We develop a theory for the pseudorelativistic fractional quantum Hall effect in graphene, which is based on a multicomponent Abelian Chern-Simons theory in the fermionic functional integral approach. Calculations are performed in the Keldysh formalism, directly giving access to real-time correlation functions at finite temperature. We obtain an exact effective action for the Chern-Simons gauge fields, which is expanded to second order in the gauge field fluctuations around the mean-field solution. The one-loop fermionic polarization tensor as well as the electromagnetic response tensor in random phase approximation are derived, from which we obtain the Hall conductivities for various FQH states, lying symmetrically around charge neutrality.

The interplay between the Kondo effect, indirect magnetic interaction, and geometrical frustration is studied in the Kondo lattice on the one-dimensional zigzag ladder. Using the density-matrix renormalization group, the ground-state and various short- and long-range spin- and density-correlation functions are calculated for the model at half filling as a function of the antiferromagnetic Kondo interaction down to $J=0.3t$, where $t$ is the nearest-neighbor hopping on the zigzag ladder. Geometrical frustration is shown to lead to at least two critical points: Starting from the strong-$J$ limit, where almost local Kondo screening dominates and where the system is a nonmagnetic Kondo insulator, antiferromagnetic correlations between nearest-neighbor and next-nearest-neighbor local spins become stronger and stronger, until at $J_{\mathrm{c}}^{\dim }\approx 0.89t$ frustration is alleviated by a spontaneous breaking of translational symmetry and a corresponding transition to a dimerized state. This is characterized by antiferromagnetic correlations along the legs and by alternating antiferro- and ferromagnetic correlations on the rungs of the ladder. A mechanism of partial Kondo screening that has been suggested for the Kondo lattice on the two-dimensional triangular lattice is not realized in the one-dimensional case. Furthermore, within the symmetry-broken dimerized state, there is a magnetic transition to a ${90}^{\circ }$ quantum spin spiral with quasi-long-range order at $J_{\mathrm{c}}^{\mathrm{mag}}\approx 0.84t$. The quantum-critical point is characterized by a closure of the spin gap (with decreasing $J$) and a divergence of the spin-correlation length and of the spin-structure factor $S\left(q\right)$ at wave vector $q=\pi /2$. This is opposed to the model on the one-dimensional bipartite chain, which is known to have a finite spin gap for all $J>0$ at half filling.

We theoretically study the three-dimensional topological semimetals with nodal surfaces protected by crystalline symmetries. Different from the well-known nodal-point and nodal-line semimetals, in these materials, the conduction and valence bands cross on closed nodal surfaces in the Brillouin zone. We propose different classes of nodal surfaces, both in the absence and in the presence of spin-orbit coupling (SOC). In the absence of SOC, a class of nodal surfaces can be protected by space-time inversion symmetry and sublattice symmetry and characterized by a ${\mathbb{Z}}_2$ index, while another class of nodal surfaces are guaranteed by a combination of nonsymmorphic twofold screw-rotational symmetry and time-reversal symmetry. We show that the inclusion of SOC will destroy the former class of nodal surfaces but may preserve the latter provided that the inversion symmetry is broken. We further generalize the result to magnetically ordered systems and show that protected nodal surfaces can also exist in magnetic materials without and with SOC, given that certain magnetic group symmetry requirements are satisfied. Several concrete nodal-surface material examples are predicted via the first-principles calculations. The possibility of multi-nodal-surface materials is discussed.

We theoretically investigate topological properties of the one-dimensional superlattice anyon-Hubbard model, which can be mapped to a superlattice bose-Hubbard model with an occupation-dependent phase factor by fractional Jordan-Wigner transformation. The topological anyon-Mott insulator is identified by topological invariant and edge modes using exact diagonalization and the density matrix renormalization group algorithm. When only the statistical angle is varied and all other parameters are fixed, a statistically induced topological phase transition can be realized, which provides insights into the topological phase transitions. What's more, we give an explanation of the statistically induced topological phase transition. The topological anyon-Mott phases can also appear in a variety of superlattice anyon-Hubbard models.

The dynamical Jahn-Teller effect of ${\mathrm{C}}_{60}^{n-}$ anions ($n=1$–5) is studied using the numerical diagonalization of the linear $p^n\otimes 8d$ Jahn-Teller Hamiltonian with the currently established coupling parameters. It is found that in all anions the Jahn-Teller effect stabilizes the low-spin states, resulting in the violation of Hund's rule. The energy gain due to the Jahn-Teller dynamics is found to be comparable to the static Jahn-Teller stabilization. The Jahn-Teller dynamics influences the thermodynamic properties via strong variation of the density of vibronic states with energy. Thus the large vibronic entropy in the low-spin states enhances the effective spin gap of ${\mathrm{C}}_{60}^{3-}$ quenching the spin crossover. From the calculations of the effective spin gap as a function of the Hund's rule coupling, we found that the latter should amount $40\pm 5$ meV in order to cope with the violation of Hund's rule and to reproduce the large spin gap. With the obtained numerical solutions, the matrix elements of electronic operators for the low-lying vibronic levels and the vibronic reduction factors are calculated for all anions.

