Viscous phenomena are the hallmark of the hydrodynamic flow exhibited by Dirac fermions in clean graphene at high enough temperatures. We report a quantitative calculation of the electronic shear and Hall viscosities in graphene based on the kinetic theory combined with the renormalization group providing a unified description at arbitrary doping levels and nonquantizing magnetic fields. At charge neutrality, the Hall viscosity vanishes, while the field-dependent shear viscosity decays from its zero-field value saturating to a nonzero value in classically strong fields. Away from charge neutrality, the field-dependent viscosity coefficients tend to agree with the semiclassical expectation.

Previous observations of metastable magnetic skyrmions have shown that close to the equilibrium pocket the metastable state has a short lifetime, and therefore, rapid cooling is required to generate a significant skyrmion population at low temperatures. Here, we report that the lifetime of metastable skyrmions in crystals of ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ is extended by a factor of 50 with the introduction of only 2.5% zinc doping, allowing over 50% of the population to survive when field cooling at a rate of just 1 K/min. Our systematic study suggests that the lifetime enhancement is due to the increase in the pinning site density, rather than an alteration to the energy barrier of the decay process. We expect that doping can be exploited to control the lifetime of the metastable SkL state in other chiral magnets, offering a method of engineering skyrmion materials towards application in future devices.

We describe how to incorporate symmetries of the Hamiltonian into auxiliary-field quantum Monte Carlo (AFQMC) calculations. Focusing on the case of Abelian symmetries, we show that the computational cost of most steps of an AFQMC calculation is reduced by $N_k^{-1}$, where $N_k$ is the number of irreducible representations of the symmetry group. We apply the formalism to a molecular system as well as to several crystalline solids. In the latter case, the lattice translational group provides increasing savings as the number of $k$ points is increased, which is important in enabling calculations that approach the thermodynamic limit. The extension to non-Abelian symmetries is briefly discussed.

Phonons and their interactions are necessary for determining a wide range of materials properties. Here we present four independent advances which facilitate the computation of phonons and their interactions from first principles. First, we implement a group-theoretical approach to construct the order $\mathcal{N}$ Taylor series of a $d$-dimensional crystal purely in terms of space group irreducible derivatives (ID), which guarantees symmetry by construction and allows for a practical means of communicating and storing phonons and their interactions. Second, we prove that the smallest possible supercell which accommodates $\mathcal{N}$ given wave vectors in a $d$-dimensional crystal is determined using the Smith normal form of the matrix formed from the corresponding wave vectors; resulting in negligible computational cost to find said supercell, in addition to providing the maximum required multiplicity for uniform supercells at arbitrary $\mathcal{N}$ and $d$. Third, we develop a series of finite displacement methodologies to compute phonons and their interactions which exploit the first two developments: lone and bundled irreducible derivative (LID and BID) approaches. LID computes a single ID, or as few as possible, at a time in the smallest supercell possible, while BID exploits perturbative derivatives for some order less than $\mathcal{N}$ (e.g., Hellman-Feynman forces) in order to extract all ID in the smallest possible supercells using the fewest possible computations. Finally, we derive an equation for the order $N$ volume derivatives of the phonons in terms of the order $\mathcal{N}=N+2$ ID. Given that the former are easily computed, they can be used as a stringent, infinite ranged test of the ID. Our general framework is illustrated on graphene, yielding irreducible phonon interactions to fifth order. Additionally, we provide a cost analysis for the rocksalt structure at $\mathcal{N}=3$, demonstrating a massive speedup compared to popular finite displacement methods in the literature.

An efficient and robust on-the-fly machine learning force field method is developed and integrated into an electronic-structure code. This method realizes automatic generation of machine learning force fields on the basis of Bayesian inference during molecular dynamics simulations, where the first-principles calculations are only executed, when new configurations out of already sampled datasets appear. The developed method is applied to the calculation of melting points of Al, Si, Ge, Sn and MgO. The applications indicate that more than 99% of the first-principles calculations are bypassed during the force field generation. This allows the machine to quickly construct first-principles datasets over wide phase spaces. Furthermore, with the help of the generated machine learning force fields, simulations are accelerated by a factor of thousand compared with first-principles calculations. Accuracies of the melting points calculated by the force fields are examined by thermodynamic perturbation theory, and the examination indicates that the machine learning force fields can quantitatively reproduce the first-principles melting points.

