Hyperbolic lattices are a revolutionary platform for tabletop simulations of holography and quantum physics in curved space and facilitate efficient quantum error correcting codes. Their underlying geometry is non-Euclidean, and the absence of Bloch's theorem precludes the straightforward application of the often indispensable energy band theory to study model Hamiltonians on hyperbolic lattices. Motivated by recent insights into hyperbolic band theory, we initiate a crystallography of hyperbolic lattices. We show that many hyperbolic lattices feature a hidden crystal structure characterized by unit cells, hyperbolic Bravais lattices, and associated symmetry groups. Using the mathematical framework of higher-genus Riemann surfaces and Fuchsian groups, we derive a list of example hyperbolic $\{p,q\}$ lattices and their hyperbolic Bravais lattices, including five infinite families and several graphs relevant for experiments in circuit quantum electrodynamics and topolectrical circuits. This dramatically simplifies the computation of energy spectra of tight-binding Hamiltonians on hyperbolic lattices, from exact diagonalization on the graph to solving a finite set of equations in terms of irreducible representations. The significance of this achievement needs to be compared to the all-important role played by conventional Euclidean crystallography in the study of solids. We exemplify the high potential of this approach by constructing and diagonalizing finite-dimensional Bloch wave Hamiltonians.

We study the dynamics of the antiferromagnetic domain wall in collinear antiferromagnet ${\mathrm{MnTiO}}_3$ by means of optical magnetochiral imaging. Antiphase domains are clearly visualized by exploiting the asymmetry in absorption coefficients between two distinct antiferromagnetic states with Néel vectors in opposite directions. Utilizing the coexistence of several types of magnetic multipoles, antiferromagnetic states in ${\mathrm{MnTiO}}_3$ are switched by longitudinal DC electric and magnetic fields applied along the propagation direction of incident light while imaging the domain pattern. The memory effect enables the imaging of millisecond dynamics with domain inversion. Detailed investigation of the domain-wall motion with varying temperature and external-field strength reveals the thermal effects on the mobility of the domain wall.

We consider the extent to which symmetry eigenvalues reveal the topological character of bands. Specifically, we compare distinct atomic limit phases (band representations) that share the same irreducible representations (irreps) at all points in the Brillouin zone and, therefore, appear equivalent in a classification based on eigenvalues. We derive examples where such “irrep-equivalent” phases can be distinguished by a quantized Berry phase or generalization thereof. These examples constitute a generalization of the Su-Schrieffer-Heeger chain: neither phase is topological, in the sense that localized Wannier functions exist, yet there is a topological obstruction between them. We refer to two phases as “Berry obstructed atomic limits” if they have the same irreps, but differ by Berry phases. This is a distinct notion from eigenvalue obstructed atomic limits, which differ in their symmetry irreps at some point in the Brillouin zone. We compute exhaustive lists of elementary band representations that are irrep equivalent, in all space groups, with and without time-reversal symmetry and spin-orbit coupling, and use group theory to derive a set of necessary conditions for irrep equivalence. Finally, we conjecture, and in some cases prove, that irrep-equivalent elementary band representations that are not equivalent can be distinguished by a topological invariant.

We explore a class of random tensor network models with “stabilizer” local tensors which we name random stabilizer tensor networks (RSTNs). For RSTNs defined on a two-dimensional square lattice, we perform extensive numerical studies of entanglement phase transitions between volume-law and area-law entangled phases of the one-dimensional boundary states. These transitions occur when either (a) the bond dimension $D$ of the constituent tensors is varied or (b) the tensor network is subject to random breaking of bulk bonds, implemented by forced measurements. In the absence of broken bonds, we find that the RSTN supports a volume-law entangled boundary state with bond dimension $D\ge 3$ where $D$ is a prime number, and an area-law entangled boundary state for $D=2$. Upon breaking bonds at random in the bulk with probability $p$, there exists a critical measurement rate $p_c$ for each $D\ge 3$ above which the boundary state becomes area-law entangled. To explore the conformal invariance at these entanglement transitions for different prime $D$, we consider tensor networks on a finite rectangular geometry with a variety of boundary conditions, and extract universal operator scaling dimensions via extensive numerical calculations of the entanglement entropy, mutual information, and mutual negativity at their respective critical points. Our results at large $D$ approach known universal data of percolation conformal field theory, while showing clear discrepancies at smaller $D$, suggesting a distinct entanglement transition universality class for each prime $D$. We further study universal entanglement properties in the volume-law phase and demonstrate quantitative agreement with the recently proposed description in terms of a directed polymer in a random environment.