The complete set of Maxwell's and hydrodynamic equations for the chiral electrons in Weyl semimetals is presented. The formulation of the Euler equation takes into account the explicit breaking of the Galilean invariance by the ion lattice. It is shown that the Chern-Simons (or Bardeen-Zumino) contributions should be added to the electric current and charge densities in Maxwell's equations that provide the information on the separation of Weyl nodes in energy and momentum. On the other hand, these topological contributions do not directly affect the Euler equation and the energy conservation relation for the electron fluid. By making use of the proposed consistent hydrodynamic framework, we show that the Chern-Simons contributions strongly modify the dispersion relations of collective modes in Weyl semimetals. This is reflected, in particular, in the existence of distinctive anomalous Hall waves, which are sustained by the local anomalous Hall currents.

We find a series of topological phase transitions of increasing order, beyond the more standard second-order phase transition in a one-dimensional topological superconductor. The jumps in the order of the transitions depend on the range of the pairing interaction, which is parametrized by an algebraic decay with exponent $\alpha$. Remarkably, in the limit $\alpha =1$ the order of the topological transition becomes infinite. We compute the critical exponents for the series of higher-order transitions in exact form and find that they fulfill the hyperscaling relation. We also study the critical behavior at the boundary of the system and discuss potential experimental platforms of magnetic atoms in superconductors.

Optical manipulation of charge on the nanoscale is of fundamental importance to an array of proposed technologies from selective photocatalysis to nanophotonics. Open plasmonic systems where collective electron oscillations release energy and charge to their environments offer a potential means to this end as plasmons can rapidly decay into energetic electron-hole pairs; however, isolating this decay from other plasmon-environment interactions remains a challenge. Here we present an analytic theory of noble-metal nanoparticles that quantitatively models plasmon decay into electron-hole pairs, demonstrates that this decay depends significantly on the nanoparticle's dielectric environment, and disentangles this effect from competing decay pathways. Using our approach to incorporate embedding material and substrate effects on plasmon-electron interaction, we show that predictions from the model agree with four separate experiments. Finally, examination of coupled nanoparticle-emitter systems further shows that the hybridized in-phase mode more efficiently decays to photons whereas the out-of-phase mode more efficiently decays to electron-hole pairs, offering a strategy to tailor open plasmonic systems for charge manipulation.

A bosonic topological transition (BTT) is a quantum critical point between the bosonic symmetry-protected topological phase and the trivial phase. In this work, we investigate such a transition in a (2+1)-dimensional lattice model with the maximal microscopic symmetry: an internal $\mathrm{SO}\left(4\right)$ symmetry. We derive a description for this transition in terms of compact quantum electrodynamics (QED) with four fermion flavors ($N_f=4$). Within a systematic renormalization group analysis, we identify the critical point with the desired $\mathrm{O}\left(4\right)$ emergent symmetry and all expected deformations. By lowering the microscopic symmetry, we recover the previous $N_f=2$ noncompact QED description of the BTT. Finally, by merging two BTTs we recover a previously discussed theory of symmetric mass generation, as an $\mathrm{SU}\left(2\right)$ quantum chromodynamics-Higgs theory with $N_f=4$ flavors of $\mathrm{SU}\left(2\right)$ fundamental fermions and one $\mathrm{SU}\left(2\right)$ fundamental Higgs boson. This provides a consistency check on both theories.

We investigate the effect of long-range Coulomb interaction on the quasiparticle properties and the dielectric function of clean three-dimensional Weyl semimetals at zero temperature using a functional renormalization group (FRG) approach. The Coulomb interaction is represented via a bosonic Hubbard-Stratonovich field which couples to the fermionic density. We derive truncated FRG flow equations for the fermionic and bosonic self-energies and for the three-legged vertices with two fermionic and one bosonic external legs. We consider two different cutoff schemes—cutoff in fermionic or bosonic propagators—in order to calculate the renormalized quasiparticle velocity and the dielectric function for an arbitrary number of Weyl nodes and the interaction strength. If we approximate the dielectric function by its static limit, our results for the velocity and the dielectric function are in good agreement with that of A. A. Abrikosov and S. D. Beneslavskiĭ [Sov. Phys. JETP 32, 699 (1971)] exhibiting slowly varying logarithmic momentum dependence for small momenta. We extend their result for an arbitrary number of Weyl nodes and finite frequency by evaluating the renormalized velocity in the presence of dynamic screening and calculate the wave function renormalization.

