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DOE OSTI2025

What causes the variation in superconducting properties of UTe 2 ?

Reaching a consensus on the superconducting order parameter of unconventional superconductors remains a central challenge in the field of magnetically-mediated superconductivity. Though UTe 2 is largely accepted as a rare example of an odd-parity superconductor, its precise order parameter remains highly debated, even at ambient conditions. A key underlying issue is the large sample-to-sample variation in superconducting properties at zero applied pressure and magnetic field. Here, we investigate the origin of the observed variation by means of single crystal x-ray diffraction (SC-XRD) and scanning transmission electron microscopy (STEM) measurements. Our results reveal highly ordered crystalline lattices, in agreement with the expected Immm structure, and no signs of uranium vacancies. Tiny amounts of interstitial defects, however, are observed on the Te2 layers that host Te chains along the b axis. We argue that these defects give rise to slightly enhanced atomic displacement parameters observed in SC-XRD data and are enough to disrupt the unconventional superconducting state in UTe 2 . Our findings highlight the need to focus future order parameter determination efforts on single crystals of UTe 2 with minimal amounts of structural disorder.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Multifractally-enhanced superconductivity in thin films

The multifractal superconducting state originates from the interplay of Anderson localization and interaction effects. In this article we overview the recent theory of the superconductivity enhancement by multifractality and extend it to describe the spectral properties of superconductors on the scales of the order of the superconducting gap. Specifically, using the approach based on renormalization group within the nonlinear sigma model, we develop the theory of a multifractal superconducting state in thin films. We derive a modified Usadel equation that incorporates the interplay of disorder and interactions at energy scales larger than the spectral gap and study the effect of such an interplay on the low-energy physics. We determine the spectral gap at zero temperature which occurs to be proportional to the multifractally enhanced superconducting transition temperature. The modified Usadel equation results in the disorder-averaged density of states that, near the spectral gap, resembles the one obtained in the model of a spatially random superconducting order parameter. We reveal strong mesoscopic fluctuations of the local density of states in the superconducting state. Such strong mesoscopic fluctuations imply that the interval of energies in which the superconducting gap establishes is parametrically large in systems with multifractally-enhanced superconductivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Revealing the Origin of Time-Reversal Symmetry Breaking in Fe-Chalcogenide Superconductor FeTe 1 - x Se x

We report that recently evidence has emerged in the topological superconductor Fe-chalcogenide FeTe 1-x Se x for time-reversal symmetry breaking (TRSB), the nature of which has strong implications on the Majorana zero modes (MZM) discovered in this system. It remains unclear however whether the TRSB resides in the topological surface state (TSS) or in the bulk, and whether it is due to an unconventional TRSB superconducting order parameter or an intertwined order. Here by performing in superconducting FeTe 1-x Se x crystals both surface-magneto-optic-Kerr effect (SMOKE) measurements using a Sagnac interferometer and bulk magnetic susceptibility measurements, we pinpoint the TRSB to the TSS, where we also detect a Dirac gap. Further, we observe surface TRSB in non-superconducting FeTe 1-x Se x of nominally identical composition, indicating that TRSB arises from an intertwined surface ferromagnetic (FM) order. The observed surface FM bears striking similarities to the two-dimensional (2D) FM found in 2D van der Waals crystals, and is highly sensitive to the exact chemical composition, thereby providing a means for optimizing the conditions for Majorana particles that are useful for robust quantum computing.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Superconductivity and Local Inversion-Symmetry Breaking

Inversion and time reversal are essential symmetries for the structure of Cooper pairs in superconductors. The loss of one or both leads to modifications to this structure and can change the properties of the superconducting phases in profound ways. Superconductivity in materials lacking inversion symmetry, or noncentrosymmetric materials, has become an important topic. These materials show unusual magnetic and magnetoelectric properties and can host topological superconductivity. Recently, crystal structures with local, but not global, inversion-symmetry breaking have attracted attention. Here, superconductivity can exhibit phenomena not naively expected in centrosymmetric materials. In this review, we first introduce the concept of locally noncentrosymmetric crystals and different material realizations. We then discuss consequences of such local symmetry breaking on the normal state electronic structure and the classification of superconducting order parameters. Finally, we review the expected and, in parts, already observed phenomenology of unconventional superconductivity and possible topological superconducting phases.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Pair wave function symmetry in UTe2 from zero-energy surface state visualization

Although nodal spin-triplet topological superconductivity appears probable in uranium ditelluride (UTe 2 ), its superconductive order parameter Δ k remains unestablished. In theory, a distinctive identifier would be the existence of a superconductive topological surface band, which could facilitate zero-energy Andreev tunneling to an s-wave superconductor and also distinguish a chiral from a nonchiral Δ k through enhanced s-wave proximity. In this study, we used s-wave superconductive scan tips and detected intense zero-energy Andreev conductance at the UTe 2 (0-11) termination surface. Imaging revealed subgap quasiparticle scattering interference signatures with a-axis orientation. The observed zero-energy Andreev peak splitting with enhanced s-wave proximity signifies that Δ k of UTe 2 is a nonchiral state: B 1u , B 2u , or B 3u . However, if the quasiparticle scattering along the a axis is internodal, then a nonchiral B 3u state is the most consistent for UTe 2 .

