Conventional superconductivity in the doped kagome superconductor Cs(V0.86Ta0.14)3Sb5 from vortex lattice studies

A hallmark of unconventional superconductors is a complex electronic phase diagram where intertwined orders of charge-spin-lattice degrees of freedom compete and coexist. While the kagome metals such as CsV3Sb5 also exhibit complex behavior, involving coexisting charge density wave order and superconductivity, much is unclear about the microscopic origin of the superconducting pairing. We study the vortex lattice in the superconducting state of Cs(V0.86Ta0.14)3Sb5, where the Ta-doping suppresses charge order and enhances superconductivity. Using small-angle neutron scattering, a strictly bulk probe, we show that the vortex lattice exhibits a strikingly conventional behavior. This includes a triangular symmetry with a period consistent with 2e-pairing, a field dependent scattering intensity that follows a London model, and a temperature dependence consistent with a uniform superconducting gap. Our results suggest that optimal bulk superconductivity in Cs(V1-xTax)3Sb5 arises from a conventional Bardeen-Cooper-Schrieffer electron-lattice coupling, different from spin fluctuation mediated unconventional copper- and iron-based superconductors.

Instrument Base of the Reactor PIK

Abstract

The program of developing the instrument base of reactor complex PIK is reviewed. This program is carried out in correspondence with the Decree of the President of the Russian Federation No. 356 on July 25, 2019 and the Federal Scientific and Technical Program for the Development of Synchrotron and Neutron Research and Research Infrastructure on the 2019–2027s. The general concept and plans of formation of the instrument base are reported in the four-volume manuscript PIK Reactor Complex (editors V.L. Aksenov and M.V. Kovalchuk), published in 2015.

Interplay of the Spin Density Wave and a Possible Fulde-Ferrell-Larkin-Ovchinnikov State in CeCoIn_{5} in Rotating Magnetic Field

The d-wave superconductor CeCoIn_{5} has been proposed as a strong candidate for supporting the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state near the low-temperature boundary of its upper critical field. Neutron diffraction, however, finds spin-density-wave (SDW) order in this part of the phase diagram for field in the a-b plane, and evidence for the SDW disappears as the applied field is rotated toward the tetragonal c axis. It is important to understand the interplay between the SDW and a possible FFLO state in CeCoIn_{5}, as the mere existence of an SDW does not necessarily exclude an FFLO state. Here, based on a model constructed on the basis of available experiments, we show that an FFLO state competes with an SDW phase. The SDW state in CeCoIn_{5} is stabilized when the field is directed close to the a-b plane. When the field is rotated toward the c axis, the FFLO state emerges, and the SDW phase disappears. In the FFLO state, the nodal planes with extra quasiparticles (where the superconducting order parameter is zero) are perpendicular to the field, and in the SDW phase, the quasiparticle density of states is reduced. We test this model prediction by measuring heat transported by normal quasiparticles in the superconducting state. As a function of field, we observe a reduction of thermal conductivity for field close to the a-b plane and an enhancement of thermal conductivity when field is close to the c axis, consistent with theoretical expectations. Our modeling and experiments, therefore, indicate the existence of the FFLO state when field is parallel to the c axis.

Visualizing heavy fermion confinement and Pauli-limited superconductivity in layered CeCoIn5

Layered material structures play a key role in enhancing electron–electron interactions to create correlated metallic phases that can transform into unconventional superconducting states. The quasi-two-dimensional electronic properties of such compounds are often inferred indirectly through examination of bulk properties. Here we use scanning tunneling microscopy to directly probe in cross-section the quasi-two-dimensional electronic states of the heavy fermion superconductor CeCoIn₅. Our measurements reveal the strong confined nature of quasiparticles, anisotropy of tunneling characteristics, and layer-by-layer modulated behavior of the precursor pseudogap gap phase. In the interlayer coupled superconducting state, the orientation of line defects relative to the d-wave order parameter determines whether in-gap states form due to scattering. Spectroscopic imaging of the anisotropic magnetic vortex cores directly characterizes the short interlayer superconducting coherence length and shows an electronic phase separation near the upper critical in-plane magnetic field, consistent with a Pauli-limited first-order phase transition into a pseudogap phase.

