Motivated by the experimental observation of a nonmagnetic phase in compounds with frustration and disorder, we study the ground state of a spin-$1/2$ square-lattice Heisenberg model with randomly distributed nearest-neighbor $J_1$ and next-nearest-neighbor $J_2$ couplings. By using the density matrix renormalization group (DMRG) calculation on a cylinder system with a circumference of up to ten lattice sites, we identify a disordered phase between the Néel and stripe magnetic phase with growing $J_2/J_1$ in the presence of strong bond randomness. The vanished spin-freezing parameter indicates the absence of spin-glass order. The large-scale DMRG results unveil the size-scaling behaviors of the spin-freezing parameter, the power-law decay of the average spin correlation, and the exponential decay of the typical spin correlation, which all agree with the corresponding behavior in the one-dimensional random-singlet (RS) state and characterize the RS nature of this disordered phase. The DMRG simulation also provides insights and opportunities for characterizing a class of nonmagnetic states in two-dimensional frustrated magnets with disorder. We also compare with existing experiments and suggest more measurements for understanding the spin-liquid-like behaviors in the double perovskite ${\mathrm{Sr}}_2{\mathrm{CuTe}}_{1-x}{\mathrm{W}}_x{\mathrm{O}}_6$.

Interplay between fermiology and electron correlation is crucial for realizing exotic quantum phases. Transition-metal dichalcogenide (TMD) $1T\text{−}{\mathrm{TaS}}_2$ has sparked tremendous attention owing to its unique Mott-insulating phase coexisting with the charge-density wave (CDW). However, how the fermiology and electron correlation are associated with such properties has yet to be clarified. Here we demonstrate that monolayer $1T\text{−}{\mathrm{NbTe}}_2$ is a new class of two-dimensional TMD which has the star-of-David lattice similarly to bulk ${\mathrm{TaS}}_2$ and isostructural monolayer ${\mathrm{NbSe}}_2$, but exhibits a metallic ground state with an unusual lattice periodicity ($\sqrt{19}\times \sqrt{19}$) characterized by the sparsely occupied star-of-David lattice. By using angle-resolved photoemission and scanning-tunneling spectroscopies in combination with first-principles band-structure calculations, we found that the hidden Fermi-surface nesting and associated CDW formation are a primary cause to realize this unique correlated metallic state with no signature of Mott gap. The present result points to a vital role of underlying fermiology to characterize the Mott phase of TMDs.

We investigate coupled electron-lattice dynamics in the topological insulator ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ with time-resolved photoemission and time-resolved x-ray diffraction. It is well established that coherent phonons can be launched by optical excitation, but selection rules generally restrict these modes to zone-center wave vectors and Raman-active branches. We find that the topological surface state couples to additional modes, including a continuum of surface-projected bulk modes from both Raman and infrared branches, with possible contributions from surface-localized modes when they exist. Our calculations show that this surface vibrational spectrum occurs naturally as a consequence of the translational and inversion symmetries broken at the surface, without requiring the splitting-off of surface-localized phonon modes. The generality of this result suggests that coherent phonon spectra are useful by providing unique fingerprints for identifying surface states in more controversial materials. These effects may also expand the phase space for tailoring surface state wave functions via ultrafast optical excitation.

Domain pattern transfer from ferroelectric to ferromagnetic materials is a critical step for the electric field control of magnetism and has the potential to provide new schemes for low-power data storage and computing devices. Here we investigate domain coupling in ${\mathrm{BaTiO}}_3\left(111\right)/\mathrm{CoFeB}$ heterostructures by direct imaging in a wide-field Kerr microscope. The magnetic easy axis is found to locally change direction as a result of the underlying ferroelectric domains and their polarization. By plotting the remanent magnetization as a function of angle in the plane of the CoFeB layer, we find that the magnetic easy axes in adjacent domains are angled at ${60}^{\circ }$ or ${120}^{\circ }$, corresponding to the angle of rotation of the polarization from one ferroelectric domain to the next, and that the magnetic domain walls may be charged or uncharged depending on the magnetic field history. Micromagnetic simulations show that the properties of the domain walls vary depending on the magnetoelastic easy axis configuration and the charged or uncharged nature of the wall. The configuration where the easy axis alternates by ${60}^{\circ }$ and a charged wall is initialized exhibits the largest change in domain wall width from 192 nm to 119 nm as a function of in-plane magnetic field. Domain wall width tuning provides an additional degree of freedom for devices that seek to manipulate magnetic domain walls using strain coupling to ferroelectrics.

