Effects of two-band superconductivity on the flux-line lattice in magnesium diboride

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.

Tunable vortex bound states in multiband CsV3Sb5-derived kagome superconductors

Vortices and bound states offer an effective means of comprehending the electronic properties of superconductors. Recently, surface-dependent vortex core states have been observed in the newly discovered kagome superconductors CsV3Sb5. Although the spatial distribution of the sharp zero energy conductance peak appears similar to Majorana bound states arising from the superconducting Dirac surface states, its origin remains elusive. In this study, we present observations of tunable vortex bound states (VBSs) in two chemically-doped kagome superconductors Cs(V1-xTrx)3Sb5 (Tr = Ta or Ti), using low-temperature scanning tunneling microscopy/spectroscopy. The CsV3Sb5-derived kagome superconductors exhibit full-gap-pairing superconductivity accompanied by the absence of long-range charge orders, in contrast to pristine CsV3Sb5. Zero-energy conductance maps demonstrate a field-driven continuous reorientation transition of the vortex lattice, suggesting multiband superconductivity. The Ta-doped CsV3Sb5 displays the conventional cross-shaped spatial evolution of Caroli-de Gennes-Matricon bound states, while the Ti-doped CsV3Sb5 exhibits a sharp, non-split zero-bias conductance peak (ZBCP) that persists over a long distance across the vortex. The spatial evolution of the non-split ZBCP is robust against surface effects and external magnetic field but is related to the doping concentrations. Our study reveals the tunable VBSs in multiband chemically-doped CsV3Sb5 system and offers fresh insights into previously reported Y-shaped ZBCP in a non-quantum-limit condition at the surface of kagome superconductor.

Effects of magnetic and non-magnetic doping on the vortex lattice in MgB2

Small-angle neutron scattering has been used to study the vortex lattice in superconducting MgB2 doped with either manganese or carbon to achieve a similar suppression of the critical temperature. Measurements were performed with the magnetic field applied along the c axis, where the vortex lattice in pure MgB2 is known to undergo a field- and temperature-driven 30° rotation transition. For Mn doping, the vortex lattice phase diagram remains qualitatively similar to that of pure MgB2, indicating only a modest effect on the vortex–vortex interaction. In contrast, the vortex lattice rotation transition is completely suppressed in the C-doped case, probably due to a change in the electronic structure which affects the two-band/two-gap nature of superconductivity in MgB2. The vortex lattice longitudinal correlation length shows the opposite behavior, remaining roughly unchanged between pure and C-doped MgB2 while it is significantly reduced in the Mn-doped case. However, the extensive vortex lattice metastability and related activated behavior, observed in conjunction with the vortex lattice transition in pure MgB2, are also seen in the Mn-doped sample. This shows that the vortex lattice disordering is not associated with a substantially increased vortex pinning.

Persistence of metastable vortex lattice domains in MgB2 in the presence of vortex motion

Recently, extensive vortex lattice metastability was reported in MgB2 in connection with a second-order rotational phase transition. However, the mechanism responsible for these well-ordered metastable vortex lattice phases is not well understood. Using small-angle neutron scattering, we studied the vortex lattice in MgB2 as it was driven from a metastable to the ground state through a series of small changes in the applied magnetic field. Our results show that metastable vortex lattice domains persist in the presence of substantial vortex motion and directly demonstrate that the metastability is not due to vortex pinning. Instead, we propose that it is due to the jamming of counterrotated vortex lattice domains which prevents a rotation to the ground state orientation.

Observation of well-ordered metastable vortex lattice phases in superconducting MgB2 using small-angle neutron scattering

The vortex lattice (VL) symmetry and orientation in clean type-II superconductors depends sensitively on the host material anisotropy, vortex density and temperature, frequently leading to rich phase diagrams. Typically, a well-ordered VL is taken to imply a ground-state configuration for the vortex-vortex interaction. Using neutron scattering we studied the VL in MgB(2) for a number of field-temperature histories, discovering an unprecedented degree of metastability in connection with a known, second-order rotation transition. This allows, for the first time, structural studies of a well-ordered, nonequilibrium VL. While the mechanism responsible for the longevity of the metastable states is not resolved, we speculate it is due to a jamming of VL domains, preventing a rotation to the ground-state orientation.

First-order reorientation transition of the flux-line lattice in CaAlSi

The flux-line lattice in CaAlSi has been studied by small-angle neutron scattering. A well-defined hexagonal flux-line lattice is seen just above H(c1) in an applied field of only 54 Oe. A 30° reorientation of this vortex lattice has been observed in a very low field of 200 Oe. This reorientation transition appears to be first-order and could be explained by nonlocal effects. The magnetic field dependence of the form factor is well-described by a single penetration depth of λ=1496(1) Å and a single coherence length of ξ=307(1) Å at 2 K. At 1.5 K, the penetration depth anisotropy is γ(λ)=2.7(1), with the field applied perpendicular to the c axis, and agrees with the coherence length anisotropy determined from critical field measurements.

