The realization of equilibrium superradiant quantum phases (photon condensates) in a spatially uniform quantum cavity field is forbidden by a “no-go” theorem stemming from gauge invariance. We here show that the no-go theorem does not apply to spatially varying quantum cavity fields. We find a criterion for its occurrence that depends solely on the static, nonlocal orbital magnetic susceptibility ${\chi }_{\mathrm{orb}}\left(q\right)$, of the electronic system (ES) evaluated at a cavity photon momentum $\hslash q$. Only 3DESs satisfying the Condon inequality ${\chi }_{\mathrm{orb}}\left(q\right)>1/\left(4\pi \right)$ can harbor photon condensation. For the experimentally relevant case of two-dimensional (2D) ESs embedded in quasi-2D cavities the criterion again involves ${\chi }_{\mathrm{orb}}\left(q\right)$ but also the vertical size of the cavity. We use these considerations to identify electronic properties that are ideal for photon condensation. Our theory is nonperturbative in the strength of electron-electron interaction and therefore applicable to strongly correlated ESs.

Electron-electron $\left(e\text{−}e\right)$ interactions in the twisted bilayer graphene (TBG) near the magic angle ∼1.1° can lift the valley degeneracy, allowing for the realization of orbital magnetism and topological phases. However, direct measurement of the orbital-based magnetism in the TBG is still lacking up to now. Here we report evidence for orbital magnetic moment generated by the moiré-scale current loops in a TBG with a twist angle $\theta \sim 1.{68}^{\circ }$. The valley degeneracy of the 1.68° TBG is removed by $e\text{−}e$ interactions when its low-energy Van Hove singularity (VHS) is nearly half filled. A large and linear response of the valley splitting to magnetic fields is observed, which we interpret as arising from the coupling to the large orbital magnetic moment induced by chiral current loops circulating in the moiré pattern. According to our experiment, the orbital magnetic moment is about $10.7{\mu }_{\mathrm{B}}$ per moiré supercell. Our result paves the way to explore magnetism that is purely orbital in a slightly twisted graphene system.

We investigate topological properties and classification of mean-field theories of stable bosonic systems. Of the three standard classifying symmetries, only time reversal represents a real symmetry of the many-boson system, while the other two, particle-hole and chiral, are simply constraints that manifest as symmetries of the effective single-particle problem. For gapped systems in arbitrary space dimension, we establish three fundamental no-go theorems that prove the absence of parity switches, symmetry-protected-topological quantum phases, and localized bosonic zero modes under open boundary conditions. We then introduce a squaring, kernel-preserving map connecting noninteracting Hermitian theories of fermions and stable boson systems, which serves as a playground to reveal the role of topology in bosonic phases and their localized midgap boundary modes. Finally, we determine the symmetry classes inherited from the fermionic tenfold-way classification, unveiling an elegant threefold-way topological classification of noninteracting bosons. We illustrate our main findings in one- and two-dimensional bosonic lattice and field-theory models.

Recently, the theory of quantized dipole polarization has been extended to account for electric multipole moments, giving rise to the discovery of multipole topological insulators (TIs). Both two-dimensional quadrupole and three-dimensional (3D) octupole TIs with robust zero-dimensional corner states have been realized in various classical systems. However, due to the intrinsic 3D limitation, the higher-dimensional multipole TIs, such as four-dimensional (4D) hexadecapole TIs, are supposed to be extremely hard to construct in real space. Here, we theoretically propose and experimentally demonstrate the realization of a classical analog of 4D hexadecapole TI based on the electric circuits in fully real space. The explicit construction of 4D hexadecapole circuits, where the connection of nodes is allowed in any desired way free from constraints of locality and dimensionality, is provided. By direct circuit simulations and impedance measurements, the in-gap corner states protected by the quantized hexadecapole moment in the 4D circuit lattices are observed and the robustness of the corner state is also demonstrated. Our work offers a pathway to study the higher-order/dimensional topological physics in real space.

We report on the direct observation of electron transfer between the surface and the second layer of the prototypical transition-metal dichalcogenide $2\mathrm{H}\text{−}\mathrm{Mo}{\mathrm{S}}_2$. We are able to disentangle the excitation and the transfer process in our measurement. Thereby, we determine both the momentum location and the duration of the electron transfer between the first two layers. Our $GW$-based tight-binding calculations reveal that the band gap in the surface layer is considerably larger than in deeper layers and that the coupling between surface and deeper layers is strongly momentum-dependent throughout the Brillouin zone. At the conduction-band minimum $\overline{\mathrm{\Sigma }}$ we find strong coupling, which explains the ultrafast interlayer charge transfer observed in our experiment at this location.