A recent experimental work on palladium hydrides suggested that metastable structures with hydrogen atoms occupying tetrahedral sites could lead to superconductivity above 50 K, a huge increase compared to the 9 K critical temperature of the stable structure with all hydrogen atoms occupying octahedral sites. By generating many structures with hydrogen atoms randomly occupying the octahedral and tetrahedral sites of the face-centered-cubic lattice and calculating their energy at different theoretical levels from first principles, we determine that metastable structures with partial or full occupation of tetrahedral sites are possible, even when the ionic quantum zero-point energy and anharmonicity are included in the calculations. Anharmonicity is crucial in palladium hydrides when hydrogen atoms occupy octahedral sites and, in fact, makes the structure with full octahedral occupation the ground state. Despite the metastable existence of structures with full or partial tetrahedral site occupation, the superconducting critical temperature is reduced with the number of tetrahedral sites occupied. Our calculations discard that the occupation of tetrahedral sites can increase the critical temperature in palladium hydrides.

We elaborate that for topological insulators and topological superconductors described by Dirac models in any dimension and symmetry class, the topological order can be mapped to lattice sites by a universal topological marker. Deriving from a recently discovered momentum-space universal topological invariant, we introduce a topological operator that consists of alternating projectors to filled and empty lattice eigenstates and the position operators, multiplied by the Dirac matrices that are omitted in the Hamiltonian. The topological operator projected to lattice sites yields the topological marker, whose form is explicitly constructed for every topologically nontrivial symmetry class from 1D to 3D. The off-diagonal elements of the topological operator yield a nonlocal topological marker, which decays with a correlation length that diverges at topological phase transitions, and represents a Wannier state correlation function. Various prototype examples, including the Su-Schrieffer-Heeger model, Majorana chain, Chern insulators, Bernevig-Hughes-Zhang model, 2D chiral and helical $p$-wave superconductors, lattice model of ${}^3\mathrm{He}$ B-phase, and 3D time-reversal-symmetric topological insulators, are employed to demonstrate the ubiquity of our formalism.

The Kitaev honeycomb model hosts a fascinating fractionalized state of matter featuring emergent Majorana fermions and a vison particle that carries the flux of an emergent gauge field. In the exactly solvable model these visons are static, but certain perturbations can induce their motion. We show that the nature of the vison motion induced by a Zeeman field is sharply distinct in the ferromagnetic vs the antiferromagnetic Kitaev models. Namely, in the ferromagnetic model the vison has a trivial nonprojective translational symmetry, whereas in the antiferromagnetic Kitaev model it has a projective translational symmetry with $\pi$ flux per unit cell. The vison band of the ferromagnetic case has zero Berry curvature and no associated intrinsic contribution to the thermal Hall effect. In contrast, in the antiferromagnetic case there are two gapped vison bands with opposite Chern numbers and an associated intrinsic vison contribution to the thermal Hall effect. We discuss these findings in light of the physics of the spin liquid candidate $\alpha \text{−}{\mathrm{RuCl}}_3$.

Motivated by recent experiments on low-carrier-density superconductors, including twisted multilayer graphene, we study signatures of the BCS-to-BEC evolution in Andreev reflection spectroscopy. We establish that in a standard quantum point contact geometry, Andreev reflection in a BEC superconductor is unable to mediate a zero-bias conductance beyond $e^2/h$ per lead channel. This bound is shown to result from a mapping that links the subgap conductance of BCS and BEC superconductors. We then demonstrate that sharp signatures of BEC superconductivity, including perfect Andreev reflection, can be recovered by tunneling through a suitably designed potential well. We propose various tunneling spectroscopy setups to experimentally probe this recovery.

${}^{151}\mathrm{Eu}$ Mössbauer spectroscopy shows that yttrium substitution in mixed-valent ${\mathrm{EuPd}}_3{\mathrm{S}}_4$ drives the initial 50:50 mix of ${\mathrm{Eu}}^{3+}$ and ${\mathrm{Eu}}^{2+}$ towards pure ${\mathrm{Eu}}^{2+}$, whereas lanthanum substitution has the opposite effect, but only for substitution levels above 50%. We find that total valence electron count and chemical pressure effects cannot account for the observed behavior; however, conserving the cell volume provides a consistent description of the changes in the ${\mathrm{Eu}}^{2+}:{\mathrm{Eu}}^{3+}$ ratio. Remarkably, lanthanum substitution also leads to a clear transition from static mixed-valent behavior at lower temperatures to dynamic mixed-valent behavior at higher temperatures, with the onset temperature monotonically increasing with Eu content and extrapolating to a value of $\sim 340$ K for the pure ${\mathrm{EuPd}}_3{\mathrm{S}}_4$ compound. Magnetic order persists at least as far as $x=0.875$ in both series, despite the drastic reduction in the amount of moment-carrying ${\mathrm{Eu}}^{2+}$ ions.

