Fulde Ferrell Larkin Ovchinnikov Research Articles

Weak and strong chirality-anomaly-manipulations in a superconducting Weyl semimetal sandwich structure

We investigate the quantum interference of the electron–hole conversions from the two interfaces in a Weyl semimetal (WSM)-based hybrid structure, in which a superconducting WSM is sandwiched in between two normal ones. The quantum interference is characterized by the chirality-anomaly-manipulation (CAM). It is found that only low energy is in favor for s-wave BCS pairing states. The Andreev reflection (AR) chirality blockade can be tuned by the stagger angle α for the relative orientation of paired Weyl points, accompanied by an AR bipolar chirality diode. Thus, a strong CAM is indicated for the electron–hole conversion. However, the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) pairing states have no energy preference, with the weak and strong CAMs being near and far away from the zero energy, respectively. More interestingly, a perfect AR with the normal reflection suppressed thoroughly can be obtained at any α as a result of the FFLO paring with the same chirality. In addition, the conductance or noise power, which incorporates the contributions of the two paired Weyl nodes, not only, in turn, embodies the respective features of their contributions but also can be experimentally measured to discern between the BCS and FFLO paring states.

Magnetically tunable supercurrent in dilute magnetic topological insulator-based Josephson junctions

A superconductor, when exposed to a spin-exchange field, can exhibit spatial modulation of its order parameter, commonly referred to as the Fulde–Ferrell–Larkin–Ovchinnikov state. Such a state can be induced by controlling the spin-splitting field in Josephson junction devices, allowing access to a wide range of the phase diagram. Here we demonstrate that a Fulde–Ferrell–Larkin–Ovchinnikov state can be induced in Josephson junctions based on the two-dimensional dilute magnetic topological insulator (Hg,Mn)Te. We do this by observing the dependence of the critical current on the magnetic field and temperature. The substitution of Mn dopants induces an enhanced Zeeman effect, which can be controlled with high precision by using a small external magnetic field. We observe multiple re-entrant behaviours of the critical current as a response to an in-plane magnetic field, which we assign to transitions between ground states with a phase shifted by π. This will enable the study of the Fulde–Ferrell–Larkin–Ovchinnikov state in much more accessible experimental conditions.

Effect of Fermi surface topology change on the Kagome superconductor CeRu2 under pressure

The cubic Laves phase compound CeRu2 with a Kagome substructure of Ru has been investigated to understand myriad fascinating phenomena resulting from competition among its various physical and geometric features. Such phenomena include flat bands, van Hove singularities, Dirac cones, reentrant superconductivity, magnetism, the Fulde–Ferrell–Larkin–Ovchinnikov state, valence fluctuations, time-irreversible anisotropic s-state superconductivity, etc. Extensive studies have thus been carried out since 1958 when the highly unusual coexistence of superconductivity and ferromagnetism was proposed for the mixed compounds (Ce,Gd)Ru2. Activity has accelerated in recent years due to increasing interest in topological states in superconductors. However, there has been little investigation of the mutual influence of these fascinating states. Therefore, we systematically investigated the superconductivity and possible Fermi surface topological change in CeRu2via magnetic, resistivity, and structural measurements under pressure up to ∼168 GPa. An unusual phase diagram that suggests an intriguing interplay between the compound's superconducting order and Fermi surface topological order has been constructed. A resurgence in its superconducting transition temperature was observed above 28 GPa. Our experiments have identified a structural transition above 76 GPa and a few tantalizing phase transitions driven by high pressure. Our high-pressure results further suggest that superconductivity and Fermi surface topology in CeRu2 are strongly intertwined.

