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Elastocaloric evidence for a multicomponent superconductor stabilized within the nematic state in Ba(Fe 1− x Co x ) 2 As 2

The iron-based high-$T_c$ superconductors (SCs) exhibit rich phase diagrams with intertwined phases, including magnetism, nematicity, and superconductivity. The superconducting $T_c$ in many of these materials is maximized in the regime of strong nematic fluctuations, making the role of nematicity in influencing the superconductivity a topic of intense research. Here, in this study, we use the AC elastocaloric effect (ECE) to map out the phase diagram of Ba(Fe 1− x Co x ) 2 As 2 near optimal doping. The ECE signature at $T_c$ on the overdoped side, where superconductivity condenses without any nematic order, is quantitatively consistent with other thermodynamic probes that indicate a single-component superconducting state. In contrast, on the slightly underdoped side, where superconductivity condenses within the nematic phase, ECE reveals a second thermodynamic transition proximate to and below $T_c$. We rule out magnetism and reentrant tetragonality as the origin of this transition and find that our observations strongly suggest a phase transition into a multicomponent superconducting state. This implies the existence of a subdominant pairing instability that competes strongly with the dominant $s^±$ instability. Our results highlight the significant role of nematic order in determining the pairing symmetry close to optimal doping in this extensively studied iron-based SC, while also demonstrating the power of ECE in uncovering strain-tuned phase diagrams of quantum materials.

Ghosh, Sayak [Stanford University, CA (United Stat↗

Single thermodynamic transition at 2 K in superconducting UTe 2 single crystals

UTe 2 is a newly-discovered unconventional superconductor wherein multicomponent topological superconductivity is anticipated based on the presence of two superconducting transitions and time-reversal symmetry breaking in the superconducting state. The observation of two superconducting transitions, however, remains controversial. Here we demonstrate that UTe 2 single crystals displaying an optimal superconducting transition temperature at 2 K exhibit a single transition and remarkably high quality supported by their large residual resistance ratio and small residual heat capacity in the superconducting state. Our results shed light on the intrinsic superconducting properties of UTe 2 and bring into question whether UTe 2 is a multicomponent superconductor at ambient pressure.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Cascade of vestigial orders in two-component superconductors: Nematic, ferromagnetic, s -wave charge- 4 e , and d -wave charge- 4 e states

Electronically ordered states that break multiple symmetries can melt in multiple stages, similarly to liquid crystals. In a partially melted phase, known as vestigial phase, a bilinear made out of combinations of the multiple components of the primary order parameter condenses. Multicomponent superconductors are thus natural candidates for vestigial order since they break both the U⁡(1)-gauge and also time-reversal or lattice symmetries. Here, we use group theory to classify all possible real-valued and complex-valued bilinears of a generic two-component superconductor on a tetragonal or hexagonal lattice. While the more widely investigated real-valued bilinears correspond to vestigial nematic or ferromagnetic order, the little explored complex-valued bilinears correspond to a vestigial charge-4e condensate, which itself can have an underlying s-wave, d x 2 –y 2 -wave, or d xy -wave symmetry. To properly describe the fluctuating regime of the superconducting Ginzburg-Landau action and thus access these competing vestigial phases, we employ both a large-N and a variational method. We show that while vestigial order can be understood as a weak-coupling effect in the large-N approach, it is akin to a moderate-coupling effect in the variational method. Despite these distinctions, both methods yield similar results in wide regions of the parameter space spanned by the quartic Landau coefficients. Specifically, we find that the nematic and ferromagnetic phases are the leading vestigial instabilities, whereas the various types of charge-4⁢e order are attractive albeit subleading vestigial channels. The only exception is for the hexagonal case, in which the nematic and s-wave charge-4e vestigial states are degenerate. Finally, we discuss the limitations of our approach, as well as the implications of our results for the realization of exotic charge-4⁢e states in material candidates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Superconducting vortices carrying a temperature-dependent fraction of the flux quantum