The temperature dependence of the complex optical properties of the layered phosphide material ${\mathrm{EuCd}}_2{\mathrm{P}}_2$ have been measured over a wide frequency range above and below $T_{\mathrm{N}}\simeq 11.5$ K for light polarized in the a-b planes. At room temperature, the optical conductivity is well described by a weak free-carrier component with a Drude plasma frequency of $\simeq 1100{\mathrm{cm}}^{-1}$ and a scattering rate of $1/{\tau }_D\simeq 700{\mathrm{cm}}^{-1}$, with the onset of interband absorptions above $\simeq 2000{\mathrm{cm}}^{-1}$. Two infrared-active $E_u$ modes are observed at $\simeq 89$ and 239 ${\mathrm{cm}}^{-1}$. As the temperature is reduced the scattering rate decreases and the low-frequency conductivity increases slightly; however, below $\simeq 50$ K the conductivity decreases until at the resistivity maximum at $\simeq 18$ K (just below $2T_{\mathrm{N}}$) the spectral weight associated with free carriers is transferred to a localized excitation at $\simeq 500{\mathrm{cm}}^{-1}$. Below $T_{\mathrm{N}}$, metallic behavior is recovered. Interestingly, the $E_u$ modes are largely unaffected by these changes, with only the position of the high-frequency mode showing any signs of anomalous behavior. While several scenarios are considered, the prevailing view is that the resistivity maximum and subsequent carrier localization is due to the formation of ferromagnetic domains below $\simeq 2T_{\mathrm{N}}$ that result in spin-polarized clusters due to spin-carrier coupling.

Classical models of spin systems traditionally retain only the dipole moments, but a quantum spin state will frequently have additional structure. Spins of magnitude $S$ have $N=2S+1$ levels. Alternatively, the spin state is fully characterized by a set of $N^2-1$ local physical observables, which we interpret as generalized spin components. For example, a spin with $S=1$ has three dipole components and five quadrupole components. These components evolve under a generalization of the classical Landau-Lifshitz dynamics, which can be extended with noise and damping terms. In this paper, we reformulate the dynamical equations of motion as a Langevin dynamics of $\mathrm{SU}(N$) coherent states in the Schrödinger picture. This viewpoint is especially useful as the basis for an efficient numerical method to sample spin configurations in thermal equilibrium and to simulate the relaxation and driven motion of topological solitons. To illustrate the approach, we simulate a nonequilibrium relaxation process that creates ${\mathrm{CP}}^2$ skyrmions, which are topological defects with both dipole and quadrupole character.

We report the discovery of ${\mathrm{CeLiBi}}_2$, the first example of a material in the tetragonal $\mathrm{Ce}T{X}_2$ ($T$ = transition metal; $X$ = pnictogen) family wherein an alkali cation replaces the typical transition metal. Magnetic susceptibility and neutron powder diffraction measurements are consistent with a crystal-field ${\mathrm{\Gamma }}_6$ ground-state Kramers doublet that orders antiferromagnetically below $T_N=3.4$ K with an incommensurate propagation wave vector $\mathbf{k}=(0,0.0724(4),0.5)$ that generates a nanometric modulation of the magnetic structure. The best model of the ordered state is an elliptical cycloid with Ce moments primarily residing in the $ab$ plane. This is highly unusual, as all other ${\mathrm{\Gamma }}_6\mathrm{Ce}T{X}_2$ members order ferromagnetically. Further, we observe an atypical hard-axis metamagnetic transition at 2 T in magnetostriction, magnetization, and resistivity measurements. ${\mathrm{CeLiBi}}_2$ is a rare example of a highly conductive material with dominant skew scattering leading to a large anomalous Hall effect. Quantum oscillations with five frequencies arise in magnetostriction and magnetic susceptibility data to $T=30$ K and ${\mu }_{0}H=55$ T, which indicate small Fermi pockets of light carriers with effective masses as low as $0.07m_e$. Density functional theory calculations indicate that square-net Dirac-like $\mathrm{Bi}-p$ bands are responsible for these ultralight carriers. Together, our results show that ${\mathrm{CeLiBi}}_2$ enables multiple atypical magnetic and electronic properties in a single clean material.