We use tools from integrability and generalized hydrodynamics to study finite-temperature dynamics in the one-dimensional Hubbard model. First, we examine charge, spin, and energy transport away from half-filling and zero magnetization, focusing on the strong coupling regime where we identify a rich interplay of temperature and energy scales, with crossovers between distinct dynamical regimes. We identify an intermediate-temperature regime analogous to the spin-incoherent Luttinger liquid, where spin degrees of freedom are hot but charge degrees of freedom are at low temperature. We demonstrate that the spin Drude weight exhibits sharp features at the crossover between this regime and the low-temperature Luttinger liquid regime, which are absent in the charge and energy response, and rationalize this behavior in terms of the properties of Bethe ansatz quasiparticles. We then turn to the dynamics along special lines in the phase diagram corresponding to half-filling and/or zero magnetization where on general grounds we anticipate that the transport is subballistic but superdiffusive. We provide analytical and numerical evidence for Kardar-Parisi-Zhang (KPZ) dynamical scaling (with length and time scales related via $x\sim t^{2/3}$) along both lines and at the $\mathrm{SO}\left(4\right)$-symmetric point where they intersect. Our results suggest that both spin-coherence crossovers and KPZ scaling may be accessed in near-term experiments with optical lattice Hubbard emulators.

We investigate the correlations of magnons inside a nanomagnet and identify an unconventional phase so-called magnon antibunching, i.e., where there is a large probability for occupation of the single-magnon state. This antibunched state is very different from magnons at thermal equilibrium and microwave-driven coherent magnons. We further obtain the steady state analytically and describe the magnon dynamics numerically, and ascertain the stability of such antibunched magnons over a large window of magnetic anisotropy, damping, and temperature. This means that the antibunched magnon state is feasible in a wide class of low-damping magnetic nanoparticles. To detect this quantum effect, we propose to transfer the quantum information of magnons to photons by magnon-photon coupling and then measure the correlations of photons to retrieve the magnon correlations. Our findings may provide a promising platform to study quantum-classical transitions and for designing a single magnon source.

Through in situ photoemission spectroscopy, we investigated the change in the electronic structures and V-V dimerization of dimensionality-controlled $\mathrm{V}{\mathrm{O}}_2$ films coherently grown on $\mathrm{Ti}{\mathrm{O}}_2\left(001\right)$ substrates. In the nanostructured films, the balance between the instabilities of a bandlike Peierls transition and a Mott transition is controlled as a function of thickness. The characteristic spectral change associated with temperature-driven metal-insulator transition in $\mathrm{V}{\mathrm{O}}_2$ thick films holds down to 1.5 nm (roughly corresponding to five V atoms along the [001] direction), whereas $\mathrm{V}{\mathrm{O}}_2$ films of less than 1.0 nm exhibit insulating nature without the V-V dimerization characteristic of $\mathrm{V}{\mathrm{O}}_2$. These results suggest that the delicate balance between a Mott instability and a bandlike Peierls instability is modulated at a scale of a few nanometers by the dimensional crossover effects and confinement effects, which consequently induce the complicated electronic phase diagram of ultrathin $\mathrm{V}{\mathrm{O}}_2$ films.

The fundamental building blocks in band theory are band representations—bands whose infinitely numbered Wannier functions are generated (by action of a space group) from a finite number of symmetric Wannier functions centered on a point in space. This paper aims to simplify questions on a multirank band representation by splitting it into unit-rank bands via the following crystallographic splitting theorem: Being a rank-$N$ band representation is equivalent to being splittable into a finite sum of bands indexed by $\{1,2,...,N\}$, such that each band is spanned by a single, analytic Bloch function of $\mathit{k}$, and any symmetry in the space group acts by permuting $\{1,2,...,N\}$. We prove this theorem for all band representations (of crystallographic space groups) whose Wannier functions transform in the integer-spin representation; in the half-integer-spin case, the only exceptions to the theorem exist for three-spatial-dimensional space groups with cubic point groups. Applying this theorem, we develop computationally efficient methods to determine whether a given energy band (of a tight-binding or Schrödinger-type Hamiltonian) is a band representation and, if so, how to numerically construct the corresponding symmetric Wannier functions. Thus we prove that rotation-symmetric topological insulators in Wigner-Dyson class AI are fragile, meaning that the obstruction to symmetric Wannier functions can be removed by addition of band representations to the filled-band subspace. An implication of fragility is that its boundary states, while robustly covering the bulk energy gap in finite-rank tight-binding models, can be destabilized if the Hilbert space is expanded to include all symmetry-allowed representations. These fragile insulators have photonic analogs that we identify; in particular, we prove that an existing photonic crystal built by Yihao Yang et al. [Nature 565, 622 (2019)] is fragile topological with removable boundary states, which disproves a widespread perception of “topologically protected” boundary states in time-reversal-invariant, gapped photonic/phononic crystals. As a final application of our theorem, we derive various symmetry obstructions on the Wannier functions of topological insulators; for certain space groups, these obstructions are proven to be equivalent to the nontrivial holonomy of Bloch functions.