The electronic properties along the out-of-plane direction of layered materials are often inferred indirectly. Here, Gyenis et al. directly probe in cross-section the quasi-two-dimensional correlated electronic states of the heavy fermion superconductor CeCoIn₅.

Resonances in the Field-Angle-Resolved Thermal Conductivity of CeCoIn_{5}

The thermal conductivity measurement in a rotating magnetic field is a powerful probe of the structure of the superconducting energy gap. We present high-precision measurements of the low-temperature thermal conductivity in the unconventional heavy-fermion superconductor CeCoIn_{5}, with the heat current J along the nodal [110] direction of its d_{x^{2}-y^{2}} order parameter and the magnetic field up to 7 T rotating in the ab plane. In contrast to the smooth oscillations found previously for J∥[100], we observe a sharp resonancelike peak in the thermal conductivity when the magnetic field is also in the [110] direction, parallel to the heat current. We explain this peak qualitatively via a model of the heat transport in a d-wave superconductor. In addition, we observe two smaller but also very sharp peaks in the thermal conductivity for the field directions at angles Θ≈±33° with respect to J. The origin of the observed resonances at Θ≈±33° at present defies theoretical explanation. The challenge of uncovering their source will dictate exploring theoretically more complex models, which might include, e.g., fine details of the Fermi surface, Andreev bound vortex core states, a secondary superconducting order parameter, and the existence of gaps in spin and charge excitations.

Exotic magnetic states in Pauli-limited superconductors

Magnetism and superconductivity compete or interact in complex and intricate ways. Here we review the special case where novel magnetic phenomena appear due to superconductivity, but do not exist without it. Such states have recently been identified in unconventional superconductors. They are different from the mere coexistence of magnetic order and superconductivity in conventional superconductors, or from competing magnetic and superconducting phases in many materials. We describe the recent progress in the study of such exotic magnetic phases, and articulate the many open questions in this field.

Robust metastable skyrmions and their triangular-square lattice structural transition in a high-temperature chiral magnet

Skyrmions, topologically protected nanometric spin vortices, are being investigated extensively in various magnets. Among them, many structurally chiral cubic magnets host the triangular-lattice skyrmion crystal (SkX) as the thermodynamic equilibrium state. However, this state exists only in a narrow temperature and magnetic-field region just below the magnetic transition temperature T_c, while a helical or conical magnetic state prevails at lower temperatures. Here we describe that for a room-temperature skyrmion material, β-Mn-type Co ₈Zn ₈Mn ₄, a field-cooling via the equilibrium SkX state can suppress the transition to the helical or conical state, instead realizing robust metastable SkX states that survive over a very wide temperature and magnetic-field region. Furthermore, the lattice form of the metastable SkX is found to undergo reversible transitions between a conventional triangular lattice and a novel square lattice upon varying the temperature and magnetic field. These findings exemplify the topological robustness of the once-created skyrmions, and establish metastable skyrmion phases as a fertile ground for technological applications.

Angle-resolved heat capacity of heavy fermion superconductors

Owing to a strong Coulomb repulsion, heavy electron superconductors mostly have anisotropic gap functions which have nodes for certain directions in the momentum space. Since the nodal structure is closely related to the pairing mechanism, its experimental determination is of primary importance. This article discusses the experimental methods of the gap determination by bulk heat capacity measurements in a rotating magnetic field. The basic idea is based on the fact that the quasiparticle density of states in the vortex state of nodal superconductors is field and direction dependent. We present our recent experimental results of the field-orientation dependence of the heat capacity in heavy fermion superconductors CeTIn5 (T  =  Co, Ir), UPt3, CeCu2Si2, and UBe13 and discuss their gap structures.