Gu, Qiangqiang [Cornell Univ., Ithaca, NY (United ↗
DOE OSTI2024

Slope of the upper critical field at T c in two-band superconductors with nonmagnetic disorder: s + + superconductivity in Ba 1 − x K x Fe 2 As 2

A recent theory of the disorder-dependent slope of the upper critical field at the superconducting transition temperature T c , defined as S ≡ |dH c2 /dT| T→T c , is extended to multiband superconductors aimed at iron-based superconductors, considering two constant gaps of different magnitudes and, potentially, different signs. Here, we show that the slope S decreases with increasing nonmagnetic scattering rate P in the s ± pairing state and increases in the s ++ superconductor for a reasonable range of parameters. The experiment shows that in a typical iron-based superconductor, Ba 1–x K x Fe 2 As 2 (BaK122), the nonmagnetic disorder induced by electron irradiation leads to an increasing S(P) across the superconducting “dome,” at different x. This implies that Ba 1–x K x Fe 2 As 2 is likely an s ++ superconductor with two effective gaps of different magnitudes, at least at moderate doping levels, x< 0.6. This work reopens a decade-long discussion about the nature of the superconducting order parameter in iron pnictides.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Effects of the Order Parameter Anisotropy on the Vortex Lattice in UPt3

We have used small-angle neutron scattering to determine the vortex lattice phase diagram in the topological superconductor UPt 3 for the applied magnetic field along the crystalline c -axis. A triangular vortex lattice is observed throughout the superconducting state, but with an orientation relative to the hexagonal basal plane that changes with field and temperature. At low temperature, in the chiral B phase, the vortex lattice undergoes a non-monotonic rotation with increasing magnetic field. The rotation amplitude decreases with increasing temperature and vanishes before reaching the A phase. Within the A phase an abrupt ±15° vortex lattice rotation was previously reported by Huxley et al. , Nature 406 , 160-164 (2000). The complex phase diagram may be understood from competing effects of the superconducting order parameter, the symmetry breaking field, and the Fermi surface anisotropy. The low-temperature rotated phase, centered around 0.8 T, reported by Avers et al. , Nature Physics 16 , 531-535 (2020), can be attributed directly to the symmetry breaking field.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Fingerprinting Superconductors by Disentangling Andreev and Quasiparticle Currents Across Tunable Tunnel Junctions

Tunneling Andreev reflection (TAR) spectroscopy provides a new approach to identify superconducting pairing symmetry at the atomic scale. Using atomistic superconducting transport simulations, we reveal the mechanism by which TAR can distinguish between pairing symmetries, which is complementary to traditional conductance-based techniques. In particular, owing to the additivity of the excess tunneling decay rate, the TAR spectrum is a weighted average of the contributions from quasiparticle currents, Andreev reflection, and higher-order scattering processes, and their relative weights depend on both the superconducting order parameter and the coupling strength. Within the local tunneling model, TAR dominates mid-gap conductance for s-wave superconductors, is suppressed for d-wave, and coexists with quasiparticle tunneling in sign-changing symmetries if the expectation value for the superconducting gap remains finite. Meanwhile, higher-order processes generally enhance the TAR signal when GN exceeds approximately 0.1G0. As a result, TAR provides a rich spectral fingerprint of the underlying pairing symmetry and electronic structure, enabling atomically resolved identification of unconventional superconducting states.

Maksymovych, Petro [Clemson University]↗
DOE OSTI2021

Topological and nematic superconductivity mediated by ferro-SU(4) fluctuations in twisted bilayer graphene

