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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Quarkonium polarization in medium from open quantum systems and chromomagnetic correlators

Here, by considering the Markovian condition and applying the Wigner transformation upon the diagonal spin components of the quarkonium density matrix with the semiclassical expansion, we systematically derive the Boltzmann transport equation for quarkonia with polarization dependence in the quantum optical limit. Unlike the spin-independent collision terms governed by certain chromoelectric field correlators, new gauge invariant correlators of chromomagnetic fields determine the recombination and dissociation terms with polarization dependence at the order we are working. We also derive a Lindblad equation describing the in-medium transitions between spin-singlet and spin-triplet heavy quark-antiquark pairs in the quantum Brownian motion limit. The Lindblad equation is governed by new transport coefficients defined in terms of the chromomagnetic field correlators. Our formalism is generic and valid for both weakly coupled and strongly coupled quark gluon plasmas. It can be further applied to study spin alignment of vector quarkonia in heavy ion collisions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Transformer spin-triplet superconductivity at the onset of isospin order in bilayer graphene

We consider the origin of superconductivity found recently in Bernal bilayer graphene at the onset of isospin-polarized order, trying to infer the pairing mechanism and superconducting order from the measurements available to date. The superconductivity is induced by a parallel magnetic field and persists well above the Pauli limit, indicating an unconventional scenario of quantum-critical pairing, where soft fluctuations of isospin give rise to spin-triplet superconductivity. We consider the scenario in which the pairing interaction is entirely repulsive, which stands in contrast to the typical quantum-critical pairing mechanisms. Superconductivity emerges through a “transformer” mechanism where, in the presence of an in-plane magnetic field, the incipient valley polarization converts a frequency-independent repulsion into one with a strong nonmonotonic frequency dependence. Such an interaction enables a nonzero solution for the pairing gap function that changes sign as a function of frequency. Furthermore, the same mechanism holds at zero field in the presence of spin-orbit coupling, providing a likely explanation for the recently observed superconductivity in bilayer graphene on the WSe 2 monolayer.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Detection of a pair density wave state in UTe2

Abstract Spin-triplet topological superconductors should exhibit many unprecedented electronic properties, including fractionalized electronic states relevant to quantum information processing. Although UTe 2 may embody such bulk topological superconductivity 1–11 , its superconductive order parameter Δ( k ) remains unknown 12 . Many diverse forms for Δ( k ) are physically possible 12 in such heavy fermion materials 13 . Moreover, intertwined 14,15 density waves of spin (SDW), charge (CDW) and pair (PDW) may interpose, with the latter exhibiting spatially modulating 14,15 superconductive order parameter Δ( r ), electron-pair density 16–19 and pairing energy gap 17,20–23 . Hence, the newly discovered CDW state 24 in UTe 2 motivates the prospect that a PDW state may exist in this material 24,25 . To search for it, we visualize the pairing energy gap with μeV-scale energy resolution using superconductive scanning tunnelling microscopy (STM) tips 26–31 . We detect three PDWs, each with peak-to-peak gap modulations of around 10 μeV and at incommensurate wavevectors P i =1,2,3 that are indistinguishable from the wavevectors Q i =1,2,3 of the prevenient 24 CDW. Concurrent visualization of the UTe 2 superconductive PDWs and the non-superconductive CDWs shows that every P i : Q i pair exhibits a relative spatial phase δϕ ≈ π. From these observations, and given UTe 2 as a spin-triplet superconductor 12 , this PDW state should be a spin-triplet PDW 24,25 . Although such states do exist 32 in superfluid 3 He, for superconductors, they are unprecedented.

