J. C. Seamus Davis

The kagome lattice of spin-1/2 copper atoms in herbertsmithite is conjectured to sustain a quantum spin liquid state with spinon quasiparticles. Ideally, the kagome crystal planes are each separated by a plane of spinless zinc atoms. However, in real crystals, some spin-1/2 copper atoms substitute randomly onto these inter-kagome zinc sites. Here we reconceptualize such ‘impurity’ atoms as quantum witness spins whose dynamics is designed to probe the spin liquid state. We then introduce spin noise spectroscopy to measure the frequency and temperature dependence of witness spin dynamics, demonstrating that their phenomenology is consistent with extensive interactions between witness spins mediated by propagation of spinons through a quantum spin liquid. Ultimately, a sharp transition occurs at around 260 mK, below which the properties of both spin noise and magnetic susceptibility suggest that the witness spins form a spin glass phase. Among the theoretical models considered, we demonstrate that our observations are only consistent with spinon-mediated interactions between witness spins by either a Z ₂ or U(1) quantum spin liquid, with the former model more closely matching the data. Our work demonstrates that quantum mechanical witness spins may now conceivably be used as a widely applicable probe of quantum spin liquid physics.

Dynamical heterogeneity, in which transitory local fluctuations occur in the conformation and dynamics of constituent particles, is widely hypothesized to be essential to the evolution of supercooled liquids into the structural glass state. Yet its microscopic spatiotemporal phenomenology is challenging to detect directly in molecular glass forming liquids. Because recent theoretical advances predict that corresponding dynamical heterogeneity could occur in supercooled magnetic monopole fluids (Proc. Nat. Acad. Sci. 112, 8549 (2015)), we searched for such phenomena in Dy ₂ Ti ₂ O ₇ . By measuring its microsecond-resolved spontaneous magnetization fluctuations M ( t , T ) we detected a sharp bifurcation in monopole noise characteristics below T ≈ 1,500   mK , with the appearance of powerful spontaneous monopole current bursts. This intense dynamics emerges upon entering the supercooled monopole fluid regime, reaches maximum strength near T ≈ 750   mK and then collapses along with coincident loss of ergodicity approaching T g ≈ 250   mK . Moreover, when the four-point dynamical susceptibility χ 4 ( τ , T ) is determined directly from temperature dependence of correlations in M ( t , T ) , it evolves as predicted when dynamical heterogeneity is present, revealing its simultaneously and rapidly escalating length and time scales, ξ ( T ) and τ 4 ( T ) . This overall phenomenology greatly expands our empirical knowledge of supercooled monopole fluids and, more generally, demonstrates techniques for detection of the time sequence, magnitude, statistics, and correlations of dynamical heterogeneity, access to which may greatly accelerate fundamental vitrification studies.

Although no known material exhibits intrinsic topological superconductivity, where a spin-triplet electron pairing potential has odd parity, UTe₂ is now the leading candidate. Generally, the parity of a superconducting order parameter can be established using Bogoliubov quasiparticle interference imaging. However, odd-parity superconductors should support a topological quasiparticle surface band at energies within the maximum superconducting energy gap. Quasiparticle interference should then be dominated by the electronic structure of the quasiparticle surface band and only reveal the characteristics of the bulk order parameter indirectly. Here we demonstrate that at the (0–11) cleave surface of UTe₂, a band of Bogoliubov quasiparticles appears only in the superconducting state. Performing high-resolution quasiparticle interference measurements then allows us to explore the dispersion of states in this superconductive surface band, showing that they exist only within the range of Fermi momenta projected onto the (0–11) surface. Finally, we develop a theoretical framework to predict the quasiparticle interference signatures of this surface band at the (0–11) surface. Its predictions are consistent with the experimental results if the bulk superconducting order parameter exhibits time-reversal conserving, odd-parity, a-axis nodal, B _{3 u} symmetry.

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 _{1 u} , B _{2 u} , or B _{3 u} . However, if the quasiparticle scattering along the a axis is internodal, then a nonchiral B _{3 u} state is the most consistent for UTe ₂ .

An emerging concept for identification of different types of spin liquids [C. Broholm et al. , Science 367 , eaay0668 (2020)] is through the use of spontaneous spin noise [S. Chatterjee, J. F. Rodriguez-Nieva, E. Demler, Phys. Rev. B 99 , 104425 (2019)]. Here, we develop spin noise spectroscopy for spin liquid studies by considering Ca ₁₀ Cr ₇ O ₂₈ , a material hypothesized to be either a quantum or a spiral spin liquid (SSL). By enhancing techniques introduced for magnetic monopole noise studies [R. Dusad et al. , Nature 571 , 234–239 (2019)], we measure the time and temperature dependence of spontaneous flux Φ ( t , T ) and thus magnetization M ( t , T ) of Ca ₁₀ Cr ₇ O ₂₈ samples. The resulting power spectral density of magnetization noise S M ω , T reveals intense spin fluctuations with S M ω , T ∝ ω - α ( T ) and 0.84 < α T < 1.04 . Both the variance σ M 2 T and the correlation function C M t , T of this spin noise undergo crossovers at a temperature T ∗ ≈ 450   mK . While predictions for quantum spin liquids are inconsistent with this phenomenology, those from Monte–Carlo simulations of a two-dimensional (2D) SSL state in Ca ₁₀ Cr ₇ O ₂₈ yield overall quantitative correspondence with the measured frequency and temperature dependences of S M ω , T ,   C M t , T , and σ M 2 T , thus indicating that Ca ₁₀ Cr ₇ O ₂₈ is an SSL.

The primordial ingredient of cuprate superconductivity is the CuO₂ unit cell. Theories usually concentrate on the intra-atom Coulombic interactions dominating the 3d⁹ and 3d¹⁰ configurations of each copper ion. However, if Coulombic interactions also occur between electrons of the 2p⁶ orbitals of each planar oxygen atom, spontaneous orbital ordering may split their energy levels. This long-predicted intra-unit-cell symmetry breaking should generate an orbitally ordered phase, for which the charge transfer energy ε separating the 2p⁶ and 3d¹⁰ orbitals is distinct for the two oxygen atoms. Here we introduce sublattice-resolved ε(r) imaging to CuO₂ studies and discover intra-unit-cell rotational symmetry breaking of ε(r). Spatially, this state is arranged in disordered Ising domains of orthogonally oriented orbital order bounded by dopant ions, and within whose domain walls low-energy electronic quadrupolar two-level systems occur. Overall, these data reveal a Q = 0 orbitally ordered state that splits the oxygen energy levels by ~50 meV, in underdoped CuO₂.