Defects are crucial in determining the overall physical properties of semiconductors. Generally, the charge-state transition level ${\varepsilon }_{\alpha }$(q/q'), one of the key physical quantities that determines the dopability of defects in semiconductors, is temperature dependent. However, little is known about the temperature dependence of ${\varepsilon }_{\alpha }$(q/q') and, as a result, almost all existing defect theories in semiconductors are built on a temperature-independent approximation. In this paper, by deriving the basic formulas for temperature-dependent ${\varepsilon }_{\alpha }$(q/q'), we have established two fundamental rules for the temperature dependence of ${\varepsilon }_{\alpha }$(q/q') in semiconductors. Based on these rules, surprisingly, it is found that the temperature dependencies of ${\varepsilon }_{\alpha }$(q/q') for different defects are rather diverse: it can become shallower, deeper, or stay unchanged. This defect-specific behavior is mainly determined by the synergistic or opposing effects between free-energy corrections (determined by the local volume change around the defect during a charge-state transition) and band-edge changes (which differ for different semiconductors). These basic formulas and rules, confirmed by a large number of state-of-the-art temperature-dependent defect calculations in GaN, may potentially be widely adopted as guidelines for understanding or optimizing doping behaviors in semiconductors at finite temperatures.

Weyl fermions are massless solutions of the Dirac equation described by two-component ($2c$) complex spinors. Such elusive objects emerge as quasiparticles in so-called Weyl semi-metals (WSM). We discuss the generalization of the standard one-component density functional theory (DFT) to a $2c$ approach (the spin-current density functional theory, SCDFT), and its application to the practical quantum-mechanical description of WSMs through a self-consistent treatment of the spin-orbit coupling (SOC) and nonlocal Fock exchange. For hybrid exchange-correlation functionals in the local density approximation or generalized gradient approximation of the SCDFT, we use Levy's constrained search formalism to map specific blocks of the SCDFT potential to specific blocks of the one-electron density matrix, which allows for a straightforward comparison of SCDFT with DFT. We show how a three-dimensional doubly degenerate bulk Dirac node is present in the TaAs WSM in the absence of SOC, lying on the $k_x=0$ mirror plane, which is split into two singly degenerate Weyl nodes off the mirror plane by the SOC. This breaking of the degeneracy and the corresponding splitting of the two Weyl nodes with opposite chirality offers a measurable way to assess different theories. We show how an SCDFT formulation is essential to a correct quantitative description of the electronic features of WSMs.

The Kitaev material $\alpha \text{−}{\mathrm{RuCl}}_3$ is among the most prominent candidates to host a quantum spin-liquid state endowed with fractionalized excitations. Recent experimental and theoretical investigations have separately revealed the importance of both the magnetoelastic coupling and the magnetic anisotropy in dependence of the applied magnetic-field direction. In this combined theoretical and experimental research, we investigate the anisotropic magnetic and magnetoelastic properties for magnetic fields applied along the main crystallographic axes as well as for fields canted out of the honeycomb plane. We found that the magnetostriction anisotropy is unusually large compared to the anisotropy of the magnetization, which is related to the strong magnetoelastic $\widetilde{{\mathrm{\Gamma }}^{\prime }}$-type coupling in our ab-initio derived model. We observed large, nonsymmetric magnetic anisotropy for magnetic fields canted out of the honeycomb $ab$ plane in opposite directions, namely, toward the $+c^{*}$ or $-c^{*}$ axes, respectively. The observed directional anisotropy is explained by considering the relative orientation of the magnetic field with respect to the coaligned ${\mathrm{RuCl}}_6$ octahedra. Magnetostriction measurements in canted fields support this nonsymmetric magnetic anisotropy; however, these experiments are affected by magnetic torque effects. Comparison of theoretical predictions with experimental findings allow us to recognize the significant contribution of torque effects in experimental setups where $\alpha \text{−}{\mathrm{RuCl}}_3$ is placed in canted magnetic fields.