Superfluids, such as superfluid ${}^3\mathrm{He}$ and ${}^4\mathrm{He}$, exhibit a broad range of quantum phenomena and excitations which are unique to these systems. Nanoscale mechanical resonators are sensitive and versatile force detectors with the ability to operate over many orders of magnitude in damping. Using nanomechanical-doubly clamped beams of extremely high quality factors ($Q>{10}^6$), we probe superfluid ${}^4\mathrm{He}$ from the superfluid transition temperature down to millikelvin temperatures at frequencies up to 11.6 MHz. Our studies show that nanobeam damping is dominated by hydrodynamic viscosity of the normal component of ${}^4\mathrm{He}$ above 1 K. In the temperature range of 0.3–0.8 K, the ballistic quasiparticles (phonons and rotons) determine the beams' behavior. At lower temperatures, damping saturates and is determined either by magnetomotive losses or by acoustic emission into helium. It is remarkable that all these distinct regimes can be extracted with just a single device, despite damping changing over six orders of magnitude.

We study the dynamics of charge transfer insulators after photoexcitation using the three-band Emery model and a nonequilibrium extension of $\mathrm{Hartree}-\mathrm{Fock}+\mathrm{EDMFT}$ (extended dynamical mean field theory) and $\mathit{GW}+\mathrm{EDMFT}$. While the equilibrium properties are accurately reproduced by the Hartree-Fock treatment of the ligand bands, dynamical correlations are essential for a proper description of the photodoped state. Photodoping leads to a renormalization of the charge transfer gap and to a substantial broadening of the bands. We calculate the time-resolved photoemission spectrum and optical conductivity and find qualitative agreement with experiments. Our formalism enables the realistic description of nonequilibrium phenomena in materials with ligand bands. It provides a tool to explore the optical manipulation of interaction and correlation effects, including insulator-metal and magnetic transitions.

We investigate the spin $S=1/2$ Heisenberg model on the body centered cubic lattice in the presence of ferromagnetic and antiferromagnetic nearest-neighbor $J_1$, second-neighbor $J_2$, and third-neighbor $J_3$ exchange interactions. The classical ground state phase diagram obtained by a Luttinger-Tisza analysis is shown to host six different (noncollinear) helimagnetic orders in addition to ferromagnetic, Néel, stripe, and planar antiferromagnetic orders. Employing the pseudofermion functional renormalization group (PFFRG) method for quantum spins ($S=1/2$) we find an extended nonmagnetic region, and significant shifts to the classical phase boundaries and helimagnetic pitch vectors caused by quantum fluctuations, while no new long-range dipolar magnetic orders are stabilized. The nonmagnetic phase is found to disappear for $S=1$. We calculate the magnetic ordering temperatures from PFFRG and quantum Monte Carlo methods, and make comparisons to available data.

Understanding the nature and behavior of excitations in quantum spin liquids, and in topological phases of matter in general, is of fundamental importance and has proven crucial for experimental detection and characterization of candidate materials. Current theoretical and numerical techniques, however, have limited capabilities, especially when it comes to studying gapped excitations. Here, we propose a semiclassical numerical method to study systems whose spin liquid behavior is underpinned by perturbative ring-exchange Hamiltonians. Our method can readily access both thermodynamic and spectral properties. We focus in particular on quantum spin ice and its photon and vison excitations. After benchmarking the method against existing results on photons, we use it to characterize visons and their thermodynamic behavior, which remained hitherto largely unexplored. We find that visons, in contrast to spinons in classical spin ice, form a weak electrolyte: Vison pairs are the dominant population at low temperatures. This is reflected in the behavior of thermodynamic quantities, such as pinch point motifs in the relevant correlators. Visons also appear to strongly hybridize with the photon background, a phenomenon that affects the way these quasiparticles may show up in inelastic response measurements. Our results demonstrate that the method, and generalizations thereof, can substantially help our understanding of quasiparticles and their interplay in quantum spin ice and other quantum spin liquids, quantum dimer models, and lattice gauge theories in general.