Recent years have seen the development of two types of nonlocal extensions to the single-site dynamical mean field theory. On one hand, cluster approximations, such as the dynamical cluster approximation, recover short-range momentum-dependent correlations nonperturbatively. On the other hand, diagrammatic extensions, such as the dual-fermion theory, recover long-ranged corrections perturbatively. The correct treatment of both strong short-ranged and weak long-ranged correlations within the same framework is therefore expected to lead to a quick convergence of results, and offers the potential of obtaining smooth self-energies in nonperturbative regimes of phase space. In this paper, we present an exact cluster dual-fermion method based on an expansion around the dynamical cluster approximation. Unlike previous formulations, our method does not employ a coarse-graining approximation to the interaction, which we show to be the leading source of error at high temperature, and converges to the exact result independently of the size of the underlying cluster. We illustrate the power of the method with results for the second-order cluster dual-fermion approximation to the single-particle self-energies and double occupancies.

Time-periodically driven systems are a versatile toolbox for realizing interesting effective Hamiltonians. Heating, caused by excitations to high-energy states, is a challenge for experiments. While most setups so far address the relatively weakly interacting regime, it is of general interest to study heating in strongly correlated systems. Using Floquet dynamical mean-field theory, we study nonequilibrium steady states (NESS) in the Falicov-Kimball model, with time-periodically driven kinetic energy or interaction. We systematically investigate the nonequilibrium properties of the NESS. For a driven kinetic energy, we show that resonant tunneling, where the interaction is an integer multiple of the driving frequency, plays an important role in the heating. In the strongly correlated regime, we show that this can be well understood using Fermi's golden rule and the Schrieffer-Wolff transformation for a time-periodically driven system. We furthermore demonstrate that resonant tunneling can be used to control the population of Floquet states to achieve “photodoping.” For driven interactions introduced by an oscillating magnetic field near a widely adopted Feshbach resonance, we find that the double occupancy is strongly modulated. Our calculations apply to shaken ultracold-atom systems and to solid-state systems in a spatially uniform but time-dependent electric field. They are also closely related to lattice modulation spectroscopy. Our calculations are helpful to understand the latest experiments on strongly correlated Floquet systems.

We numerically investigate the link between the delocalization-localization transition and entanglement in a disordered long-range hopping model of spinless fermions by studying various static and dynamical quantities. This includes the inverse participation ratio, level statistics, entanglement entropy, and number fluctuations in the subsystem along with quench and wave-packet dynamics. Finite systems show delocalized, quasilocalized, and localized phases. The delocalized phase shows strong area-law violation, whereas the (quasi)localized phase adheres to (for large subsystems) the strict area law. The idea of “entanglement contour” nicely explains the violation of area law and its relationship with “fluctuation contour” reveals a signature at the transition point. The relationship between entanglement entropy and number fluctuations in the subsystem also carries signatures for the transition in the model. Results from the Aubry-Andre-Harper model are compared in this context. The propagation of charge and entanglement are contrasted by studying quench and wave-packet dynamics at the single-particle and many-particle levels.

The nonequilibrium boron nitride (BN) phase of zinc oxide (ZnO) has been reported for thin films and nanostructures, however, its properties are not well understood due to a persistent controversy that prevents reconciling experimental and first-principles results for its atomic coordinates. We use first-principles theoretical spectroscopy to accurately compute electronic and optical properties, including single-quasiparticle and excitonic effects: Band structures and densities of states are computed using density functional theory, hybrid functionals, and the $GW$ approximation. Accurate optical absorption spectra and exciton binding energies are computed by solving the Bethe-Salpeter equation for the optical polarization function. Using this data we show that the band-gap difference between BN-ZnO and wurtzite (WZ) ZnO agrees very well with experiment when the theoretical lattice geometry is used, but significantly disagrees for the experimental atomic coordinates. We also show that the optical anisotropy of BN-ZnO differs significantly from that of WZ-ZnO, allowing us to optically distinguish both polymorphs. By using the transfer-matrix method to solve Maxwell's equations for thin films composed of both polymorphs, we illustrate that this opens up a promising route for tuning optical properties.

Laser-based angle-resolved photoelectron spectroscopy is performed on tin-phthalocyanine (SnPc) adsorbed on silver Ag(111). Upon adsorption of SnPc, strongly dispersing bands are observed which are identified as secondary Mahan cones formed by surface umklapp processes acting on photoelectrons from the silver substrate as they transit through the ordered adsorbate layer. We show that the photoemission data carry quantitative structural information on the adsorbate layer similar to what can be obtained from a conventional low-energy electron diffraction (LEED) study. More specifically, we compare photoemission data and LEED data probing an incommensurate-to-commensurate structural phase transition of the adsorbate layer. Based on our results we propose that Mahan-cone spectroscopy operated in a pump-probe configuration can be used in the future to probe structural dynamics at surfaces with a temporal resolution in the sub-100-fs regime.