It was recently shown that the XX central spin model is integrable in the presence of a magnetic field perpendicular to the plane in which the coupling exists. A large number of its eigenstates are such that the central spin is not correlated to the environmental spins it is coupled to. In this work, we first demonstrate that the XX-central spin model remains integrable in the presence of an arbitrarily oriented magnetic field. We then show that, provided the coupling is strong enough, dark states can actually be found even in the presence of an in-plane magnetic field. We finally provide a simple explanation of this result and demonstrate its universality for a variety of distinct distributions of the coupling of the central spin to the various bath spins.

Applied magnetic fields are an important tuning parameter for artificial spin ice (ASI) systems, as they can drive phase transitions between different magnetic ground states or tune through regimes with high populations of emergent magnetic excitations (e.g., monopole-like quasiparticles). Here, using simulations supported by experiments, we investigate the thermodynamic properties and magnetic phases of square and quadrupolar ASI as a function of applied in-plane magnetic fields. Monte Carlo simulations are used to generate field-dependent maps of the magnetization, the magnetic specific heat, the thermodynamic magnetization fluctuations, and the magnetic order parameters, all under equilibrium conditions. These maps reveal the diversity of magnetic orderings and the phase transitions that occur in different regions of the phase diagrams of these ASIs, and are experimentally supported by magnetooptical measurements of the equilibrium “magnetization noise” in thermally active ASIs.

The investigations of the interconnection between micro- and macroscopic properties of materials hosting noncollinear antiferromagnetic ground states are challenging. These forefront studies are crucial for unraveling the underlying mechanisms at play, which may prove beneficial in designing cutting-edge multifunctional materials for future applications. In this context, $M{n}_{5}S{i}_3$ has regained scientific interest since it displays an unusual and complex ground state, which is considered to be the origin of the anomalous transport and thermodynamic properties that it exhibits. Here, we report the magnetic exchange couplings of the noncollinear antiferromagnetic phase of $M{n}_{5}S{i}_3$ using inelastic neutron scattering measurements and density functional theory calculations. We determine the ground-state spin configuration and compute its magnon dispersion relations which are in good agreement with the ones obtained experimentally. Furthermore, we investigate the evolution of the spin texture under the application of an external magnetic field to demonstrate theoretically the multiple field-induced phase transitions that $M{n}_{5}S{i}_3$ undergoes. Finally, we model the stability of some of the material's magnetic moments under a magnetic field and we find that very susceptible magnetic moments in a frustrated arrangement can be tuned by the field.