Magnetic field penetrates type-II bulk superconductors by forming quantum vortices that enclose a magnetic flux equal to the magnetic flux quantum. The flux quantum is a universal quantity that depends only on fundamental constants. In this study, we investigated isolated vortices in the hole-overdoped Ba 1–x K x Fe 2 As 2 (x = 0.77) by using scanning superconducting quantum interference device (SQUID) magnetometry. In many locations, we observed objects that carried only part of a flux quantum, with a magnitude that varied continuously with temperature. Here, we demonstrated mobility and manipulability of these objects and interpreted them as quantum vortices with nonuniversally quantized (fractional) magnetic flux whose magnitude is determined by the temperature-dependent parameters of a multicomponent superconductor.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Manufacturing in space and materials sciences on Skylab

Two main groups of manufacturing and materials studies were performed during the Skylab missions. The first group of experiments studied processes which are important in orbital assembly and construction, including melting, solidification, brazing, welding, and cutting. The second group concerned the manufacture of specific materials, including metallic alloys, single crystals, doped semiconductors, composite materials, and multicomponent superconductors. The present paper discusses several specific experiments conducted on Skylab. In general, the processes tested produced materials of higher quality in space than they would have on earth. The experiments prove that the elimination of gravitational forces has a decisive effect on a number of materials processes.

Stuhlinger, E.↗

Charge-4e Superconductivity from Multicomponent Nematic Pairing: Application to Twisted Bilayer Graphene

We show that unconventional nematic superconductors with multicomponent order parameter in lattices with three- and sixfold rotational symmetries support a charge-4e vestigial superconducting phase above T c . The charge-4e state, which is a condensate of four-electron bound states that preserve the rotational symmetry of the lattice, is nearly degenerate with a competing vestigial nematic state, which is nonsuperconducting and breaks the rotational symmetry. This robust result is the consequence of a hidden discrete symmetry in the Ginzburg-Landau theory, which permutes quantities in the gauge sector and in the crystalline sector of the symmetry group. We argue that random strain generally favors the charge-4e state over the nematic phase, as it acts as a random mass to the former but as a random field to the latter. Furthermore, we propose that two-dimensional inhomogeneous systems displaying nematic superconductivity, such as twisted bilayer graphene, provide a promising platform to realize the elusive charge-4e superconducting phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Observation of Vortex Stripes in UTe 2

In conventional type-II superconductors, quantum vortices determine the magnetic response of the system and tend to form regular lattices. UTe 2 is a recently discovered heavy Fermion superconductor exhibiting many anomalous macroscopic behaviors, but whether it has a multicomponent order parameter remains open. Here, in this work, we study the vortices of UTe 2 by employing scanning superconducting quantum interference device microscopy. While a small out-of-plane magnetic field produces typical isolated vortices, a higher field generates vortex stripe patterns that evolve with the vortex density. The stripes form at different locations and along different directions in the surface plane when the field is along the b or c axis. The behavior is reproduced by our simulation based on an anisotropic two-component order parameter. This study shows that UTe 2 has a nontrivial disparity of multiple length scales, placing constraints on the multicomponent superconductivity.

UTe2↗

Flavour-selective localization in interacting lattice fermions

Abstract A large repulsion between particles in a quantum system can lead to their localization, an effect responsible for the Mott insulator phases in strongly correlated materials. In a system with multiple orbitals, an orbital-selective Mott insulator can form, where electrons in some orbitals are predicted to localize while others remain itinerant. Here we demonstrate a more general version of this phenomenon by observing flavour-selective localization in an atom-based quantum simulator. Our experiment realizes Fermi–Hubbard models with an SU(3) symmetry that can be broken using a tunable coupling between flavours. We observe an enhancement of the localization associated with a selective Mott transition and the emergence of flavour-dependent correlations. Our realization of flavour-selective Mott physics demonstrates the potential of cold atoms to simulate interacting multicomponent materials such as superconductors and topological insulators.