Quantum Critical Quasiparticle Scattering within the Superconducting State of CeCoIn_{5}

The thermal conductivity κ of the heavy-fermion metal CeCoIn_{5} was measured in the normal and superconducting states as a function of temperature T and magnetic field H, for a current and field parallel to the [100] direction. Inside the superconducting state, when the field is lower than the upper critical field H_{c2}, κ/T is found to increase as T→0, just as in a metal and in contrast to the behavior of all known superconductors. This is due to unpaired electrons on part of the Fermi surface, which dominate the transport above a certain field. The evolution of κ/T with field reveals that the electron-electron scattering (or transport mass m^{⋆}) of those unpaired electrons diverges as H→H_{c2} from below, in the same way that it does in the normal state as H→H_{c2} from above. This shows that the unpaired electrons sense the proximity of the field-tuned quantum critical point of CeCoIn_{5} at H^{⋆}=H_{c2} even from inside the superconducting state. The fact that the quantum critical scattering of the unpaired electrons is much weaker than the average scattering of all electrons in the normal state reveals a k-space correlation between the strength of pairing and the strength of scattering, pointing to a common mechanism, presumably antiferromagnetic fluctuations.

From Kondo lattices to Kondo superlattices

The realization of new classes of ground states in strongly correlated electron systems continues to be a major issue in condensed matter physics. Heavy fermion materials, whose electronic structure is essentially three-dimensional, are one of the most suitable systems for obtaining novel electronic states because of their intriguing properties associated with many-body effects. Recently, a state-of-the-art molecular beam epitaxy technique was developed to reduce the dimensionality of heavy electron systems by fabricating artificial superlattices that include heavy fermion compounds; this approach can produce a new type of electronic state in two-dimensional (2D) heavy fermion systems. In artificial superlattices of the antiferromagnetic heavy fermion compound CeIn3 and the conventional metal LaIn3, the magnetic order is suppressed by a reduction in the thickness of the CeIn3 layers. In addition, the 2D confinement of heavy fermions leads to enhancement of the effective electron mass and deviation from the standard Fermi liquid electronic properties, which are both associated with the dimensional tuning of quantum criticality. In the superconducting superlattices of the heavy fermion superconductor CeCoIn5 and nonmagnetic metal YbCoIn5, signatures of superconductivity are observed even at the thickness of one unit-cell layer of CeCoIn5. The most remarkable feature of this 2D heavy fermion superconductor is that the thickness reduction of the CeCoIn5 layers changes the temperature and angular dependencies of the upper critical field significantly. This result is attributed to a substantial suppression of the Pauli pair-breaking effect through the local inversion symmetry breaking at the interfaces of CeCoIn5 block layers. The importance of the inversion symmetry breaking in this system has also been supported by site-selective nuclear magnetic resonance spectroscopy, which can resolve spectroscopic information from each layer separately, even within the same CeCoIn5 block layer. In addition, recent experiments involving CeCoIn5/YbCoIn5 superlattices have shown that the degree of the inversion symmetry breaking and, in turn, the Rashba splitting are controllable, offering the prospect of achieving even more fascinating superconducting states. Thus, these Kondo superlattices pave the way for the exploration of unconventional metallic and superconducting states.

Controllable Rashba spin-orbit interaction in artificially engineered superlattices involving the heavy-fermion superconductor CeCoIn5

By using a molecular beam epitaxy technique, we fabricate a new type of superconducting superlattices with controlled atomic layer thicknesses of alternating blocks between the heavy-fermion superconductor CeCoIn5, which exhibits a strong Pauli pair-breaking effect, and nonmagnetic metal YbCoIn5. The introduction of the thickness modulation of YbCoIn5 block layers breaks the inversion symmetry centered at the superconducting block of CeCoIn5. This configuration leads to dramatic changes in the temperature and angular dependence of the upper critical field, which can be understood by considering the effect of the Rashba spin-orbit interaction arising from the inversion symmetry breaking and the associated weakening of the Pauli pair-breaking effect. Since the degree of thickness modulation is a design feature of this type of superlattices, the Rashba interaction and the nature of pair breaking are largely tunable in these modulated superlattices with strong spin-orbit coupling.