Science & Technology - Other Topics↗
DOE OSTI2021

Topological band and superconductivity in UTe 2

UTe 2 is a likely spin-triplet superconductor that also exhibits evidence for chiral Majorana edge states. A characteristic structural feature of UTe 2 is inversion-symmetry related pairs of U atoms, forming rungs of ladders. Here we show how each rung's two sublattice degrees of freedom play a key role in understanding the electronic structure and the origin of superconductivity. In particular, DFT + U calculations generically reveal a topological band near the chemical potential originating from a band inversion associated with 5f electrons residing on these rungs, necessitating a microscopic description that includes these rung degrees of freedom. Furthermore, we show that a previously identified strong ferromagnetic interaction within a U-U rung leads to a pseudospin-triplet superconducting state that accounts for a nonzero polar Kerr angle, the observed magnetic field-temperature phase diagrams, and nodal Weyl fermions. Finally, our analysis may also be relevant for other U-based superconductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Pair Fluctuation Effects on Quasiparticle Transport in Fermi Systems

The leading corrections to Fermi liquid theory for non-equilibrium quasiparticle transport near a Cooper instability arise from the virtual emission and absorption of incipient Cooper pairs. We formulate the corrections to the Landau-Boltzmann transport equation starting from Keldysh's field theory for non-equilibrium, strongly interacting Fermions. The theory is applicable to quasiparticle transport in conventional and unconventional superconductors, dense nuclear matter and the low temperature phases of liquid $^3$He. Validation of the theory is provided by our analysis, and quantitative agreement between theory and experiment, of the excess attenuation of zero sound in liquid $^3$He near the superfluid transition. We propose an additional experimental test of the theory based on the effects of a Zeeman field on the spectrum of pairing fluctuations for the Cooper instability in spin-triplet superfluids.

Lin, Wei-Ting↗
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↗
DOE OSTI2025

Possible Spin-Triplet Excitonic Insulator in the Ultraquantum Limit of HfTe 5

More than 50 years ago, excitonic insulators formed by the pairing of electrons and holes due to Coulomb interactions were first predicted [A. N. Kozlov and L. A. Maksimov, Sov. J. Exp. Theor. Phys. 21, 790 (1965); L. V. Keldysh and Y. V. Kopaev, Sov. Phys. Solid State 6, 2219 (1965); D. Jérome, T. M. Rice, and W. Kohn, Phys. Rev. 158, 462 (1967)]. Since then, excitonic insulators have been observed in various classes of materials, including quantum Hall bilayers, graphite, transition metal chalcogenides, and more recently in moiré superlattices. In these excitonic insulators, an electron and a hole with the same spin bind together, and the resulting exciton is a spin singlet. Here, we report the experimental observation of a spin-triplet excitonic insulator in the ultra-quantum limit of a three-dimensional topological material HfTe 5 . We observe that the spin-polarized zeroth Landau bands dispersing along the field direction cross each other beyond a characteristic magnetic field in HfTe 5 , forming the one-dimensional Weyl mode. Transport measurements reveal the emergence of a gap of about 2⁢5⁢0 μ⁢eV when the field surpasses a critical threshold. By performing the material-specific modeling, we identify this gap as a consequence of a spin-triplet exciton formation, where electrons and holes with opposite spin form bound states, and the translational symmetry is preserved. The system reaches charge neutrality following the gap opening, as evidenced by the zero Hall conductivity over a wide magnetic field range (10–72 T). In conclusion, our finding of the spin-triplet excitonic insulator paves the way for studying novel spin transport including spin superfluidity, spin Josephson currents, and Coulomb drag of spin currents in analogy to the transport properties associated with the layer pseudospin in quantum Hall bilayers.

36 MATERIALS SCIENCE↗
DOE OSTI2025

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 ↗
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 OSTI2023

Fractional magnetoresistance oscillations in spin-triplet superconducting rings

Abstract Half-quantum vortices in spin-triplet superconductors are predicted to host Majorana zero modes and may provide a viable platform for topological quantum computation. Recent works also suggested that, in thin mesoscopic rings, the superconducting pairing symmetry can be probed via Little-Parks-like magnetoresistance oscillations of periodicity Φ 0 = h /2 e that persist below the critical temperature. Here we use the London limit of Ginzburg-Landau theory to study these magnetoresistance oscillations resulting from thermal vortex tunneling in spin-triplet superconducting rings. For a range of temperatures in the presence of disorder, we find magnetoresistance oscillations with an emergent fractional periodicity Φ 0 / n , where the integer n ≥ 3 is entirely determined by the ratio of the spin and charge superfluid densities. These fractional oscillations can unambiguously confirm the spin-triplet nature of superconductivity and directly reveal the tunneling of half-quantum vortices in real-world candidate materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Absence of bulk charge density wave order in the normal state of UTe 2