The out-of-time-ordered correlator has been proposed as an indicator of chaos in quantum systems due to its simple interpretation in the semiclassical limit. In particular, its rate of possible exponential growth at $\hslash \to 0$ is closely related to the classical Lyapunov exponent. Here we explore how this approach to quantum chaos relates to the random-matrix theoretical description. To do so, we introduce and study the level statistics of the logarithm of the out-of-time-ordered operator, $\widehat{\mathrm{\Lambda }}\left(t\right)=ln\left(-{\left[\widehat{x}\left(t\right),{\widehat{p}}_x\left(0\right)\right]}^2\right)/\left(2t\right)$, that we dub the “Lyapunovian” or “Lyapunov operator” for brevity. The Lyapunovian's level statistics is calculated explicitly for the quantum stadium billiard. It is shown that in the bulk of the filtered spectrum, this statistics perfectly aligns with the Wigner-Dyson distribution. One of the advantages of looking at the spectral statistics of this operator is that it has a well-defined semiclassical limit where it reduces to the matrix of uncorrelated classical finite-time Lyapunov exponents in a partitioned phase space. We provide a heuristic picture interpolating these two limits using Moyal quantum mechanics. Our results show that the Lyapunov operator may serve as a useful tool to characterize quantum chaos and in particular quantum-to-classical correspondence in chaotic systems by connecting the semiclassical Lyapunov growth at early times, when the quantum effects are weak, to universal level repulsion that hinges on strong quantum interference effects.

Bosonic condensates of exciton polaritons (light-matter quasiparticles in a semiconductor) provide a solid-state platform for studies of nonequilibrium quantum systems with a spontaneous macroscopic coherence. These driven, dissipative condensates typically coexist and interact with an incoherent reservoir, which undermines measurements of key parameters of the condensate. Here, we overcome this limitation by creating a high-density exciton-polariton condensate in an optically induced box trap. In this so-called Thomas-Fermi regime, the condensate is fully separated from the reservoir and its behavior is dominated by interparticle interactions. We use this regime to directly measure the polariton-polariton interaction strength, and reduce the existing uncertainty in its value from four orders of magnitude to within three times the theoretical prediction. The Thomas-Fermi regime has previously been demonstrated only in ultracold atomic gases in thermal equilibrium. In a nonequilibrium exciton-polariton system, this regime offers a novel opportunity to study interaction-driven effects unmasked by an incoherent reservoir.

Fractons are particles that cannot move in one or more directions without paying energy proportional to their displacement. Here we introduce the concept of symmetry-enforced fractonicity, in which particles are fractons in the presence of a global symmetry, but are free to move in its absence. A simple example is dislocation defects in a two-dimensional crystal, which are restricted to move only along their Burgers vector due to particle number conservation. Utilizing a recently developed dual rank-2 tensor gauge description of elasticity, we show that accounting for the symmetry-enforced one-dimensional nature of dislocation motion dramatically alters the structure of quantum crystal melting phase transitions. We show that, at zero temperature, sufficiently strong quantum fluctuations of the crystal lattice favor the formation of a supersolid phase that spontaneously breaks the symmetry enforcing fractonicity of defects. The defects can then condense to drive the crystal into a supernematic phase via a phase transition in the $(2+1)$-dimensional XY universality class to drive a melting phase transition of the crystal to a nematic phase. This scenario contrasts the standard Halperin-Nelson scenario for thermal melting of two-dimensional solids in which dislocations can proliferate via a single continuous thermal phase transition. We comment on the application of these results to other scenarios such as vortex lattice melting at a magnetic field induced superconductor-insulator transition, and quantum melting of charge-density waves of stripes in a metal.