Laser-heated diamond-anvil cell (LHDAC) experiments reveal electronic changes in KBr at pressures between $\sim 13–81\mathrm{GPa}$ when heated to high temperatures that cause runaway heating to temperatures in excess of $\sim 5000\mathrm{K}$. The drastic changes in absorption behavior of KBr are interpreted as rapid formation of high-pressure F-center defects. The defects are localized to the heated region and thus do not change the long-range crystalline order of KBr. The results have significant consequences for temperature measurements in LHDAC experiments and extend the persistence of F centers in alkali halides to at least 81 GPa.

We report the results of a high-resolution laser-spectroscopy study of dysprosium atoms injected into superfluid ${}^4\mathrm{He}$. A special attention is paid to the transitions between the inner $4f$ and $5d$ electronic shells of Dy. The characteristic gap is observed between the zero-phonon line and the phonon wing in the experimental excitation spectrum that arises due to the peculiar structure of the phonon-roton spectrum of superfluid He. This observation resolves the longstanding discrepancy between the studies of bulk superfluid He and He nanodroplets.

We prepared two superconducting phases, which are called ‘‘low-$T_{\mathrm{c}}$ phase’’ and ‘‘high-$T_{\mathrm{c}}$ phase’’ of ${\left(\mathrm{N}{\mathrm{H}}_3\right)}_y\mathrm{N}{\mathrm{a}}_x\mathrm{FeSe}$ showing $T_{\mathrm{c}}$’s of 35 and 44 K, respectively, at ambient pressure, and studied the superconducting behavior and structure of each phase under pressure. The $T_{\mathrm{c}}$ of the 35 K at ambient pressure rapidly decreases with increasing pressure up to 10 GPa, and it remains unchanged up to 22 GPa. Finally, superconductivity was not observed down to 1.4 K at 29 GPa, i.e., $T_{\mathrm{c}}<1.4\mathrm{K}$. The $T_{\mathrm{c}}$ of the 44 K phase also shows a monotonic decrease up to 15 GPa and it weakly decreases up to 25 GPa. These behaviors suggest no pressure-driven high-$T_{\mathrm{c}}$ phase (called ‘‘SC-II’’) between 0 and 25 GPa for the low-$T_{\mathrm{c}}$ and high-$T_{\mathrm{c}}$ phases of ${\left(\mathrm{N}{\mathrm{H}}_3\right)}_y\mathrm{N}{\mathrm{a}}_x\mathrm{FeSe}$, differing from the behavior of ${\left(\mathrm{N}{\mathrm{H}}_3\right)}_y\mathrm{C}{\mathrm{s}}_x\mathrm{FeSe}$, which has a pressure-driven high-$T_{\mathrm{c}}$ phase (SC-II) in addition to the superconducting phase (SC-I) observed at ambient and low pressures. The $T_{\mathrm{c}}-c$ phase diagram for both low-$T_{\mathrm{c}}$ and high-$T_{\mathrm{c}}$ phases shows that the $T_{\mathrm{c}}$ can be linearly scaled with $c$ (or FeSe plane spacing), where $c$ is a lattice constant. The reason why a pressure-driven high-$T_{\mathrm{c}}$ phase (SC-II) was found for neither low-$T_{\mathrm{c}}$ nor high-$T_{\mathrm{c}}$ phases of ${\left(\mathrm{N}{\mathrm{H}}_3\right)}_y\mathrm{N}{\mathrm{a}}_x\mathrm{FeSe}$ is fully discussed, suggesting a critical $c$ value as the key to forming the pressure-driven high-$T_{\mathrm{c}}$ phase (SC-II). Finally, the precise $T_{\mathrm{c}}-c$ phase diagram is depicted using the data obtained thus far from FeSe codoped with a metal and $\mathrm{N}{\mathrm{H}}_3$ or amine, indicating two distinct $T_{\mathrm{c}}-c$ lines below $c=17.5\AA$.

We image simultaneously the geometric, the electronic, and the magnetic structures of a buckled iron bilayer film that exhibits chiral magnetic order. We achieve this by combining spin-polarized scanning tunneling microscopy and magnetic exchange force microscopy (SPEX) to independently characterize the geometric as well as the electronic and magnetic structures of nonflat surfaces. This new SPEX imaging technique reveals the geometric height corrugation of the reconstruction lines resulting from strong strain relaxation in the bilayer, enabling the decomposition of the real-space from the electronic structure at the atomic level and the correlation with the resultant spin-spiral ground state. By additionally utilizing adatom manipulation, we reveal the chiral magnetic ground state of portions of the unit cell that were not previously imaged with spin-polarized scanning tunneling microscopy alone. Using density functional theory, we investigate the structural and electronic properties of the reconstructed bilayer and identify the favorable stoichiometry regime in agreement with our experimental result.