Reentrant Proximity-Induced Superconductivity for GeTe Semimetal

We experimentally investigate charge transport in In–GeTe and In–GeTe–In proximity devices, which are formed as junctions between superconducting indium leads and thick single crystal flakes of α-GeTe topological semimetal. We observe nonmonotonic effects of the applied external magnetic field, including reentrant superconductivity in In–GeTe–In Josephson junctions: supercurrent reappears at some finite magnetic field. For a single In–GeTe Andreev junction, the superconducting gap is partially suppressed in zero magnetic field, while the gap is increased nearly to the bulk value for some finite field before its full suppression. We discuss possible reasons for the results obtained, taking into account spin polarization of Fermi arc surface states in topological semimetal \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}-GeTe with a strong spin–orbit coupling. In particular, the zero-field surface state spin polarization partially suppresses the superconductivity, while it is recovered due to the modified spin-split surface state configuration in finite fields. As an alternative possible scenario, the transition into the Fulde–Ferrell–Larkin–Ovchinnikov state is discussed. However, the role of strong spin–orbit coupling in forming the nonmonotonic behavior has not been analyzed for heterostructures in the Fulde–Ferrell–Larkin–Ovchinnikov state, which is crucial for junctions involving GeTe topological semimetal.

Multiple-q current states in a multicomponent superconducting channel

It is well-established that multicomponent superconductors can host different nonstandard phenomena such as broken-time reversal symmetry (BTRS) states, exotic Fulde–Ferrell–Larkin–Ovchinnikov phases, the fractional Josephson effect as well as plenty of topological defects like phase solitons, domain walls and unusual vortex structures. We show that in the case of a two-component superconducting quasi-one-dimensional channel this catalogue can be extended by a novel inhomogeneous current state, which we have termed as a multiple-q state, characterized by the coexistence of two different interpenetrating Cooper pair condensates with different total momenta. Within the Ginzburg–Landau formalism for a dirty two-band superconductor with sizable impurity scattering treated in the Born-approximation we reveal that under certain conditions, the occurrence of multiple-q states can induce a cascade of transitions involving switching between them and the homogeneous BTRS (non-BTRS) states and vice versa leading this way to a complex interplay of homogeneous and inhomogeneous current states. We find that hallmarks of such a multiple-q state within a thin wire or channel can be a saw-like dependence of the depairing current and the existence of two distinct stable branches on it (a bistable current state).

Unconventional pairing in few-fermion systems at finite temperature

Attractively interacting two-component mixtures of fermionic particles confined in a one-dimensional harmonic trap are investigated. Properties of balanced and imbalanced systems are systematically explored with the exact diagonalization approach, focusing on the finite-temperature effects. Using single- and two-particle density distributions, specific non-classical pairing correlations are analyzed in terms of the noise correlations—quantity directly accessible in state-of-the-art experiments with ultra-cold atoms. It is shown that along with increasing temperature, any imbalanced system hosting Fulde–Ferrel–Larkin–Ovchinnikov pairs crossovers to a standard Bardeen-Cooper-Schrieffer one characterized by zero net momentum of resulting pairs. By performing calculations for systems with different imbalances, the approximate boundary between the two phases on a phase diagram is determined.

Emergent anisotropy in the Fulde–Ferrell–Larkin–Ovchinnikov state

Exotic superconductivity is formed by unconventional electron pairing and exhibits various unique properties that cannot be explained by the basic theory. The Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state is known as an exotic superconducting state in that the electron pairs have a finite center-of-mass momentum leading to a spatially modulated pattern of superconductivity. The spatial modulation endows the FFLO state with emergent anisotropy. However, the anisotropy has never been experimentally verified despite numerous efforts over the years. Here, we report detection of anisotropic acoustic responses depending on the sound propagation direction appearing above the Pauli limit. This anisotropy reveals that the two-dimensional FFLO state has a center-of-mass momentum parallel to the nesting vector on the Fermi surface. The present findings will facilitate our understanding of not only superconductivity in solids but also exotic pairings of various particles.