While electron-phonon coupling (EPC) is crucial for Cooper pairing in conventional superconductors, its role in high-$T_c$ superconducting cuprates is debated. Using resonant inelastic x-ray scattering at the oxygen $K$ edge, we study the EPC in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$ (Bi2212) and ${\mathrm{Nd}}_{1+x}{\mathrm{Ba}}_{2-x}{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ (NBCO) at different doping levels ranging from heavily underdoped ($p=0.07$) to overdoped ($p=0.21$). We analyze the data with a localized Lang-Firsov model that allows for the coherent excitations of two phonon modes. While electronic band dispersion effects are non-negligible, we are able to perform a study of the relative values of EPC matrix elements in these cuprate families. In the case of NBCO, the choice of the excitation energy allows us to disentangle modes related to the CuO chains and the $\mathrm{Cu}{\mathrm{O}}_2$ planes. Combining the results from the two families, we find the EPC strength decreases with doping at ${\mathbf{q}}_{\parallel }=(-0.25,0)$ r.l.u., but has a nonmonotonic trend as a function of doping at smaller momenta. This behavior is attributed to the screening effect of charge carriers. We also find that the phonon intensity is enhanced in the vicinity of the charge-density-wave excitations while the extracted EPC strength appears to be less sensitive to their proximity. By performing a comparative study of two cuprate families, we are able to identify general trends in the EPC for the cuprates and provide experimental input to theories invoking a synergistic role for this interaction in $d$-wave pairing.

We report the observation of an in-plane nodal loop accompanying highly dispersive Dirac fermions with a velocity of $1.2\times {10}^6$ m/s in a superconductor ${\text{ZrP}}_{1.24}{\text{Se}}_{0.57}$ by employing angle-resolved photoemission spectroscopy. This nodal loop arises in principle from the P square net as long as nonsymmorphic symmetry is preserved. We have also found that two quasisquare Fermi surfaces that branch from the nodal loop at $-1.2$ eV are largely parallel in favor of nesting, and that two additional electron pockets are present at the Brillouin-zone center unlike in the case of ZrSiS. Our findings demonstrate that a P square net embedded in a superconductor provides a new playground for emergent exotic phenomena coexisting with superconductivity.

It was recently discovered that atoms subject to a time-periodic drive can give rise to a crystal structure in phase space. In this work, we point out that the atom-atom interactions give rise to collective phonon excitations of phase space crystal via a pairing interaction with intrinsically complex phases that can lead to a phononic Chern insulator, accompanied by topologically robust chiral transport along the edge of the phase space crystal. This topological phase is realized even in scenarios in which the time-reversal transformation is a symmetry, which is surprising because the breaking of time-reversal symmetry is a strict precondition for topological chiral transport in the standard setting of real space crystals. Our work has also important implications for the dynamics of two-dimensional charged particles in a strong magnetic field.

We present a comprehensive experimental and theoretical study of the kagome ice Coulomb phase that explores the fine-tuning of critical correlations by applied field, temperature, and crystal orientation. The continuous modification of algebraic correlations is observed by polarized neutron scattering experiments and is found to be well described by numerical simulations of an idealized model. We further clarify the thermodynamics of field-tuned Kasteleyn transitions and demonstrate some dramatic finite-size-scaling properties that depend on how topological string defects wind around the system boundaries. We conclude that kagome ice is a remarkable example of a critical and topological state in a real system that may be subject to fine experimental control.

I overview the properties of nonaxisymmetric isolated skyrmions (ISs), which arise within a cone phase of cubic helimagnets. The nascent conical state is shown to shape skyrmion internal structure and to substantiate the attracting skyrmion-skyrmion interaction. In bulk cubic helimagnets, skyrmion cluster formation with the hexagonal arrangement of constituent skyrmions is explained by the reduction of the total energy due to the overlap of skyrmion shells—circular domain boundaries with the positive energy density formed with respect to the surrounding host phase. In thin layers, however, such a shell localizes within two bags on the opposite sides from the skyrmion cores, which underlies the formation of polar skyrmion chains with the most effective suppression of the shell energy. A systematic analysis of skyrmion trio-clusters and trio-chains reveals that their thickness-dependent advantage rests on a subtle energetic balance between the “lost” negative energy of the skyrmion rings and the “gained” energy due to the suppressed shells. Such a polar ordering of nonaxisymmetric skyrmions was recently observed within the “schools” of liquid-crystal skyrmions powered into motion by an applied electric field [Nat. Commun. 10, 4744 (2019)]. Thus, the fundamental insights provided by this work imply deep physical relations and common physical features of skyrmions in different condensed-matter systems such as chiral liquid crystals and chiral magnets.