Mechanical straining of skyrmion hosting materials has previously demonstrated increased phase stability through the expansion of the skyrmion equilibrium pocket. Additionally, metastable skyrmions can be generated via rapid field cooling to form significant skyrmion populations at low temperatures. Using small-angle x-ray scattering and x-ray holographic imaging on a thermally strained 200-nm-thick FeGe lamella, we observe temperature-induced strain effects on the structure and metastability of the skyrmion lattice. We find that in this sample orientation ($H \parallel \left[\overline{1}10\right]$) with no strain, metastable skyrmions produced by field cooling through the equilibrium skyrmion pocket vanish from the sample upon dropping below the well-known helical reorientation temperature. However, when strain is applied along the $\left[110\right]$ axis, and this procedure is repeated, a substantial volume fraction of metastable skyrmions persist upon cooling below this temperature down to 100 K. Additionally, we observe a large number of skyrmions retained after a complete magnetic field polarity reversal, implying that the metastable energy barrier protecting skyrmions from decay is enhanced.

Graphene is a quantum spin Hall insulator with a $45\mathrm{\mu }\mathrm{eV}$-wide nontrivial topological gap induced by the intrinsic spin-orbit coupling. Even though this zero-field spin splitting is weak, it makes graphene an attractive candidate for applications in quantum technologies, given the resulting long spin-relaxation time. On the other side, the staggered sublattice potential, resulting from the coupling of graphene with its boron nitride substrate, compensates intrinsic spin-orbit coupling and decreases the nontrivial topological gap, which may lead to the phase transition into trivial band insulator state. In this work, we present extensive experimental studies of the zero-field splittings in monolayer and bilayer graphene in a temperature range 2–12 K by means of subterahertz photoconductivity-based electron spin-resonance technique. Surprisingly, we observe a decrease of the spin splittings with increasing temperature. We discuss the origin of this phenomenon by considering possible physical mechanisms likely to induce a temperature dependence of the spin-orbit coupling. These include the difference in the expansion coefficients between the graphene and the boron nitride substrate or the metal contacts, the electron-phonon interactions, and the presence of a magnetic order at low temperature. Our experimental observation expands knowledge about the nontrivial topological gap in graphene.

Femtosecond optical pumping of magnetic materials has been used to achieve ultrafast switching and recently to nucleate symmetry-broken magnetic states. However, when the magnetic order parameter already presents a broken-symmetry state, such as a domain pattern, the dynamics are poorly understood and consensus remains elusive. Here, we resolve the controversies in the literature by studying the ultrafast response of magnetic domain patterns with varying degrees of translation symmetry with ultrafast x-ray resonant scattering. A data analysis technique is introduced to disentangle the isotropic and anisotropic components of the x-ray scattering. We find that the scattered intensity exhibits a radial shift restricted to the isotropic component, indicating that the far-from-equilibrium magnetization dynamics are intrinsically related to the spatial features of the domain pattern. Our results suggest alternative pathways for the spatiotemporal manipulation of magnetism via far-from-equilibrium dynamics and by carefully tuning the ground-state magnetic textures.

The feedback of the geometrical Berry phase, accumulated in an electron system, on the slow dynamics of classical degrees of freedom is governed by the Berry curvature. Here, we study local magnetic moments, modeled as classical spins, which are locally exchange coupled to the (spinful) Haldane model for a Chern insulator. In the emergent equations of motion for the slow classical-spin dynamics there is a an additional anomalous geometrical spin torque, which originates from the corresponding spin Berry curvature. Due to the explicitly broken time-reversal symmetry, this is nonzero but usually small in a condensed-matter system. We develop the general theory and compute the spin Berry curvature, mainly in the limit of weak exchange coupling, in various parameter regimes of the Haldane model, particularly close to a topological phase transition and for spins coupled to sites at the zigzag edge of the model in a ribbon geometry. The spatial structure of the spin Berry curvature tensor, its symmetry properties, the distance dependence of its nonlocal elements, and further properties are discussed in detail. For the case of two classical spins, the effect of the geometrical spin torque leads to an anomalous non-Hamiltonian spin dynamics. It is demonstrated that the magnitude of the spin Berry curvature is decisively controlled by the size of the insulating gap, the system size, and the strength of local exchange coupling.

