum favor to be pinned at the impurity site. The local density of states and the fixed-bias map reveal the subtle effects of an impurity on the subgap ene…
The effect of impurities on Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states in a layered superconductor with d-wave pairing symmetry is investigated using the tight-binding model and the Bogoliubov-de Gennes equations. At low temperature and a strong exchange field applied parallel to its conducting plane, a two-dimensional (2D) square lattice-like Larkin-Ovchinnikov state is more energetically favorable in a clean system. In the presence of impurities, the spatial profile of the order parameter remains as a 2D square lattice, and it is distorted only near the impurities when the impurity conce…
Angular dependent magnetothermal conductivity experiments on CeCoIn_5 indicate that this compound is a d-wave superconductor. In this study, the low-temperature behavior of the upper critical field is measured in a single crystal of CeCoIn_5 along the directions H parallel a and H parallel c. The data is compared with model calculations of the upper critical field in a d-wave superconductor. It is found that the observed H_c2(T) along H parallel a is consistent with a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state at low temperatures, T < 0.7K, whereas for H parallel c the FFLO state appears to…
We solve a long-standing problem about a theoretical description of the upper critical magnetic field, parallel to conducting layers and perpendicular to conducting chains, in (TMTSF)$_2$ClO$_4$ superconductor. In particular, we explain why the experimental upper critical field, $H^{b'}_{c2} \simeq 6 \ T$, is higher than both the quasi-classical upper critical field and Clogston paramagnetic limit. We show that this property is due to the coexistence of the hidden Reentrant and Larkin-Ovchinnikov-Fulde-Ferrell phases in a magnetic field in a form of three plane waves with non-zero momenta of t…
In this paper we demonstrate the necessity of including the generally omitted collective mode contributions in calculations of the Meissner effect for non-uniform superconductors. We consider superconducting pairing with non-zero center of mass momentum, as is relevant to high transition temperature cuprates, cold atoms, and quantum chromodynamic superconductors. For the concrete example of the Fulde-Ferrell phase we present a quantitative calculation of the superfluid density, showing the collective mode contributions are not only appreciable but that they derive from the amplitude mode of th…
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states for two-dimensional s- and d-wave superconductors (s- and d-SC) are self-consistently studied under an in-plane magnetic field. While the stripe solution of the order parameter (OP) is found to have lower free energy in s-SC, a square lattice solution appears to be energetically more favorable in the case of d-SC. At certain symmetric sites, we find that the features in the local density of states (LDOS) can be ascribed to two types of bound states. We also show that the LDOS maps for d-SC exhibit bias-energy-dependent checkerboard patterns. T…
Effect of the phase fluctuations of the order parameter on the stability of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states are examined in exactly two-dimensional (2D) type-II superconductors with cylindrically symmetric Fermi surface on the basis of a generalized Ginzburg-Landau theory. It is found that for the FFLO states with oscillations in a single direction, not only the long-range order but also quasi-long-range order (QLRO), which is characterized by a power law decay of the order parameter correlation function, is suppressed by the phase fluctuations at any finite temperatures. On…
We study the effect of a parallel magnetic field in a thin and small superconductor. The field suppresses superconductivity through Zeeman coupling while stabilizes the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state at high fields before superconductivity is destroyed. When the spatial period of FFLO state is comparable to the size of the superconductor, there is a strong commensuration effect, which modifies the superconducting phase diagram. We investigate the FFLO state and the phase diagram in the presence of strong commensuration effect both for the $s$-wave and $d$-wave superconductors us…
We have investigated the magnetic phase diagram near the upper critical field of KFe2As2 by magnetic torque and specific heat experiments, using a high-resolution piezo-rotary positioner to precisely control the parallel orientation of the magnetic field with respect to the FeAs layers. We observe a clear double transition when the field is oriented strictly in-plane, and a characteristic upturn of the upper critical field line well beyond the Pauli limit at 4.7 T. This provides firm evidence that an FFLO state is realized in this iron-based KFe2As2 superconductor.