We propose an SU(4) spin-valley-fermion model to investigate the superconducting instabilities of twisted bilayer graphene (TBG). In this approach, bosonic fluctuations associated with an emergent SU(4) symmetry, corresponding to combined rotations in valley and spin spaces, couple to the low-energy fermions that comprise the flat bands. These fluctuations are peaked at zero wave vector, reflecting the “ferromagnetic-like” SU(4) ground state recently found in strong-coupling solutions of microscopic models for TBG. Focusing on electronic states related to symmetry-imposed points of the Fermi surface, dubbed here “valley hot-spots” and “van Hove hot-spots,” we find that the coupling to the itinerant electrons partially lifts the huge degeneracy of the ferro-SU(4) ground state manifold, favoring intervalley order, spin-valley coupled order, ferromagnetic order, spin-current order, and valley-polarized order, depending on details of the band structure. Here, these fluctuations, in turn, promote attractive pairing interactions in a variety of closely competing channels, including a nodeless f-wave state, a nodal i-wave state, and topological d+id and p+ip states with unusual Chern numbers 2 and 4, respectively. Nematic superconductivity, although not realized as a primary instability of the system, appears as a consequence of the near-degeneracy of superconducting order parameters that transform as one-dimensional and two-dimensional irreducible representations of the point group D 6 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Role of locally polar regions in the superconductivity of SrTiO 3

Understanding the interaction between polar and superconducting order parameters may hold the key to several classes of superconductors that remain poorly understood, including SrTiO 3 and several tellurides. Here we show that doped, strained SrTiO 3 films can exhibit both global or local polar order, respectively, depending on the amount of epitaxial mismatch strain, thereby providing a platform to understand how inversion symmetry breaking affects superconductivity. We find that the superconducting critical temperature correlates with the length scale of polar order. In particular, the transition temperature is enhanced when polar nanodomains are sufficiently large or, in the extreme limit, films are globally ferroelectric. In these cases, the Cooper pairs reside in a noncentrosymmetric environment. Conversely, low transition temperatures are found when the nanodomains are small. The findings point to the length scale of polar nanodomains and spin-orbit coupling as important parameters controlling the superconductivity of SrTiO 3 . Furthermore, the ability to control the size of the polar domains opens up new opportunities to design and control the nature of superconductivity in a wide range of materials.

36 MATERIALS SCIENCE↗
DOE OSTI2020

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. In this work, 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.

36 MATERIALS SCIENCE↗
DOE OSTI2024

An Efficient Numerical Algorithm for Solving Coupled Time-Dependent Ginzburg-Landau Equation for Superconductivity and Elasticity

A decoupled finite element algorithm is developed for simulating the vortex dynamics on an elastic superconductor which couples the time-dependent Ginzburg- Landau equation with the complex-valued superconducting order parameter and the vector-valued magnetic potential, and the elasticity equation. We present an iterative algorithm for the decoupled system arising from the time and spatial discretization using a combination of preconditioner, algebraic multigrid method (AMG) and preconditioned conjugate gradient method (PCG). The iterative algorithm allows us to perform large-scale three-dimensional simulations of mesoscale pattern formation during superconducting phase transitions with arbitrary elastic boundary conditions. Here, the performance and efficiency of the algorithm are numerically verified by several benchmark problems, exhibiting up to two orders of magnitude improvement depending on the scale of discrete system compared to the exact solver.

Efficiency↗
DOE OSTI2020

Majorana-based quantum computing in nanowire devices

The boundary of one-dimensional topological superconductors might lead to the appearance of Majorana zero modes, whose nontrivial exchange statistics can be used for quantum computing. In branched nanowire networks, one can exchange Majorana modes by time dependently tuning topologically nontrivial parameter regions. In this paper, we simulate the exchange of four Majorana modes in T-shaped junctions made out of $\textit{p}$-wave superconducting Rashba wires. Specifically, we derive concrete experimental predictions for (quasi-)adiabatic braiding times and determine geometric conditions for successful Majorana exchange processes. Moreover, we prove that, in the adiabatic limit, the gating time needs to be smaller than the inverse of the squared superconducting order parameter and scales linearly with the gating potential. Furthermore, we show how to circumvent the formation of additional Majorana modes in branched nanowire systems, arising at wire intersection points of narrow junctions. Finally, we propose a multiqubit setup, allowing for universal quantum computing.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Nuclear spin coherence and RKKY interaction in superconducting Nb 3 Sn

We have investigated the normal and superconducting states of the technologically important compound Nb$_3$Sn using $^{93}$Nb nuclear magnetic resonance. From spin-lattice relaxation we find strong suppression of the zero-temperature superconducting order parameter by magnetic field. Additionally we have identified an anomalously large electron-nuclear exchange interaction from spin-spin relaxation measurements, an order of magnitude beyond that of the nuclear dipolar coupling. This RKKY interaction evolves from normal to superconducting states, becoming essentially Lorentzian in the low temperature limit.