We present a comprehensive study of the magnetic exchange Hamiltonian of elemental gadolinium. We use neutron scattering to measure the magnon spectrum over the entire Brillouin zone and fit the excitations to a spin wave model to extract the first 26 nearest-neighbor magnetic exchange interactions with rigorously defined uncertainty. We find these exchange interactions to follow RKKY behavior, oscillating from ferromagnetic to antiferromagnetic as a function of distance. Finally, we discuss the topological features and degeneracies in Gd, and HCP ferromagnets in general. We show theoretically how, with asymmetric exchange, topological properties could be tuned with a magnetic field.

The two-dimensional Su-Schrieffer-Heeger model of electrons coupled to quantum phonons is investigated using Langevin dynamics within the framework of auxiliary-field quantum Monte Carlo. Based on an explicit determination of the density of zeros of the fermion determinant, it is argued that the method is efficient in the challenging adiabatic limit. Large-scale simulations at the O(4)-symmetric point establish that the ground state of the 2D SSH model undergoes a transition from a $(\pi ,\pi )$ valence bond solid to an antiferromagnet with increasing phonon frequency, yet still in the adiabatic regime. The single-particle spectrum illustrates the renormalization of the electronic band and suggests the existence of a gapped polaronic band, whereas the particle-hole channels show gapless modes associated with long-range bond and magnetic order, respectively. The simulations are supplemented with a mean-field analysis and a self-consistent Born approximation.

Radiative recombination of excitons dressed by the interactions with free charge carriers often occurs under simultaneous excitation of either electrons or holes to unbound states. This phenomenon, known as the electron recoil effect, manifests itself in pronounced, asymmetric spectral line shapes of the resulting emission. We study the electron recoil effect experimentally in electrically tunable monolayer semiconductors and derive it theoretically using both trion and Fermi polaron pictures. Time-resolved analysis of the recoil line shapes is employed to access transient, nonequilibrium states of the exciton-carrier complexes. We demonstrate cooling of the initially overheated populations on picosecond timescales and reveal the impact of lattice temperature and free carrier density. Both thermally activated phonons and the presence of free charges are shown to accelerate equilibration. Finally, we find similar values of relaxation times from recoil analysis and luminescence rise times, providing additional insight into trion dynamics.

We investigate the role of the chiral anomaly in hydrodynamic and crossover regimes of transport in a Weyl or Dirac semimetal film. We show that the magnetic-field-dependent part of the electric conductivity in the direction of the magnetic field develops an unusual nonmonotonic dependence on temperature dubbed the anomalous Gurzhi effect. This effect is realized in sufficiently clean semimetals subject to a classically weak magnetic field where the electron-electron scattering dominates and the relaxation of the valley-imbalance charge density happens at the boundaries. Moreover, the conditions for the realization of the conventional Gurzhi effect in hydrodynamic and crossover regimes of transport in three-dimensional Dirac and Weyl semimetals are determined.

Using the density-matrix renormalization group method for the ground state and excitations of the Shastry-Sutherland spin model, we demonstrate the existence of a narrow quantum spin liquid phase between the previously known plaquette-singlet and antiferromagnetic states. Our conclusions are based on the finite-size scaling of excited level crossings and order parameters. Together with previous results on candidate models for deconfined quantum criticality and spin liquid phases, our results point to a unified quantum phase diagram where the deconfined quantum-critical point separates a line of first-order transitions and a gapless spin liquid phase. The frustrated Shastry-Sutherland model is close to the critical point but slightly inside the spin liquid phase, while previously studied unfrustrated models cross the first-order line. We also argue that recent heat capacity measurements in ${\mathrm{SrCu}}_2{\left({\mathrm{BO}}_3\right)}_2$ show evidence of the proposed spin liquid at pressures between 2.6 and 3 GPa.