Here we report measurements of the electron-boson coupling in single-layer FeSe films grown on ${\mathrm{SrTiO}}_3$ by means of inelastic electron scattering using two complementary spectroscopic techniques. Scanning tunneling spectroscopy shows that the excitation spectrum becomes fully gapped below $T_c$ whereas significant electron-phonon coupling is limited to spatially confined regions. Further, high-resolution electron energy loss spectroscopy shows neither strong nor $k$-dependent electron-phonon coupling. Our results strongly support a predominantly electronic pairing mechanism.

Ultrafast relaxation dynamics of hot electrons with excess energies exceeding 1 eV in Si is studied using time-resolved photoemission spectroscopy and ab initio calculations. Experimentally, the photoemission peaks from hot electrons excited in bulk electronic states along the $\mathrm{\Gamma }-L$ and $\mathrm{\Gamma }-X$ directions with excess energy ($E_{\mathrm{ex}}$) 1.1–3.2 eV with respect to the conduction band minimum are identified, and the time constants that characterize the decay of transient populations are determined. The decay time, which is $30\pm 3\mathrm{fs}$ at $E_{\mathrm{ex}}=3.0\mathrm{eV}$ and increases to $115\pm 5\mathrm{fs}$ at $E_{\mathrm{ex}}=1.1\mathrm{eV}$, has the same scaling with $E_{\mathrm{ex}}$ irrespective of the location of hot electrons in the Brillouin zone. The calculations show that the momentum scattering time due to electron-phonon coupling is shorter than 10 fs for $E_{\mathrm{ex}}$ larger than 1.5 eV, being too short to be measured. The combination of theoretical and experimental results reveals that hot electrons with high excess energy in Si are transformed into hot-electron ensembles quasiequilibrated only in momentum space by the ultrafast momentum scattering, and that the experimentally determined time constant of population decay corresponds to the energy relaxation taking place as a whole on a time scale ten times longer than that of the momentum relaxation. The detailed methodology of the analysis of experimental data which we provide in this work, as well as our conclusions which concern the relaxation dynamics of electrons with $E_{\mathrm{ex}}$ exceeding 1 eV in Si, can be applied to interpret hot-carrier relaxation phenomena in a wide range of semiconducting materials.

Scanning tunneling spectroscopy requires the application of a potential difference between the sample and a tip. In metal-vacuum-metal junctions, one can safely assume that the potential is constant along the metallic substrate. Here, we show that the inhomogeneous shape of the electric potential has to be taken into account when probing spatially extended molecules on a decoupling layer. To this end, oligothiophene-based molecules were deposited on a monolayer of molybdenum disulfide (${\mathrm{MoS}}_2$) on a Au(111) surface. By probing the delocalized molecular orbital along the thiophene backbone, we found an apparent intramolecular shift of the positive ion resonance, which can be ascribed to a perturbation potential caused by the tip. Using a simple model for the electrostatic landscape, we show that such a perturbation is caused by the inhomogeneity of the applied bias potential in the junction and may be further modified by an electric dipole of a functionalized tip. The two effects can be disentangled in tunneling spectra by probing the apparent energy shift of vibronic resonances along the molecular backbone. We suggest that extended molecules on ${\mathrm{MoS}}_2$ can be used as a sensor for the shape of the electrostatic potential of arbitrary tips.

Spin excitations of magnetoelectric ${\mathrm{LiNiPO}}_4$ are studied by infrared absorption spectroscopy in the THz spectral range as a function of magnetic field through various commensurate and incommensurate magnetically ordered phases up to 33 T. Six spin resonances and a strong two-magnon continuum are observed in zero magnetic field. Our systematic polarization study reveals that some of the excitations are usual magnetic-dipole active magnon modes, while others are either electromagnons, being only electric-dipole active, or magnetoelectric, that is both electric- and magnetic-dipole active spin excitations. Field-induced shifts of the modes for all three orientations of the field along the orthorhombic axes allow us to refine the values of the relevant exchange couplings, single-ion anisotropies, and the Dzyaloshinskii-Moriya interaction on the level of a four-sublattice mean-field spin model. This model also reproduces the spectral shape of the two-magnon absorption continuum, found to be electric-dipole active in the experiment.