Phase diagrams for two-component D-wave fermion superfluids with density imbalance

Finite-temperature phase structures for asymmetric two-component D-wave fermion superfluids in the weak coupling BCS regime are investigated. The Fulde–Ferrell–Larkin-Ovchinnikov (FFLO) state becomes non-degenerate with the orientation of Cooper pair momentum due to the anisotropic pairing gap for D-wave pairing. The new parameter θ 0, corresponding to the orientation of Cooper pair momentum, greatly enriches the phase structures. Especially, the phase separation (PS) region in the phase diagram is significantly reduced comparing to that for S-wave pairing. Theoretically, the stability condition of solutions is equivalent to the positive definite Hessian matrix of free energy in the hyperplane defined by the number density constraints in the parameter space spanned by the average chemical potential μ, relative chemical potential h, paring gap Δ, pair momentum q, and θ 0. In addition, the stability condition of the superfluid density is essentially included in the positive definite Hessian matrix. Moreover, the positiveness of imbalance number susceptibility is always equivalent to the positiveness of the smaller eigenvalue λ − of the number susceptibility matrix. While the criteria ∂2Ω/∂Δ2 and against PS in previous studies are equivalent to λ − only under the prerequisite that the solution is a local minimum in the corresponding hyperplane.

Competition between orbital effects, Pauli limiting, and Fulde–Ferrell–Larkin–Ovchinnikov states in 2D transition metal dichalcogenide superconductors

We compare the upper critical field of bulk single-crystalline samples of the two intrinsic transition metal dichalcogenide 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–Ferrell–Larkin–Ovchinnikov (FFLO) state, while orbital effects suppress superconductivity in NbSe2 just below the Pauli limit, which excludes the formation of the FFLO state. From the out-of-plane anisotropies, the coherence length perpendicular to the layers of 31 Å in NbSe2 is much larger than the interlayer distance, leading to a significant orbital effect suppressing superconductivity before the Pauli limit is reached, in contrast to the more 2D NbS2.

Formation of tungsten carbide by focused ion beam process: A route to high magnetic field resilient patterned superconducting nanostructures

A scale for magnetic field resilience of a superconductor is set by the paramagnetic limit. Comparing the condensation energy of the Bardeen–Cooper–Schrieffer (BCS) singlet ground state with the paramagnetically polarized state suggests that for an applied field μ0H>1.8 Tc (in SI), singlet pairing is not energetically favorable. Materials exceeding or approaching this limit are interesting from fundamental and technological perspectives. This may be a potential indicator of triplet superconductivity, Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) pairing, and other mechanisms involving topological aspects of surface states and may also allow Cooper pair injection at high magnetic fields. We have analyzed the microscopic composition of such a material arising from an unexpected source. A microjet of an organo-metallic gas, W[(CO)6], can be decomposed by a gallium ion-beam, leaving behind a track of complex residue of gallium, tungsten, and carbon with remarkable superconducting properties, like an upper critical field, Hc2>10 T, above its paramagnetic limit. We carried out atomic probe tomography to establish the formation of nano-crystalline tungsten carbide (WC) in the tracks and the absence of free tungsten. Supporting calculations show that for Ga distributed on the surface of WC, its s,p-orbitals enhance the density of states near the Fermi energy. The observed variation of Hc2(T) does not show features typical of enhancement of critical field due to granularity. Our observations may be significant in the context of some recent theoretical calculation of the band structure of WC and experimental observation of superconductivity in a WC-metal interface.

Fermi Surface Structure and Isotropic Stability of Fulde-Ferrell-Larkin-Ovchinnikov Phase in Layered Organic Superconductor β″-(BEDT-TTF)2SF5CH2CF2SO3

The Fermi surface structure of a layered organic superconductor β″-(BEDT-TTF)2SF5CH2CF2SO3 was determined by angular-dependent magnetoresistance oscillations measurements and band-structure calculations. This salt was found to have two small pockets with the same area: a deformed square hole pocket and an elliptic electron pocket. Characteristic corrugations in the field dependence of the interlayer resistance in the superconducting phase were observed at any in-plane field directions. The features were ascribed to the commensurability (CM) effect between the Josephson vortex lattice and the periodic nodal structure of the superconducting gap in the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) phase. The CM effect was observed in a similar field region for various in-plane field directions, in spite of the anisotropic nature of the Fermi surface. The results clearly showed that the FFLO phase stability is insensitive to the in-plane field directions.