We examine the possible phase diagram in an $H$-$T$ plane for Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states in a two-band Pauli-limiting superconductor. We here demonstrate that, as a result of the competition of two different modulation length scales, the FFLO phase is divided into two phases by the first-order transition: the $Q_1$- and $Q_2$-FFLO phases at the higher and lower fields. The $Q_2$-FFLO phase is further divided by successive first order transitions into an infinite family of FFLO subphases with rational modulation vectors, forming a {\it devil's staircase structure} for the fi…
We study the effects of Fermi-liquid interactions on quasi-two-dimensional d-wave superconductors in a magnetic field. The phase diagram of the superconducting state, including the periodic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in high magnetic fields, is discussed for different strengths of quasiparticle many-body interactions within Landau's theory of Fermi liquids. Decreasing the Fermi-liquid parameter $F_0^a$ causes the magnetic spin susceptibility to increase, which in turn leads to a reduction of the FFLO phase. It is shown that a negative $F_0^a$ results in a first-order phase t…
We investigate pairing symmetry in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) vortex state and vortex lattice, and explain the electronic structure in these states in terms of pairing symmetry. We show analytically that at the intersection point of FFLO nodal plane and vortex line, only even frequency pairing is present if the Zeeman splitting is negligibly small. With increasing Zeeman splitting, odd frequency pairing emerges there. This makes it possible to interpret the gap structure of the density of states at the intersection point as a manifestation of the even frequency pairing. In the…
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 115^In 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//ab, the FFLO region for H perpendicular to the ab-plane shows a sizable decrease, and the critical field sep…
Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) inhomogeneous superconducting (SC) state, first- and second-order phase transitions, and quantum criticality induced by spin accumulation in a ferromagnet-$d_{x^{2}-y^{2}}$-wave superconductor-ferromagnet tunnel junction are theoretically predicted. A complex phase diagram in the temperature-bias voltage plane is determined. It is found that the phase transitions from the homogeneous BCS state to the inhomogeneous FFLO state, and from the FFLO state with the momentum $\mathbf{% q}$'s azimuthal angle $θ_{\mathbf{q}}=0$ to that with $θ_{% \mathbf{q}}=π/4$, …
Motivated by a striking observation of a Fulde-Ferell-Larkin-Ovchinnikov (FFLO) vortex state in the heavy fermion material CeCoIn5 in fields {\it perpendicular} to the superconducting planes (${\bf H} \parallel c$), superconducting phase diagrams including an FFLO state of quasi two-dimensional (Q2D) superconductors are systematically studied. In the clean {\it limit}, the high field superconducting state in the low temperature limit should be not the FFLO state modulating along ${\bf H}$, appeared in CeCoIn5 in both ${\bf H} \parallel c$ and ${\bf H} \perp c$, but a different vortex state wit…
We present magnetic torque, specific heat and thermal expansion measurements combined with a piezo rotary positioner of the bulk transition metal dichalcogenide (TMD) superconductor NbS2 in high magnetic fields applied strictly parallel to its layer structure. The upper critical field of superconducting TMDs in the 2D form is known to be dramatically enhanced by a special form of Ising spin orbit coupling. This Ising superconductivity is very robust against the Pauli limit for superconductivity. We find that superconductivity beyond the Pauli limit still exists in bulk single crystals of NbS2.…
An experimental phase diagram of the field-induced superconductivity in the lambda-(BETS)_2FeCl_4 compound is theoretically reproduced by a combination of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state and the Jaccarino-Peter mechanism. Semi-quantitative agreement is obtained in the presence of a very weak subdominant triplet pairing interaction between electrons with antiparallel spins, in addition to a dominant singlet pairing interaction. An order-parameter mixing effect enhances the FFLO state, and plays an essential role in the semi-quantitative agreement. As a possible origin of the s…
When the inversion symmetry is broken, the spin-orbit coupling reduces the transition temperature of some types of spin triplet superconductivity, which is similar to the case that magnetic field reduces the spin singlet superconductivity due to Zeeman splitting. It is well known that Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state of spin singlet superconductivity is realized near the Pauli limit (or Chandrasekhar-Clogston limit) of external magnetic field. In FFLO state the amplitude of the order parameter is not uniform in space. In this paper we study the FFLO state in the spin triplet superc…
Resolving the high-field superconducting phase (HFSP), often called as the Q-phase, and the antiferromagnetic or spin-density-wave (SDW) order appearing in the phase remains a crucial issue on the superconductor CeCoIn$_5$. It is shown that a switching of the SDW domain due to a tiny change of the magnetic field direction in HFSP, reported and interpreted as an evidence of the presence of a $π$-triplet pairing inducing the SDW order [S. Gerber et al., Nature Physics 10, 126 (2014)], can be explained with no triplet pairing component if the $d$-wave superconducting order in HFSP includes the Fu…
We compare the upper critical field of bulk single-crystalline samples of the two intrinsic transition metal dichalcogenide (TMD) superconductors, 2H-NbSe2 and 2H-NbS2, in high magnetic fields where their layer structure is aligned strictly parallel and perpendicular to the field, using magnetic torque experiments and a high-precision piezo-rotary positioner. While both superconductors show that orbital effects still have a significant impact when the layer structure is aligned parallel to the field, the upper critical field of NbS2 rises above the Pauli limiting field and forms a Fulde-Ferrel…
We present magnetic-torque measurements of the organic superconductor k-(BEDT-TTF)2Cu(NCS)2 for in-plane magnetic fields up to 32 T. In this layered two-dimensional compound the superconductivity can persist even in fields above the Pauli limit of about 21 T. There, a pronounced upturn of the upper-critical-field line occurs and the superconducting phase-transition line splits and forms an additional high magnetic field phase. k-(BEDT-TTF)2Cu(NCS)2 is a spin-singlet superconductor, therefore, such a superconducting high-field phase beyond the Pauli limit can originate only from Cooper pairing …
We derive the Ginzburg-Landau theory of unconventional singlet superconductors in the presence of a Zeeman field and impurities, in order to examine the resulting Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases. We show that the behavior of the FFLO phases in unconventional superconductors in the presence of impurities is qualitatively different from that found for s-wave superconductors.