The magnetoconductance of Bi films grown epitaxially on $\mathrm{Si}\left(111\right)$ for a film thickness between 10 and 100 bilayers (BL) was investigated at a temperature of $T=9\mathrm{K}$ in magnetic fields up to 4 T oriented perpendicular to the surface plane. The thickness dependence of magnetoconductance (MC) and Hall resistivity was investigated in order to derive thickness dependent charge carrier concentrations as well as their mobilities and to identify corrections by weak antilocalization (WAL) to magnetoconductance. While the electronic transport in ultrathin films up to 30 bilayers (BL) turned out to take place mainly within the surface states, contributions of (bulk derived) quantum well states mix in at larger thicknesses and dominate incoherent transport above 70 BL. On the contrary, for the WAL contribution at magnetic fields normal to the surface, scattering within the surface states dominates at all thicknesses, as evident from the gradual change from values of $\alpha =-0.35$ to $\alpha =-1$ as a function of thickness. This finding reflects the decrease of coupling between the two interfaces going from a single combined conduction channel to two independent channels at the highest film thickness. Quick changes of both parts of magnetoconductance as a function of film thickness at the thinnest films seem to be strain induced by the Bi/Si interface. These results will advance the understanding of the transport properties of Bi thin films and reveal exotic quantum phenomena.

Quantum-well states appear in metallic thin films due to the confinement of the wave function by the film interfaces. Using angle-resolved photoemission spectroscopy, we unexpectedly observe quantum-well states in fractured single crystals of ${\mathrm{CeCoIn}}_5$. We confirm that confinement occurs by showing that these states' binding energies are photon-energy independent and are well described with a phase accumulation model, commonly applied to quantum-well states in thin films. This indicates that atomically flat thin films can be formed by fracturing hard single crystals. For the two samples studied, our observations are explained by free-standing flakes with thicknesses of 206 and 101 Å. We extend our analysis to extract bulk properties of ${\mathrm{CeCoIn}}_5$. Specifically, we obtain the dispersion of a three-dimensional band near the zone center along in-plane and out-of-plane momenta. We establish part of its Fermi surface, which corresponds to a hole pocket centered at $\mathrm{\Gamma }$. We also reveal a change of its dispersion with temperature, a signature that may be caused by the Kondo hybridization.

Low-energy excitations associated with the amplitude fluctuation of an order parameter in condensed-matter systems can mimic the Higgs boson, an elementary particle in the standard model, and are dubbed as Higgs modes. Identifying the condensed-matter Higgs mode is challenging because it is known in many cases to decay rapidly into other low-energy bosonic modes, which renders the Higgs mode invisible. Therefore, it is desirable to find a way to stabilize the Higgs mode, which can offer an insight into the stabilization mechanism of the Higgs mode in condensed-matter physics. In quantum magnets, magnetic order caused by spontaneous symmetry breaking supports transverse (magnons) and longitudinal (Higgs modes) fluctuations. When a continuous symmetry is broken, the Goldstone magnon mode generally has an excitation energy lower than that of the Higgs mode, causing a rapid decay of the latter. In this work, we show that a stable Higgs mode exists in anisotropic quantum magnets near the quantum critical point between the dimerized and magnetically ordered phases. We find that an easy axis anisotropy increases the magnon gap such that the magnon mode is above the Higgs mode near the quantum critical point, and the decay of the Higgs mode into the magnon mode is forbidden kinematically. Our results suggest that the anisotropic quantum magnets provide ideal platforms to explore the Higgs physics in condensed-matter systems.