A spatially modulated superconducting state, known as pair density wave (PDW), is a tantalizing state of matter with unique properties. Recent scanning tunneling microscopy (STM) studies revealed that spin-triplet superconductor UTe 2 hosts an unprecedented spin-triplet, multi-component PDW whose three wavevectors are indistinguishable from a preceding charge-density wave (CDW) order that survives to temperatures well above the superconducting critical temperature, T c . Whether the PDW is the mother or a subordinate order remains unsettled. Here, based on a systematic search for bulk charge order above T c using resonant elastic X-ray scattering (REXS), we show that the structure factor of charge order previously identified by STM is absent in the bulk within the sensitivity of REXS. Our results invite two scenarios: either the density-wave orders condense simultaneously at T c in the bulk, in which case PDW order is likely the mother phase, or the charge modulations are restricted to the surface.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Identifying $\textit{f}$-electron symmetries of UTe 2 with O-edge resonant inelastic x-ray scattering

The recent discovery of spin-triplet superconductivity emerging from a nonmagnetic parent state in UTe 2 has stimulated great interest in the underlying mechanism of Cooper pairing. Experimental characterization of short-range electronic and magnetic correlations is vital to understanding these phenomena. Here we use resonant inelastic x-ray scattering (RIXS), x-ray absorption spectroscopy (XAS), and atomic-multiplet-based modeling to shed light on the active debate between $5f^26d^1$-based models with singlet crystal field states versus $5f^3$-based models that predict atomic Kramers doublets and much greater $5\textit{f}$ itinerancy. In this work, the XAS and RIXS data are found to agree strongly with predictions for a $5f^26d^1$-like valence electron configuration with weak intradimer magnetic correlations, and provide a context for interpreting recent investigations of the electronic structure and superconducting pairing mechanism.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Higher-order topological superconductivity in twisted bilayer graphene

In this work, we show that introducing spin-singlet or spin-triplet superconductivity into twisted bilayer graphene induces higher-order topological superconductivity. Multiple copies of C 2z ⁢T-protected Majorana Kramers pairs appear at corners on pairing domain walls. The topology originates from the anomaly analyzed in Song et al.—the absence of a lattice support—of the single-valley band structure of twisted bilayer graphene, which is protected by C 2z ⁢T and approximate particle-hole symmetry $\mathcal{P}$. We prove that any pairing (spin-singlet or spin-triplet) term preserving valley-U(1), spin-SU(2), time-reversal, C 2z ⁢T, and $\mathcal{P}$ must drive the system into a higher-order topological superconductor. Here spin-SU(2) is the global spin-SU(2) for the singlet pairing and is broken to U(1) for the triplet pairing. Using a Dirac Hamiltonian, we derive the corner modes and confirm with numerics. These corner states are stable even if $\mathcal{P}$ is weakly broken, which is true in experimental setups. Finally, we suggest experimental detection via the fractional Josephson effect in a TBG-TSC Josephson junction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Revisiting superconductivity in the extended one-band Hubbard model: Pairing via spin and charge fluctuations

The leading superconducting instabilities of the two-dimensional extended repulsive one-band Hubbard model within spin-fluctuation pairing theory depend sensitively on electron density, band, and interaction parameters. We map out the phase diagrams within a random-phase-approximation spin- and charge-fluctuation approach, and find that while B 1g (d x 2 –y 2 ) and B 2g (d xy ) pairing dominates in the absence of repulsive longer-range Coulomb interactions V NN , the latter induces pairing in other symmetry channels, including, e.g., A 2g (g-wave), nodal A 1g (extended s-wave), or nodal E u (p-wave) spin-triplet superconductivity. At the lowest temperatures, transition boundaries in the phase diagrams between symmetry-distinct spin-singlet orders generate complex time-reversal symmetry broken superpositions. By contrast, we find that boundaries between singlet and triplet regions are characterized by first-order transitions. Finally, motivated by recent photoemission experiments, we have determined the influence of an additional explicitly attractive nearest-neighbor interaction, V NN < 0, on the superconducting gap structure. Furthermore, depending on the electronic filling, such an attraction boosts E u (p-wave) spin-triplet or B 1g (d x 2 –y 2 ) spin-singlet ordering.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Spin-triplet superconductivity from excitonic effect in doped insulators