Search for Fulde–Ferrell–Larkin–Ovchinnikov Superfluidity in an Ultracold Gas of Fermi Atoms

Search for Fulde–Ferrell–Larkin–Ovchinnikov Superfluidity in an Ultracold Gas of Fermi Atoms

Josephson current in an irradiated Weyl semimetal junction* *Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0303203) and the National Natural Science Foundation of China (Grant No. 11474149).

The influence of the off-resonant circularly polarized light on the Josephson current in the time-reversal broken superconducting Weyl semimetal junctions is investigated by using the Bogoliubov–de Gennes equation and the transfer matrix approach. Both the zero momentum BCS pairing states and the finite momentum Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) pairing states are considered for the Weyl superconductors. When a circularly polarized light is applied, it is shown that the current phase relation remains unchanged for the BCS pairing with the increasing of incident radiation intensity A 0. For FFLO pairing, the Josephson current exhibits the 0–π transition and periodic oscillation as a function of A 0. The dependence of free energy and critical current on A 0 are also investigated.

Fulde–Ferrell–Larkin–Ovchinnikov State in Perpendicular Magnetic Fields in Strongly Pauli-Limited Quasi-Two-Dimensional Superconductors

We examine the Fermi-surface effect called the nesting effect for the FFLO state in strongly Pauli-limited Q2D superconductors, focusing on the effect of 3D factors, such as interlayer electron transfer, interlayer pairing, and off-plane magnetic fields including those perpendicular to the most conductive layers. We examine the systems with a large Maki parameter so that the orbital pair-breaking effect is negligible, except for the locking of the direction of the FFLO vector q in the field direction.It is known that the nesting effect for the FFLO state can be strong in QLD systems in which the orbital pair-breaking effect is suppressed by applying the mag. field parallel to the layers. Hence, it has sometimes been suggested that the nesting effect may hardly enhance the stability of the FFLO state for perpendicular fields. We illustrate that, contrary to this view, the nesting effect can strongly stabilize the FFLO state for perpendicular fields as well as for parallel fields when tz is small so that the Fermi surfaces are open in the kz-direction, where tz denotes the interlayer transfer energy. In particular, the nesting effect in perpendicular fields can be strong in interlayer states. For example, in systems with cylindrical Fermi surfaces warped by tz /= 0, interlayer states with Dlt_k prop sin k_z exhibit mu_e Hc=1.65 Dlt_a0 for perpendicular fields, which is much larger than typical values for parallel fields, such as mu_e Hc=Dlt_s0 of the s-wave state and mu_e Hc = 1.28 Delta_d0 of the d-wave state in cylindrical systems with tz=0. The present result could potentially provide a physical reason why the areas in the phase diagrams occupied by the high-field phases for the perpendicular and parallel fields are of the same order in CeCoIn5 and FeSe.

Fulde–Ferrell–Larkin–Ovchinnikov states in equally populated Fermi gases in a two-dimensional moving optical lattice* *Project supported by the Beijing Natural Science Foundation, China (Grant No. Z180013), the National Natural Science Foundation of China (Grant Nos. 11522436, 11774425, and 12074428), the National Key R&D Program of China (Grant No. 2018YFA0306501), and the Research Funds of Renmin University of China (Grant Nos. 16XNLQ03

We study the possibility of stabilizing a Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state in an equally populated two-component Fermi gas trapped in a moving two-dimensional optical lattice. For a system with nearly half filling, we find that a finite pairing momentum perpendicular to the moving direction can be spontaneously induced for a proper choice of lattice velocity. As a result, the total pairing momentum is tilted towards the nesting vector to take advantage of the significant enhancement of the density of states.