We report pair distribution function measurements of the iron-based superconductor FeSe above and below the structural transition temperature. Structural analysis reveals a local orthorhombic distortion with a correlation length of about 4 nm at temperatures where an average tetragonal symmetry is observed. The analysis further demonstrates that the local distortion is larger than the global distortion at temperatures where the average observed symmetry is orthorhombic. Our results suggest that the low-temperature macroscopic nematic state in FeSe forms from an imperfect ordering of orbital-degeneracy-lifted nematic fluctuations which persist up to at least 300 K.

Fractional quantum Hall states at half-integer filling factors have been observed in many systems beyond the $\frac{5}{2}$ and $\frac{7}{2}$ plateaus in GaAs quantum wells. This includes bilayer states in GaAs, several half-integer plateaus in ZnO-based heterostructures, and quantum Hall liquids in graphene. In all cases, Cooper pairing of composite fermions is believed to explain the plateaus. The nature of Cooper pairing and the topological order on those plateaus are hotly debated. Different orders are believed to be present in different systems. This makes it important to understand experimental signatures of all proposed orders. We review the expected experimental signatures for all possible composite-fermion states at half-integer filling. We address Mach-Zehnder interferometry, thermal transport, tunneling experiments, and Fabry-Pérot interferometry. For this end, we introduce a uniform description of the topological orders of Kitaev's sixteenfold way in terms of their wave functions, effective Hamiltonians, and edge theories.

Graphene charge carriers behave as relativistic massless fermions, thereby exhibiting a variety of counterintuitive behaviors. In particular, at p-n junctions, they behave as photons encountering a negative index media, therefore experiencing a peculiar refraction known as Veselago lensing. However, the way Dirac fermions flow through a Veselago lens remains largely unexplored experimentally. Here, an approach to create a movable and tunable circular p-n junction in graphene is proposed, using the polarized tip of a scanning gate microscope. Scanning the tip in the vicinity of a graphene constriction while recording the device conductance yields images related to the electron flow through a circular Veselago lens, revealing a high current density in the lens core, as well as two low current density zones along the transport axis. Tight-binding simulations reveal the crucial role of the p-n junction smoothness on these phenomena. The present research adds dimensions in the control and understanding of Dirac fermions optical elements, a prerequisite to engineer relativistic electron optics devices.

The zero-temperature phase diagram of the spin-$\frac{1}{2}{J}_1\text{−}{J}_2\text{−}{J}_1^{\perp }$ model on an $AA$-stacked square-lattice bilayer is studied using the coupled cluster method implemented to very high orders. Both nearest-neighbor (NN) and frustrating next-nearest-neighbor Heisenberg exchange interactions, of strengths $J_1>0$ and $J_2\equiv \kappa J_1>0$, respectively, are included in each layer. The two layers are coupled via a NN interlayer Heisenberg exchange interaction with a strength $J_1^{\perp }\equiv \delta J_1$. The magnetic order parameter $M$ (viz., the sublattice magnetization) is calculated directly in the thermodynamic (infinite-lattice) limit for the two cases when both layers have antiferromagnetic ordering of either the Néel or the striped kind, and with the layers coupled so that NN spins between them are either parallel (when $\delta <0$) or antiparallel (when $\delta >0$) to one another. Calculations are performed at $n\mathrm{th}$ order in a well-defined sequence of approximations, which exactly preserve both the Goldstone linked-cluster theorem and the Hellmann-Feynman theorem, with $n\le 10$. The sole approximation made is to extrapolate such sequences of $n\mathrm{th}$-order results for $M$ to the exact limit $n\to \infty$. By thus locating the points where $M$ vanishes, we calculate the full phase boundaries of the two collinear AFM phases in the $\kappa \text{−}\delta$ half-plane with $\kappa >0$. In particular, we provide the accurate estimate ($\kappa \approx 0.547,\delta \approx -0.45$) for the position of the quantum triple point (QTP) in the region $\delta <0$. We also show that there is no counterpart of such a QTP in the region $\delta >0$, where the two quasiclassical phase boundaries show instead an “avoided crossing” behavior, such that the entire region that contains the nonclassical paramagnetic phases is singly connected.