Nonuniform superconducting state due to strong spin magnetism is studied in two-dimensional type-II superconductors near the second order phase transition line between the normal and the superconducting states. The optimum spatial structure of the orderparameter is examined in systems with cylindrical symmetric Fermi surfaces. It is found that states with two-dimensional structures have lower free energies than the traditional one-dimensional solutions, at low temperatures and high magnetic fields. For s-wave pairing, triangular, square, hexagonal states are favored depending on the temperatur…
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in quasi-one-dimensional systems with warped Fermi surfaces is examined in strong parallel magnetic fields. It is shown that the state is extremely stable for field directions around nontrivial optimum directions, at which the upper critical field exhibits cusps, and that the stabilization is due to a Fermi-surface effect analogous to the nesting effect for the spin density wave and charge density wave. Interestingly, the behavior with cusps is analogous to that in a square lattice system in which the hole density is controlled. For the organic…
We study the angular Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, in which the rotation symmetry is spontaneously broken, in population imbalanced fermion gases. The superfluid gases at near T=0 are investigated on the basis of the Bogoliubov-de Gennes (BdG) equation. We find that the angular FFLO state is stabilized in the gases confined in the toroidal trap, but not in the harmonic trap. We discuss the mechanism of the angular FFLO state based on the self-one-dimensionalization of the superfluid gas.
We investigate, mostly analytically, the nature of the Fulde-Ferrell- Larkin-Ovchinnikov superfluid phases for an isotropic two-dimensional superconductor, which is relevant for the experimental observation of these phases. We show that there is, in the low temperature range, a cascade of transitions toward order parameters with ever increasing complexity.
We theoretically investigate the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state by using the microscopic quasi-classical Eilenberger equation. The Pauli paramagnetic effects and the orbital depairing effects due to vortices are treated in an equal footing for three dimensional spherical Fermi surface model and $s$-wave pairing. The field evolution of the LO state is studied in detail, such as the $H$-$T$ phase diagram, spatial structures of the order parameter, the paramagnetic moment, and the internal filed. Field-dependences of various thermodynamic quantities: the paramagnetic moment, entrop…
We study an effect of rotation on the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state of two component Fermi superfluid gases in a toroidal trap. We investigate a stability of the FFLO states in the quasi-one-dimensional regime on the basis of the Bogoliubov-de Gennes equation. We find that two novel FFLO phases, i.e., the half quantum vortex state and the intermediate state of Fulde-Ferrell (FF) state and Larkin-Ovchinnikov (LO) state, are stabilized by the rotation. The phase diagram for the FF state, LO state, intermediate state, and half quantum vortex state is shown in both T-P plane and T-…
Flat-band Fulde-Ferrell-Larkin-Ovchinnikov State from Quantum Geometric Discrepancy
Hong Kong University of Science and Technology（香港科技大学）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Nanyang Technological University（南洋理工大学）
For an isotropic two-dimensional system, when the temperature is lowered toward T=0, it has been found recently that, for the transition from the normal to the superfluid state in the paramagnetic limit, the order parameter describing the Fulde-Ferrell-Larkin-Ovchinnikov phase has an increasingly complex structure with contributions from an increasing number of wavevectors. This cascade of phase transitions is directly linked to the fact that, due to the rotational invariance, all the wavevectors directions which can enter the order parameter are degenerate. We study how this cascade of phase …
Fe-based superconductors (FeSC) exhibit all the properties of systems that allow the formation of a superconducting phase with oscillating order parameter, called the Fulde--Ferrell--Larkin--Ovchinnikov (FFLO) phase. By the analysis of the Cooper pair susceptibility in two-band FeSC, such systems are shown to support the existence of a FFLO phase, regardless of the exhibited order parameter symmetry. We also show the state with nonzero Cooper pair momentum, in superconducting FeSC with $\sim \cos(k_{x}) \cdot \cos (k_{y})$ symmetry, to be the ground state of the system in a certain parameter r…