Strong pressure dependence of the magnetic penetration depth in single crystals of the heavy-fermion superconductor CeCoIn5 studied by muon spin rotation

In the tetragonal heavy fermion system CeCoIn(5) the unconventional superconducting state is probed by means of muon spin rotation. The pressure dependence (0-1 GPa) of the basal-plane magnetic penetration depth (λ(a)), the penetration depth anisotropy (γ = λ(c)/λ(a)) and the temperature dependence of 1/λ(i)(2) (i = a, c) were studied in single crystals. A strong decrease of λ(a) with pressure was observed, while γ and λ(i)(2)(0)/λ(i)(2)(T) are pressure independent. A linear relationship between 1/λ(a)(2)(270 mK) and T(c) was also found. The large decrease of λ(a) with pressure is the signature of an increase of the number of superconducting quasiparticles by a factor of about 2.

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.

Berezinskii-Kosterlitz-Thouless transition to the superconducting state of heavy-fermion superlattices

We propose an explanation of the superconducting transitions discovered in the heavy-fermion superlattices by Mizukami et al. [Nature Phys. 7, 849 (2011)] in terms of Berezinskii-Kosterlitz-Thouless (BKT) transition. We observe that the effective mass mismatch between the heavy-fermion superconductor and the normal metal regions provides an effective barrier that enables quasi-2D superconductivity in such systems. We show that the resistivity data, both with and without magnetic field, are consistent with BKT transition. Furthermore, we study the influence of a nearby magnetic quantum critical point on the vortex system and find that the vortex core energy can be significantly reduced due to magnetic fluctuations. Further reduction of the gap with decreasing number of layers is understood as a result of pair breaking effect of Yb ions at the interface.

Superconducting gap structure of the 115s revisited

Density functional theory calculations of the electronic structure of Ce- and Pu-based heavy fermion superconductors in the so-called 115 family are performed. The gap equation is used to consider which superconducting order parameters are most favorable assuming a pairing interaction that is peaked at (π, π, qz)—the wavevector for the antiferromagnetic ordering found in close proximity. In addition to the commonly accepted dx2−y2 order parameter, there is evidence that an extended s-wave order parameter with nodes is also plausible. We discuss whether these results are consistent with current observations and possible measurements that could help distinguish between these scenarios.

Vortex lattice studies in CeCoIn5 with H is orthogonal to c

We present small angle neutron scattering studies of the vortex lattice (VL) in CeCoIn5 with magnetic fields applied parallel (H) to the antinodal [100] and nodal [110] directions. For H is parallel to [100], a single VL orientation is observed, while a 90° reorientation transition is found for H is parallel to [110]. For both field orientations and VL configurations we find a distorted hexagonal VL with an anisotropy, Γ=2.0±0.05. The VL form factor shows strong Pauli paramagnetic effects similar to what have previously been reported for H is parallel to [001]. At high fields, above which the upper critical field (H(c2)) becomes a first-order transition, an increased disordering of the VL is observed.

Strong magnetic fluctuations in a superconducting state of CeCoIn5

We show results on the vortex core dissipation through current-voltage measurements under applied pressure and magnetic field in the superconducting phase of CeCoIn{5}. We find that as soon as the system becomes superconducting, the vortex core resistivity increases sharply as the temperature and magnetic field decrease. The sharp increase in flux-flow resistivity is due to quasiparticle scattering on critical antiferromagnetic fluctuations. The strength of magnetic fluctuations below the superconducting transition suggests that magnetism is complementary to superconductivity and therefore must be considered in order to fully account for the low-temperature properties of CeCoIn{5}.

A 17 T horizontal field cryomagnet with rapid sample change designed for beamline use

We describe a new 17 T cryomagnet for neutron, x-ray or optical experiments with rapid in situ sample change. Sample temperatures are controllable from below 2 K to 300 K in vacuum. Alternatively a room temperature bore insert can be used for experiments at the field center under atmospheric conditions. Some of the advantages of this system include very low background scattering due to the small amount of material in the beam path, rapid cooldown, and fast field ramping. Access is available in a ±10°-11° cone around the field direction on both sides.