Thermodynamic properties of spin-imbalance harmonically trapped one-dimensional attractive 6Li atomic gas

The thermodynamic properties of 6Li atomic gas system, with imbalanced spin populations trapped in one-dimension, were systematically investigated using the Static Fluctuation Approximation. The two-body interaction used is an attractive contact potential. The effects of gas parameter [Formula: see text] and spin polarization [Formula: see text], on the thermodynamic properties and effective magnetic field were investigated. We observed a decrease in [Formula: see text] and an enhancement in [Formula: see text] and [Formula: see text] with increasing [Formula: see text]. At strong interaction and at [Formula: see text], the behavior of entropy with [Formula: see text] indicated two different phases. At small spin polarization [Formula: see text], the system could be in Fulde–Ferrell–Larkin Ovchinnikov (FFLO) state, while above [Formula: see text], the system might be in normal state. In addition, we found a clear decrease in both [Formula: see text] and [Formula: see text] and an enhancement in [Formula: see text] with the increase of the interaction strength. Our results are consistent with the reported results obtained by the mean-field Bogoliubov–de Gennes method, the Bardeen–Cooper–Schrieffer (BCS) approximation and Nozieres–Schmitt–Rink (NSR) theory.

Charge density waves beyond the Pauli paramagnetic limit in 2D systems

Two-dimensional materials are ideal candidates to host Charge Density Waves (CDWs) that exhibit paramagnetic limiting behavior, similar to the well-known case of superconductors. Here, we study how CDWs in two-dimensional systems can survive beyond the Pauli limit when they are subjected to a strong magnetic field by developing a generalized mean-field theory of CDWs under Zeeman fields that includes incommensurability, imperfect nesting, and temperature effects and the possibility of a competing or coexisting Spin Density Wave (SDW) order. Our numerical calculations yield rich phase diagrams with distinct high-field phases above the Pauli limiting field. For perfectly nested commensurate CDWs, a q-modulated CDW phase that is completely analogous to the superconducting Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) phase appears at high fields. In the more common case of imperfect nesting, the commensurate CDW ground state undergoes a series of magnetic-field-induced phase transitions first into a phase where commensurate CDW and SDW coexist and subsequently into another phase where CDW and SDW acquire a q-modulation that is, however, distinct from the pure FFLO CDW phase. The commensurate CDW + SDW phase occurs for fields comparable to but less than the Pauli limit and survives above it. Thus, this phase provides a plausible mechanism for the CDW to survive at high fields without the need for forming the more fragile FFLO phase. We suggest that the recently discovered 2D materials like the transition metal dichalcogenides offer a promising platform for observing such exotic field-induced CDW phenomena.

The Gor'kov and Melik‐Barkhudarov Correction to the Mean‐Field Critical Field Transition to Fulde–Ferrell–Larkin–Ovchinnikov States

AbstractThe Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) states, characterized by Cooper pairs condensed at finite‐momentum are, at the same time, exotic and elusive. It is partially due to the fact that the FFLO states allow superconductivity to survive even in strong magnetic fields at the mean‐field level. The effects of induced interactions at zero temperature are calculated in both clean and dirty cases, and it is found that the critical field at which the quantum phase transition to an FFLO state occurs at the mean‐field level is strongly suppressed in imbalanced Fermi gases. This strongly shrinks the phase space region where the FFLO state is unstable and more exotic ground state is to be found. In the presence of high level impurities, this shrinkage may destroy the FFLO state completely.

The Physics of Pair-Density Waves: Cuprate Superconductors and Beyond

We review the physics of pair-density wave (PDW) superconductors. We begin with a macroscopic description that emphasizes order induced by PDW states, such as charge-density wave, and discuss related vestigial states that emerge as a consequence of partial melting of the PDW order. We review and critically discuss the mounting experimental evidence for such PDW order in the cuprate superconductors, the status of the theoretical microscopic description of such order, and the current debate on whether the PDW is a mother order or another competing order in the cuprates. In addition, we give an overview of the weak coupling version of PDW order, Fulde–Ferrell–Larkin–Ovchinnikov states, in the context of cold atom systems, unconventional superconductors, and noncentrosymmetric and Weyl materials.

Fulde–Ferrell–Larkin–Ovchinnikov State in Quasi-One-Dimensional Systems: Correlation between Fermi-Surface Distortion and Optimal In-Plane Magnetic-Field Direction

The Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state is systematically examined in a generic model of quasi-one-dimensional (Q1D) type-II superconductors that has six hopping integrals of electrons as...