Twisted bilayer graphene (TBG) at twist angles $\theta \approx 1^{\circ }$ has recently attracted a great deal of interest for its rich transport phenomenology. We present a theoretical study of the local optical conductivity, plasmon spectra, and thermoelectric properties of TBG at different filling factors and twist angles $\theta$. Our calculations are based on the electronic band structures obtained from a continuum model that has two tunable parameters $u_0$ and $u_1$ which parametrize the intrasublattice interlayer and intersublattice interlayer tunneling rate, respectively. In this article we focus on two key aspects: (i) we study the dependence of our results on the value of $u_0$, exploring the whole range $0\le u_0\le u_1$; and (ii) we take into account effects arising from the intrinsic charge density inhomogeneity present in TBG, by calculating the band structures within the self-consistent Hartree approximation. At zero filling factor, i.e., at the charge neutrality point, the optical conductivity is quite sensitive to the value of $u_0$ and twist angle, whereas the charge inhomogeneity brings about only modest corrections. On the other hand, away from zero filling, static screening dominates and the optical conductivity is appreciably affected by the charge inhomogeneity, the largest effects being seen on the intraband contribution to it. These findings are also reflected by the plasmonic spectra. We compare our results with existing ones in the literature, where effects (i) and (ii) above have not been studied systematically. As natural byproducts of our calculations, we obtain the Drude weight and Seebeck coefficient. The former displays an enhanced particle-hole asymmetry stemming from the inhomogeneous ground-state charge distribution. The latter is shown to display a broad sign-changing feature even at low temperatures ($\approx 5\mathrm{K}$) due to the reduced slope of the bands, as compared to those of single-layer graphene.

The nonlinear supermatrix $\sigma$ model is widely used to understand the physics of Anderson localization and the level statistics in noninteracting disordered electron systems. In contrast to the general belief that the supersymmetry method applies only to systems of noninteracting particles, we adopt this approach to the disorder averaging in the interacting models. In particular, we apply supersymmetry to study the Sachdev-Ye-Kitaev (SYK) model where the disorder averaging has so far been performed only within the replica approach. We use a slightly modified time-reversal invariant version of the SYK model and perform calculations in real time. As a demonstration of how the supersymmetry method works, we derive saddle-point equations. In the semiclassical limit, we show that the results are in agreement with those found using the replica technique. We also develop the formally exact superbosonized representation of the SYK model. In the latter, the supersymmetric theory of original fermions and their superpartner bosons is reformulated as a model of unconstrained collective excitations. We argue that the supersymmetry description of the model paves the way for precise calculations in SYK-like models used in condensed matter, gravity, and high-energy physics.

Scalar waves such as airborne sound lack an intrinsic spin degree of freedom, making the realization of sonic ${\mathbb{Z}}_2$ topological phases based on spin degeneracy challenging. Here, we demonstrate the relevance of synthetic dimensions and higher-dimensional topological physics for exploring topological phases based on acoustic pseudo-spin with exact Kramers degeneracy. Interestingly, we find that a carefully designed two-band one-dimensional Hamiltonian with two additional phason degrees of freedom can enter a ${\mathbb{Z}}_2$ semimetallic phase with nonzero topological invariants carried by pairs of Weyl points in a three-dimensional synthetic momentum space. Taking advantage of the high localization of sonic quasibound states, embedded in the modal continuum of a one-dimensional acoustic waveguide, we implement a ${\mathbb{Z}}_2$ topological Weyl system and experimentally observe its signature in far-field sound scattering experiments. Our findings establish sonic quasibound states in continuum as a fertile ground for exploring higher dimensional Weyl physics in scattering media, and provide a viable experimental path to study spin-related topological effects in acoustics.

We argue that the $q$-deformed spin-1 Affleck-Kennedy-Lieb-Tasaki (AKLT) Hamiltonian should be regarded as a representative of a symmetry-protected topological phase. Even though it fails to exhibit any of the standard symmetries known to protect the Haldane phase, it still displays all characteristics of this phase: fractionalized spin-$\frac{1}{2}$ boundary spins, nontrivial string order, and—when using an appropriate definition—a twofold degeneracy in the entanglement spectrum. We trace these properties back to the existence of an $S{O}_q\left(3\right)$ quantum group symmetry and speculate about potential links to discrete duality symmetries. We expect our findings and methods to be relevant for the identification, characterization, and classification of other symmetry-protected topological phases with nonstandard symmetries.