We study the intrinsic scattering of phonons by a general quantum degree of freedom, i.e., a fluctuating “field” $Q$, which may have completely general correlations, restricted only by unitarity and translational invariance. From the induced scattering rates, generalizing the model studied in a companion paper [Mangeolle et al., Phys. Rev. X 12, 041031 (2022)], we obtain the consequences on the thermal conductivity tensor of the phonons. We confirm that, even within our generalized model, the off-diagonal scattering rates involve a minimum of three- to four-point correlation functions of the $Q$ fields, and we discuss the “semiclassical” versus “quantum” nature of all contributions. We obtain general and explicit forms for these correlations which isolate the contributions to the Hall conductivity, and we provide a general discussion of the implications of symmetry and equilibrium; this elaborates on, and extends, the results of Mangeolle et al. [Phys. Rev. X 12, 041031 (2022)]. We also extend the discussion and evaluation of these two- (diagonal scattering) and four-point correlation functions, and hence the thermal transport, for the illustrative example of an ordered two-dimensional antiferromagnet, where the $Q$ field is a composite of magnon operators arising from spin-lattice coupling, and confirm numerically that the results, while satisfying all the necessary symmetry restrictions, lead to nonvanishing scattering and Hall effects. In particular, we investigate, both analytically and numerically, the dependence of such intrinsic scattering on a crucial parameter—the magnon to phonon velocity ratio $\upsilon$. We in particular confirm that within some range of $\upsilon$ of order 1 the skew-scattering mechanism leads to comparable thermal Hall conductivity for thermal currents within and normal to the plane of the antiferromagnetism, and we discover that the temperature scaling of the longitudinal conductivity displays a threshold effect and a nonuniversal, continuous variation of the scaling exponent with $\upsilon$.

In most superconductors, optical excitations require impurity scattering or the presence of multiple bands. This is because in clean single-band superconductors, the combination of particle-hole and inversion symmetries prevents momentum-conserving transitions. In this Letter we show how the flow of supercurrent can lead to new contributions to optical conductivity. As the supercurrent breaks inversion symmetry, transitions across the superconducting gap become allowed even in clean superconductors and dominate over impurity-induced contributions for energies comparable to the gap width. The response is dependent on the nature of the underlying normal state as well as on the type of superconducting order. Use of an external magnetic field to produce a screening supercurrent with controllable magnitude and direction, enables a detailed investigation of the superconducting state, allowing determination of the gap symmetry in unconventional superconductors for which other techniques have not been practicable.

We investigate the optical properties of silicon-vacancy (SiV) and germanium-vacancy (GeV) color centers in nanodiamonds under hydrostatic pressure up to 180 GPa. The nanodiamonds were synthesized by Si- or Ge-doped plasma-assisted chemical vapor deposition and, for our experiment, pressurized in a diamond anvil cell. Under hydrostatic pressure we observe blueshifts of the SiV and GeV zero-phonon lines by 17 THz (70 meV) and 78 THz (320 meV), respectively. These measured pressure-induced shifts are in good agreement with ab initio calculations that take into account the lattice compression based on the equation of state of diamond and that are extended to the case of the tin-vacancy (SnV) center. This work provides guidance on the use of group-IV-vacancy centers as quantum sensors under extreme pressures that will exploit their specific optical and spin properties induced by their intrinsic inversion-symmetric structure.

We consider the effects of leakage on the ability to realize a discrete time crystal (DTC) in a semiconductor quantum dot linear array being operated as a chain of singlet-triplet (ST) qubits. This system realizes an Ising model with an effective applied magnetic field, plus additional terms that can cause leakage out of the computational subspace. We demonstrate that, in the absence of these leakage terms, this model theoretically realizes a DTC phase over a broad parameter regime for six and eight qubits, with a broader parameter range for the eight-qubit case. We then reintroduce the leakage terms and find that the DTC phase disappears entirely over the same parameter range if the system is only subject to a uniform magnetic field, which does not suppress leakage. However, we find that the DTC phase can be restored if the system is instead subject to a magnetic field that alternates from qubit to qubit, which suppresses leakage. We thus show that leakage is a serious problem for the realization of a DTC phase in a chain of ST qubits, but is by no means insurmountable. Our work suggests that experiments manifesting small-system stable DTC should be feasible with currently existing quantum dot spin qubits.