Effect of two length scales on the properties of MgB(2) for arbitrary applied magnetic field

Experiments carried out on the intermetallic superconducting material MgB(2) have shown anomalous magnetic field dependence of upper critical field, small angle neutron scattering form factor, specific heat, critical current etc. Similarly, scanning tunnelling microscopy (STM) experiments on vortex structures have shown unusually large vortex core size and two different magnetic and spatial field scales. Also, whereas the specific heat measurements and isotope shift experiments have shown Bardeen-Cooper-Schrieffer-like (BCS-like) behaviour, the temperature dependences of the penetration depth experiments have shown non-BCS-like behaviour. These anomalous behaviours have been attributed to the multiband superconductivity of this material and the nature of the local spatial behaviour of the magnetic induction and the order parameter components having two length scales. We report an analytical investigation of the effect of two length scales on the temperature and the applied magnetic field dependence of several properties of MgB(2), such as, the penetration depth, single vortex and vortex lattice structure, vortex core radius, reversible magnetization, critical current, small angle neutron scattering form factor and the shear modulus of the vortex lattice within the framework of two-order parameter Ginzburg-Landau theory. We solve the corresponding nonlinear Ginzburg-Landau equations numerically exactly using an iterative method for arbitrary applied field H(c1) < H < H(c2), the Ginzburg-Landau parameter and vortex lattice symmetry. This enables us to compute the local spatial behaviour of the magnetic induction and the order parameters accurately for arbitrary applied field and a wide range of temperature. Comparison of the analytical results with experiments on MgB(2) gives very good agreement.

Anisotropy of the Sommerfeld coefficient in magnesium diboride single crystals

The anisotropic field dependence of the Sommerfeld coefficient gamma has been measured down to B-->0 by combining specific heat and Hall probe magnetization measurements in MgB2 single crystals. We find that gamma(B,theta) is the sum of two contributions arising from the sigma and pi band, respectively. We show that gammasigma(B,theta)=B/Bc2(theta) where Bc2(theta)=Bc2ab/sqrt[sin2theta+Gamma2cos2theta] with Gamma approximately 5.4 (theta being the angle between the applied field and the c axis) and gammapi(B,theta)=gammapi(B)=B/Bpi(B). The "critical field" of the pi band Bpi is fully isotropic but field dependent increasing from approximately 0.25 T for B< or =0.1 T up to 3 T approximately Bc2c for B-->3 T. Because of the coupling of the two bands, superconductivity survives in the pi band up to 3 T but is totally destroyed above for any orientation of the field.

Experimental evidence for two gaps in the high-temperature La1.83Sr0.17CuO4 superconductor

The in-plane magnetic field penetration depth (lambda(ab)) in single-crystal La1.83Sr0.17CuO4 was investigated by muon-spin rotation (muSR). The temperature dependence of lambda(ab)(-2) has an inflection point around 10-15 K, suggesting the presence of two superconducting gaps: a large gap (Delta(1)(d)) with d-wave and a small gap (Delta(2)(s)) with s-wave symmetry. The zero-temperature values of the gaps at mu(0)H=0.02 T were found to be Delta(1)(d)(0)=8.2(1) meV and Delta(2)(s)(0)=1.57(8) meV.

Local superconducting density of States of ErNi2B2C

We present local tunneling microscopy and spectroscopy measurements at low temperatures in single crystalline samples of the magnetic superconductor ErNi2B2C . The electronic local density of states shows a striking departure from s-wave BCS theory with a finite value at the Fermi level, which amounts to half of the normal phase density of states.

Field dependence of the vortex core size in a multiband superconductor

The magnetic field dependence of the vortex core size in the multiband superconductor NbSe2 has been determined from muon spin rotation measurements. The spatially extended nature of the quasiparticle core states associated with the smaller gap leads to a rapid field-induced shrinkage of the core size at low fields, while the more tightly bound nature of the states associated with the larger gap leads to a field-independent core size for fields greater than 4 kOe. A simple model is proposed for the density of delocalized core states that establishes a direct relationship between the field-induced reduction of the vortex core size and the corresponding enhancement of the electronic thermal conductivity. We show that this model accurately describes both NbSe2 and the single-band superconductor V3Si.

Temperature-dependent anisotropy of the penetration depth and coherence length of MgB2

We report measurements of the temperature-dependent anisotropies (gamma(lambda) and gamma(xi)) of both the London penetration depth lambda and the upper critical field of MgB2. Data for gamma(lambda)=lambda(c)/lambda(a) was obtained from measurements of lambda(a) and lambda(c) on a single crystal sample using a tunnel diode oscillator technique. gamma(xi)=H(perp)c(c2)/H(||c)(c2) was deduced from field-dependent specific heat measurements on the same sample. Gamma(lambda) and gamma(xi) have opposite temperature dependencies, but close to T(c) tend to a common value (gamma(lambda) similar or equal to gamma(xi)=1.75 +/- 0.05). These results are in good agreement with theories accounting for the two-gap nature of MgB2.

Effect of two gaps on the flux-lattice internal field distribution: evidence of two length scales in Mg(1-x)AlxB2 from muSR

We have measured the transverse field muon spin precession in the flux-lattice (FL) state of the two-gap superconductor MgB2 and of the electron doped compounds Mg(1-x)AlxB2 in magnetic fields up to 2.8 T. We show the effect of the two gaps on the internal field distribution in the FL, from which we determine two coherence length parameters and the doping dependence of the London penetration depth. This is an independent determination of the complex vortex structure already suggested by the STM observation of large vortices in a MgB2 single crystal. Our data agree quantitatively with STM and we thus validate a new phenomenological model for the internal fields.

Anisotropies of the lower and upper critical fields in MgB2 single crystals

The temperature dependence of the upper (H(c2)) and lower (H(c1)) critical fields has been deduced from Hall probe magnetization measurements of high quality MgB2 single crystals along the two main crystallographic directions. We show that Gamma(H(c2))=H(c2 axially ab)/H(c2 axially c) and Gamma(H(c1))=H(c1 axially c)/H(c1 axially ab) differ significantly at low temperature (being approximately 5 and approximately 1, respectively) and have opposite temperature dependencies. We suggest that MgB2 can be described by a single field dependent anisotropy parameter gamma(H) (=lambda(c)/lambda(ab)=xi(ab)/xi(c)) that increases from Gamma(H(c1)) at low field to Gamma(H(c2)) at high field.