By applying a self-consistent Hartree-Fock approximation, we show that the mechanism of dynamical symmetry breaking can account for the insulating phase that develops about the charge neutrality point of twisted bilayer graphene around the magic angle. (i) If the Coulomb interaction is screened by metallic gates, the opening of a gap between the lowest-energy valence and conduction bands proceeds through the breakdown of chiral symmetry at strong coupling. Increasing the dielectric screening, however, we find a critical coupling at which chiral symmetry breaking is suppressed, triggering a very strong signal for time-reversal symmetry breaking with Haldane mass. (ii) If the long-range tail of the Coulomb interaction is not screened, we see the appearance of yet a different dominant pattern at strong coupling, which is characterized by breaking the time-reversal invariance but with opposite flux in the two sublattices of each carbon layer, with the consequent valley symmetry breaking. In this case a gap is also opened in the Dirac cones, but superposed to the splitting of the degeneracy of the low-energy bands at the $K$ points of the moiré Brillouin zone.

We have succeeded in visualizing the local atomic structures around Sm in $R{\mathrm{B}}_6$ ($R=$ Yb, La), in which a rare-earth atom is located in the boron cage, using the newly developed technique for local structure investigations, multiple-wavelength neutron holography in a pulsed neutron facility. From the local atomic structures, we were able to clarify the behavior of Sm in the boron cage. Doped Sm in $\mathrm{Yb}{\mathrm{B}}_6$ fluctuates within the boron cage with a mean displacement of 0.25(4) Å, while that of Sm in $\mathrm{La}{\mathrm{B}}_6$ is approximately 0.15 Å. The Sm doping causes the fluctuation of the first-nearest-neighbor B with a mean displacement of 0.28 Å, while its effect on La, Yb, and the rest of the boron atoms is negligible. These are the first observations of the local behavior of doped rare-earth atoms and B in rare-earth borides with boron cages.

We explore the magnetic excitations of the spin-$\frac{1}{2}$ triangular antiferromagnet ${\mathrm{Ba}}_3{\mathrm{CoSb}}_2{\mathrm{O}}_9$ in its ${120}^{\circ }$ ordered phase using single-crystal high-resolution inelastic neutron scattering. Sharp magnons with no decay are observed throughout reciprocal space, with a strongly renormalized dispersion and multiple soft modes compared to linear spin-wave theory. We propose an empirical parametrization that can quantitatively capture the complete dispersions in the three-dimensional Brillouin zone and explicitly show that the dispersion renormalizations have the direct consequence that $\mathrm{one}\to \mathrm{two}$ magnon decays are avoided throughout reciprocal space, whereas such decays would be allowed for the unrenormalized dispersions. At higher energies, we observe a very strong continuum of excitations with highly structured intensity modulations extending up at least $4\times$ the maximum one-magnon energy. The one-magnon intensities decrease much faster upon increasing energy than predicted by linear spin-wave theory and the higher-energy continuum contains much more intensity than can be accounted for by a two-magnon cross-section, suggesting a significant transfer of spectral weight from the high-energy magnons into the higher-energy continuum states. We attribute the strong dispersion renormalizations and substantial transfer of spectral weight to continuum states to the effect of quantum fluctuations and interactions beyond the spin-wave approximation, and we make connections to theoretical approaches that might capture such effects. Finally, through measurements in a strong applied magnetic field, we find evidence for magnetic domains with opposite senses for the spin rotation in the ${120}^{\circ }$ ordered ground state, as expected in the absence of Dzyaloshinskii-Moriya interactions, when the sense of spin rotation is selected via spontaneous symmetry breaking.

For hybrid organic-inorganic as well as all-inorganic lead halide perovskites a Rashba effect has been invoked to explain the high efficiency in energy conversion by prohibiting direct recombination. Both a bulk and surface Rashba effect have been predicted. In the valence band of methylammonium (MA) lead bromide a Rashba effect has been reported by angle-resolved photoemission and circular dichroism with giant values of 7–11 eV Å. We present band dispersion measurements of $\mathrm{MA}\mathrm{Pb}{\mathrm{Br}}_3$ and spin-resolved photoemission of $\mathrm{Cs}\mathrm{Pb}{\mathrm{Br}}_3$ to show that a large Rashba effect detectable by photoemission or circular dichroism does not exist and cannot be the origin of the high effciency.