Physics↗

Spatially inhomogeneous superconductivity in UTe 2

The newly discovered superconductor UTe 2 is a strong contender for a topological spin-triplet state wherein a multicomponent order parameter arises from two nearly degenerate superconducting states. A key issue is whether both of these states intrinsically exist at ambient pressure. Through thermal expansion and calorimetry, we show that UTe 2 at ambient conditions exhibits two detectable transitions only in some samples, and the size of the thermal expansion jump at each transition varies when the measurement is performed in different regions of the sample. This result indicates that the two transitions arise from two spatially separated regions that are inhomogeneously mixed throughout the volume of the sample, each with a discrete superconducting transition temperature (T c ). Notably, samples with higher T c only show a single transition at ambient pressure. Above 0.3 GPa, however, two transitions are invariably observed in ac calorimetry. Our results not only point to a nearly vertical line (constant pressure) in the pressure-temperature phase diagram but also provide a consistent scenario for the sample dependence of UTe 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Chemical vapor deposition of high T sub c superconductors

The results are reported of an investigation into the synthesis and properties of high temperature superconducting materials. A chemical vapor deposition apparatus was designed and built which is suitable for the preparation of multicomponent metal films This apparatus was used to prepare a series of high T sub c A-15 structure superconducting films in the binary system Nb-Ge. The effect on T sub c of a variety of substrate materials was investigated. An extensive series of ternary alloys were also prepared. Conditions allowing the brittle high T sub c (approximately 18 K) A-15 structure superconductor Nb3A1 to be prepared in a low T sub c but ductile form were found. Some of the ways that the ductile (bcc) form can be cold worked or machined are described. Measurements of rate of transformation of cold worked bcc material to the high T sub c A-15 structure with low temperature annealing are given. Preliminary measurements indicate that this material has attractive high field critical current densities.

Webb, G. W.↗

Competing Electronic Ground States in the Heavy-Fermion Superconductor CeRh 2 As 2

CeRh 2 ⁢As 2 is rare among superconductors, in that the magnetic field tunes it between two distinct superconducting phases. Combined with a lack of local inversion symmetry and an upper critical field exceeding the Pauli paramagnetic limit, this excitingly suggests triplet multicomponent superconductivity. Preceding the superconducting onset, 𝑓-electron correlations cause long-range order, attributed both to local antiferromagnetism and itinerant (quadrupole) density waves. A magnetic field provides a significant perturbation of the 𝑓 electrons and may reveal the nature of the many-body correlations. Therefore, we report comprehensive magnetization and magnetotransport studies on microstructured devices in fields of up to 73 T. Applied along the 𝑐 axis, the field causes a low-temperature change of majority (hole) carrier density at 𝜇 0⁢ 𝐻 ≈ 2⁢4 T. By contrast, in-plane fields produce a cascade of phase transitions; the field-induced in-plane conductivity anisotropy and lack of accompanying magnetic features, plus the closed-dome nature of the overall phase boundary is consistent with a hierarchy of field-induced density-wave states.

36 MATERIALS SCIENCE↗

Strain tuning of vestigial three-state Potts nematicity in a correlated antiferromagnet

Electronic nematicity is a state of matter in which rotational symmetry is spontaneously broken and translational symmetry is preserved. In strongly correlated materials, nematicity often emerges from fluctuations of a multicomponent primary order, such as spin or charge density waves, and is termed vestigial nematicity. One widely studied example is Ising nematicity, which arises as a vestigial order of collinear antiferromagnetism in the tetragonal iron pnictide superconductors. Because nematic directors in crystals are restricted by the underlying crystal symmetry, recently identified quantum materials with three-fold rotational symmetry offer a new platform to investigate nematic order with three-state Potts character. Here, in this study, we demonstrate strain control of three-state Potts nematicity as a vestigial order of zigzag antiferromagnetism in FePSe 3 . Optical linear dichroism measurements reveal the nematic state and demonstrate the rotation of the nematic director by uniaxial strain. We show that the nature of the nematic phase transition can also be controlled by strain, inducing a smooth crossover transition between a Potts nematic transition and an Ising nematic flop transition. Elastocaloric measurements demonstrate the signatures of two coupled phase transitions, indicating that the vestigial nematic transition is separated from the antiferromagnetic transition. This establishes FePSe 3 as a system to explore three-state Potts vestigial nematicity.