Zhai, Gan [Northwestern U.] (ORCID:000000016623956↗
DOE OSTI2024

Multimodal synchrotron x-ray diffraction across the superconducting transition of Sr 0.1 Bi 2 Se 3

Here, in the doped topological insulator Sr x Bi 2 ⁢Se 3 , a pronounced in-plane twofold symmetry is observed in electronic properties below the superconducting transition temperature T c ~ 3 K, despite the threefold symmetry of the observed $R\overline{3}m$ space group. The axis of twofold symmetry is nominally pinned to one of three rotationally equivalent crystallographic directions and crystallographic strain has been proposed to be the origin of this pinning. We carried out multimodal synchrotron diffraction and resistivity measurements down to and in magnetic fields up to 45 kG on a single crystal of to probe the effect of superconductivity on the crystallographic distortion. Our results indicate that there is no in-plane crystallographic distortion at the level of 1 x 10 -5 associated with the superconducting transition. These results further support the model that the large twofold in-plane anisotropy of superconducting properties of Sr x Bi 2 ⁢Se 3 is not structural in origin, but electronic, namely, it is caused by a nematic superconducting order parameter of E u symmetry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Evidence of a distinct collective mode in Kagome superconductors

The collective modes of the superconducting order parameter fluctuation can provide key insights into the nature of the superconductor. Recently, a family of superconductors has emerged in non-magnetic kagome materials AV 3 Sb 5 (A = K, Rb, Cs), exhibiting fertile emergent phenomenology. However, the collective behaviors of Cooper pairs have not been studied. Here, we report a distinct collective mode in CsV 3-x Ta x Sb 5 using scanning tunneling microscope/spectroscopy. The spectral line-shape is well-described by one isotropic and one anisotropic superconducting gap, and a bosonic mode due to electron-mode coupling. With increasing x, the two gaps move closer in energy, merge into two isotropic gaps of equal amplitude, and then increase synchronously. The mode energy decreases monotonically to well below 2Δ and survives even after the charge density wave order is suppressed. We propose the interpretation of this collective mode as Leggett mode between different superconducting components or the Bardasis-Schrieffer mode due to a subleading superconducting component.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Microscopic Scattering Approach to In-Gap States

We develop a microscopic scattering formalism to describe Yu-Shiba-Rusinov (YSR) states due to a single Cr adatom on the Bi-terminated surface of beta Bi2Pd, by combining ab initio Wannier functions with a real-space Green's function approach in the Bogoliubov-de Gennes formalism[1]. Our framework reproduces key scanning tunneling spectroscopy features, including a single particle-hole asymmetric YSR peak and isotropic dIdV maps around the impurity. Decomposing the YSR states reveals contributions from four nearly degenerate C4v representations, with energy broadening masking their individual signatures. Spin-orbit coupling induces partial spin polarization, while the spatial asymmetry between particle and hole components arises from Cr d-Bi p hybridization. These results highlight the importance of realistic band structures and microscopic modeling for interpreting STM data for magnetic in-gap states on superconductors. Further advances examining layered 2D material surfaces, such as NbSe2, will be described[2]. For this system the superconducting properties are obtained from a full anisotropic Eliashberg calculation of the superconducting order parameter along with the charge density wave gap. Additional features associated with proposals to measure the dynamics of these individual YSR states will be presented. [1] arXiv:2507.08740 [2] arXiv:2507.11856

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Observation of Persistent Zero Modes and Superconducting Vortex Doublets in UTe 2

Superconducting vortices can reveal electron pairing details and nucleate topologically protected states. Yet, vortices of bulk spin-triplet superconductors have never been visualized at the atomic scale. Recently, UTe 2 has emerged as a prime spin-triplet superconductor, but its superconducting order parameter is elusive, and whether time-reversal symmetry (TRS) is broken remains unsettled. Here, in this work, we visualize vortices on the (011) surface of ultraclean UTe 2 single crystals (T c = 2.1 K) using scanning tunneling microscopy (STM). We introduce $\frac{d^{2}𝐼}{d𝑉^{2}}$ imaging as an effective technique for vortex visualization in superconductors with substantial residual zero-energy density of states (DOS), as in UTe 2 . Anisotropic single-flux-quantum vortices, with coherence lengths of ∼12 nm (4 nm) parallel (perpendicular) to the a -axis, form a triangular vortex lattice (VL) under a small out-of-plane magnetic field. The invariance of vortex structures and VL under changes of field polarity and cooling history strongly supports time-reversal invariant superconductivity under zero field. At vortex cores (VCs), nonsplit, spectrally sharp zero-bias conductance peaks (ZBPs) persist up 8 T that are consistent with symmetry-protected Majorana zero modes (MZMs) in a topological vortex line. Close examination of vortex structures reveals a mirror-asymmetric doublet─one with ZBPs and another with an enhanced apparent gap, possibly originating from a field-induced multicomponent order parameter.

UTe2↗