Evidence for a magnetically driven superconducting Q phase of CeCoIn5

We have studied the magnetic order inside the superconducting phase of CeCoIn5 for fields along the [1 0 0] crystallographic direction using neutron diffraction. We find a spin-density wave order with an incommensurate modulation Q=(q,q,1/2) and q=0.45(1), which within our experimental uncertainty is indistinguishable from the spin-density wave found for fields applied along [1 -1 0]. The magnetic order is thus modulated along the lines of nodes of the d{x{2}-y{2}} superconducting order parameter, suggesting that it is driven by the electron nesting along the superconducting line nodes. We postulate that the onset of magnetic order leads to reconstruction of the superconducting gap function and a magnetically induced pair density wave.

Sign reversal of field-angle resolved heat capacity oscillations in a heavy Fermion superconductor CeCoIn5 and d{x{2}-y{2}} pairing symmetry

To identify the superconducting gap symmetry in CeCoIn5 (T{c}=2.3 K), we measured the angle-resolved specific heat (C{phi}) in a field rotated around the c axis down to a very low temperature, 0.05T{c}, and made detailed theoretical calculations. In a field of 1 T, a sign reversal of the fourfold angular oscillation in C{phi} was observed at T approximately 0.1T{c} upon entering a quasiclassical regime where the maximum of C{phi} corresponds to the antinodal direction, coinciding with the angle-resolved density of states (ADOS) calculation. The C{phi} behavior, which exhibits minima along the [110] directions, unambiguously allows us to conclude d{x{2}-y{2}} symmetry of this system. The ADOS-quasiclassical region is confined to a narrow T and H domain within T/T{c} approximately 0.1 and 1.5 T (0.13H{c2}).

Field-induced coupled superconductivity and spin density wave order in the heavy fermion compound CeCoIn5

The high-field superconducting state in CeCoIn(5) has been studied by transverse field muon spin rotation measurements with an applied field parallel to the crystallographic c axis close to the upper critical field mu(0)H(c2) = 4.97 T. At magnetic fields mu(0)H > or = 4.8 T the muon Knight shift is enhanced and the superconducting transition changes from second order towards first order as predicted for Pauli-limited superconductors. The field and temperature dependence of the transverse muon spin relaxation rate sigma reveal paramagnetic spin fluctuations in the field regime from 2 T < or = mu(0)H < 4.8 T. In the normal state close to H(c2) correlated spin fluctuations as described by the self-consistent renormalization theory are observed. The results support the formation of a mode-coupled superconducting and antiferromagnetically ordered phase in CeCoIn(5) for H directed parallel to the c axis.

Morphology of the superconducting vortex lattice in ultrapure niobium

The morphology of the superconducting flux line lattice (FLL) of Nb comprises gradual variations with various lock-in transitions and symmetry breaking rotations. We report a comprehensive small-angle neutron scattering study of the FLL in an ultrapure single crystal of Nb as a function of the orientation of the applied magnetic field. We attribute the general morphology of the FLL and its orientation to three dominant mechanisms; first, nonlocal contributions, second, the transition between open and closed Fermi surface sheets and, third, the intermediate mixed state between the Meissner and the Shubnikov phase.

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.

Instability of square vortex lattice in d-wave superconductors is due to paramagnetic depairing

The effects of paramagnetic depairing on structural transitions between vortex lattices of a quasi-two-dimensional d-wave superconductor are examined. We find that, when the Maki parameter alphaM is of order unity, a square lattice induced by a d-wave pairing is destabilized with increasing fields, and that a reentrant rhombic lattice occurs in higher fields. Further, a weak Fermi surface anisotropy competitive with the pairing symmetry induces another structural transition near Hc2. These results are consistent with the structure changes of the vortex lattice in CeCoIn5 in H parallel c determined from recent neutron scattering data.