Hwangbo, Kyle↗

$\testit{d}$-wave superconductivity and Bogoliubov-Fermi surfaces in Rarita-Schwinger-Weyl semimetals

In this work, we uncover the properties of complex tensor ($\textit{d}$-wave) superconducting order in three-dimensional Rarita-Schwinger-Weyl semimetals that host pseudospin-$\frac{3}{2}$ fermions at a fourfold linear band-crossing point. Although the general theory of $\textit{d}$-wave order was originally developed for materials displaying quadratic band touching, it directly applies to the case of semimetals with linear dispersion, several candidate compounds of which have been discovered experimentally very recently. The spin-$\frac{3}{2}$ nature of the fermions allows for the formation of spin-2 Cooper pairs which may be described by a complex second-rank tensor order parameter. In the case of linear dispersion, for the chemical potential at the Fermi point and at strong coupling, the energetically preferred superconducting state is the uniaxial nematic state, which preserves time-reversal symmetry and provides a full (anisotropic) gap for quasiparticle excitations. In contrast, at a finite chemical potential, we find that the usual weak-coupling instability is toward the “cyclic state,” well known from the studies of multicomponent Bose-Einstein condensates, which breaks time-reversal symmetry maximally, has vanishing average value of angular momentum, and features 16 small Bogoliubov-Fermi surfaces. The Rarita-Schwinger-Weyl semimetals provide therefore the first example of weakly coupled, three-dimensional, isotropic $\textit{d}$-wave superconductors where the $\textit{d}$-wave superconducting phase is uniquely selected by the quartic expansion of the mean-field free energy, and is not afflicted by the accidental degeneracy first noticed by Mermin over 40 years ago. We discuss the appearance and stability of the Bogoliubov-Fermi surfaces in absence of inversion symmetry in the electronic Hamiltonian, as in the case at hand.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

High-field superconducting halo in UTe 2

The heavy fermion material UTe 2 is a candidate topological superconductor that exhibits multiple magnetic field–induced superconducting phases. One such phase exists only at fields greater than 40 tesla, a considerable scale given its critical temperature of only 2 K. Here, in this work, we extend measurements of this state with fields outside of the bc crystallographic plane and reveal its core structure: The superconducting phase wraps around the b axis in a halo-like fashion and appears to be stabilized by a field component perpendicular to the magnetic easy axis. This angle dependence points to a multicomponent spin-triplet order parameter with a finite angular momentum of the Cooper pairs. The pairing mechanism remains enigmatic, and UTe 2 ’s specific magnetophilic superconducting tendencies seem incompatible with existing models for field-enhanced superconductivity.

Lewin, Sylvia K. [National Inst. of Standards and ↗

Observing and Modeling the Sequential Pairwise Reactions that Drive Solid‐State Ceramic Synthesis

Abstract Solid‐state synthesis from powder precursors is the primary processing route to advanced multicomponent ceramic materials. Designing reaction conditions and precursors for ceramic synthesis can be a laborious, trial‐and‐error process, as heterogeneous mixtures of precursors often evolve through a complicated series of reaction intermediates. Here, ab initio thermodynamics is used to model which pair of precursors has the most reactive interface, enabling the understanding and anticipation of which non‐equilibrium intermediates form in the early stages of a solid‐state reaction. In situ X‐ray diffraction and in situ electron microscopy are then used to observe how these initial intermediates influence phase evolution in the synthesis of the classic high‐temperature superconductor YBa 2 Cu 3 O 6+ x (YBCO). The model developed herein rationalizes how the replacement of the traditional BaCO 3 precursor with BaO 2 redirects phase evolution through a low‐temperature eutectic melt, facilitating the formation of YBCO in 30 min instead of 12+ h. Precursor selection plays an important role in tuning the thermodynamics of interfacial reactions and emerges as an important design parameter in planning kinetically favorable synthesis pathways to complex ceramic materials.

36 MATERIALS SCIENCE↗

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↗