Despite being of fundamental importance and potential interest for topological quantum computing, spin-triplet superconductors remain rare in solid state materials after decades of research. In this work, we present a three-particle mechanism for spin-triplet superconductivity in multiband systems, where an effective attraction between doped electrons is produced from the Coulomb repulsion via a virtual interband transition involving a third electron [V. Crépel, L. Fu, Sci. Adv. 7, eabh2233 (2021)]. Our theory is analytically controlled by an interband hybridization parameter and explicitly demonstrated in doped band insulators with the example of an extended Hubbard model. Our theory of exciton-mediated pairing reveals how, as a matter of principle, a two-particle bound state can arise from the strong electron repulsion upon doping, opening a viable path to Bose–Einstein condensate (BEC)–Bardeen–Cooper–Schrieffer (BCS) physics in solid state systems. In light of this theory, we propose that recently discovered dilute superconductors such as ZrNCl, WTe 2 , and moiré materials can be spin-triplet and compare the expected consequences of our theory with experimental data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Correlated metals and unconventional superconductivity in rhombohedral trilayer graphene: A renormalization group analysis

Here, motivated by recent experimental observations of correlated metallic phases and superconductivity in rhombohedral trilayer graphene (RTG), we perform an unbiased study of electronic ordering instabilities in hole-doped RTG. Specifically, we focus on electronic states energetically proximate to Van Hove singularities (VHSs), where a large density of states promotes different interaction-induced symmetry-breaking electronic orders. To resolve the Fermi surface near VHSs, we construct a fermionic hot-spot model and demonstrate that a perpendicular electric field can tune different nesting structures of the Fermi surface. Subsequently, we apply a renormalization group analysis to describe the low-energy phase diagrams of our model under both short-range repulsive interactions as well as realistic (long-range) Coulomb interactions. Our analysis shows instabilities towards either intervalley coherent metallic phases or superconducting phases. The dominant pairing channel depends crucially on the nature of Fermi surface nesting—repulsive Coulomb interaction favors spin-singlet d-wave pairing for relatively small displacement field and spin-singlet i-wave pairing for larger displacement field. We argue that the phase diagram of RTG can be well-understood by modeling the realistic Coulomb interaction as the sum of repulsive density-density interaction and ferromagnetic spin-triplet intervalley coherence (IVC) Hund's coupling, while phonon-mediated electronic interactions have a negligible effect on this system, in sharp contrast to twisted graphene multilayers.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Inhomogeneous high temperature melting and decoupling of charge density waves in spin-triplet superconductor UTe 2

Charge, spin and Cooper-pair density waves have now been widely detected in exotic superconductors. Understanding how these density waves emerge — and become suppressed by external parameters — is a key research direction in condensed matter physics. Here we study the temperature and magnetic-field evolution of charge density waves in the rare spin-triplet superconductor candidate UTe 2 using scanning tunneling microscopy/spectroscopy. We reveal that charge modulations composed of three different wave vectors gradually weaken in a spatially inhomogeneous manner, while persisting to surprisingly high temperatures of 10–12 K. We also reveal an unexpected decoupling of the three-component charge density wave state. Our observations match closely to the temperature scale potentially related to short-range magnetic correlations, providing a possible connection between density waves observed by surface probes and intrinsic bulk features. Importantly, charge density wave modulations become suppressed with magnetic field both below and above superconducting T c in a comparable manner. Our work points towards an intimate connection between hidden magnetic correlations and the origin of the unusual charge density waves in UTe 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Nonsymmorphic symmetry and field-driven odd-parity pairing in Ce Rh 2 As 2

Recently, evidence has emerged for a field-induced even- to odd-parity superconducting phase transition in CeRh 2 As 2 . In this paper we argue that the P4/nmm nonsymmorphic crystal structure of CeRh 2 As 2 plays a key role in enabling this transition by ensuring large spin-orbit interactions near the Brillouin zone boundaries, which naturally leads to the required near-degeneracy of the even- and odd-parity channels. We further comment on the relevance of our theory to FeSe, which crystallizes in the same structure.

36 MATERIALS SCIENCE↗