We discuss Bragg scattering on both Bose and Fermi gases with strong short-range interactions in the deep inelastic regime of large wave vector transfer $q$, where the dynamic structure factor is dominated by a resonance near the free-particle energy $\hslash \omega ={ϵ}_{\mathbf{q}}={\hslash }^2{q}^2/2m$. Using a systematic short-distance expansion, the structure factor at high momentum is shown to exhibit a nontrivial dependence on frequency characterized by two separate scaling regimes. First, for frequencies that differ from the single-particle energy by terms of order $\mathcal{O}(q)$ (i.e., small deviations compared to the single-particle energy), the dynamic structure factor is described by the impulse approximation of Hohenberg and Platzman. Second, deviations of order $\mathcal{O}(q^2)$ (i.e., of the same order or larger than the single-particle energy) are described by the operator product expansion, with a universal crossover connecting both regimes. The scaling is consistent with the leading asymptotics for a number of sum rules in the large momentum limit. Furthermore, we derive an exact expression for the shift and width of the single-particle peak at large momentum due to interactions, thus extending a result by Beliaev [J. Exp. Theor. Phys. 7, 299 (1958)] for the low-density Bose gas to arbitrary values of the scattering length $a$. The shift exhibits a maximum around $qa\simeq 1$, which is connected with a maximum in the static structure factor due to strong short-range correlations. For Bose gases with moderate interaction strengths, the theoretically predicted shift is consistent with the value observed by Papp et al. [Phys. Rev. Lett. 101, 135301 (2008)]. Finally, we develop a diagrammatic theory for the dynamic structure factor which accounts for the correlations beyond Bogoliubov theory. It covers the full range of momenta and frequencies and provides an explicit example for the emergence of asymptotic scaling at large momentum.

We consider symmetry-protected topological (SPT) phases with crystalline point group symmetry, dubbed point group SPT (pgSPT) phases. We show that such phases can be understood in terms of lower-dimensional topological phases with on-site symmetry and that they can be constructed as stacks and arrays of these lower-dimensional states. This provides the basis for a general framework to classify and characterize bosonic and fermionic pgSPT phases, which can be applied for arbitrary crystalline point group symmetry and in arbitrary spatial dimensions. We develop and illustrate this framework by means of a few examples, focusing on three-dimensional states. We classify bosonic pgSPT phases and fermionic topological crystalline superconductors with ${\mathbb{Z}}_2^P$ (reflection) symmetry, electronic topological crystalline insulators (TCIs) with $\mathrm{U}(1)\times {\mathbb{Z}}_2^P$ symmetry, and bosonic pgSPT phases with $C_{2v}$ symmetry, which is generated by two perpendicular mirror reflections. We also study surface properties, with a focus on gapped, topologically ordered surface states. For electronic TCIs, we find a ${\mathbb{Z}}_8\times {\mathbb{Z}}_2$ classification, where the ${\mathbb{Z}}_8$ corresponds to known states obtained from noninteracting electrons, and the ${\mathbb{Z}}_2$ corresponds to a “strongly correlated” TCI that requires strong interactions in the bulk. Our approach may also point the way toward a general theory of symmetry-enriched topological phases with crystalline point group symmetry.

We investigate many-body dynamics in a one-dimensional interacting periodically driven system, based on a partially filled version of Thouless’s topologically quantized adiabatic pump. The corresponding single-particle Floquet bands are chiral, with the Floquet spectrum realizing nontrivial cycles around the quasienergy Brillouin zone. For generic filling, with either bosons or fermions, the system is gapless and is expected to rapidly absorb energy from the driving field. We identify parameter regimes where scattering between Floquet bands of opposite chirality is exponentially suppressed, opening a long time window in which the system prethermalizes to an infinite-temperature state restricted to a single Floquet band. In this quasi-steady state, the time-averaged current takes a universal value determined solely by the density of particles and the topological winding number of the populated Floquet band. This remarkable behavior may be readily studied experimentally in recently developed cold atom systems.

Condensed matter physics has been driven forward by significant experimental and theoretical progress in the study and understanding of equilibrium phase transitions based on symmetry and topology. However, nonequilibrium phase transitions have remained a challenge, in part due to their complexity in theoretical descriptions and the additional experimental difficulties in systematically controlling systems out of equilibrium. Here, we study a one-dimensional chain of 72 microwave cavities, each coupled to a superconducting qubit, and coherently drive the system into a nonequilibrium steady state. We find experimental evidence for a dissipative phase transition in the system in which the steady state changes dramatically as the mean photon number is increased. Near the boundary between the two observed phases, the system demonstrates bistability, with characteristic switching times as long as 60 ms—far longer than any of the intrinsic rates known for the system. This experiment demonstrates the power of circuit QED systems for studying nonequilibrium condensed matter physics and paves the way for future experiments exploring nonequilbrium physics with many-body quantum optics.

Nonequilibrium phase transitions exist in damped-driven open quantum systems when the continuous tuning of an external parameter leads to a transition between two robust steady states. In second-order transitions this change is abrupt at a critical point, whereas in first-order transitions the two phases can coexist in a critical hysteresis domain. Here, we report the observation of a first-order dissipative quantum phase transition in a driven circuit quantum electrodynamics system. It takes place when the photon blockade of the driven cavity-atom system is broken by increasing the drive power. The observed experimental signature is a bimodal phase space distribution with varying weights controlled by the drive strength. Our measurements show an improved stabilization of the classical attractors up to the millisecond range when the size of the quantum system is increased from one to three artificial atoms. The formation of such robust pointer states could be used for new quantum measurement schemes or to investigate multiphoton phases of finite-size, nonlinear, open quantum systems.

Circulators are nonreciprocal circuit elements that are integral to technologies including radar systems, microwave communication transceivers, and the readout of quantum information devices. Their nonreciprocity arises from the interference of microwaves over the centimeter scale of the signal wavelength, in the presence of bulky magnetic media that breaks time-reversal symmetry. Here, we realize a completely passive on-chip microwave circulator with size $1/1000\mathrm{th}$ the wavelength by exploiting the chiral, “slow-light” response of a two-dimensional electron gas in the quantum Hall regime. For an integrated GaAs device with $330\mu \mathrm{m}$ diameter and about 1-GHz center frequency, a nonreciprocity of 25 dB is observed over a 50-MHz bandwidth. Furthermore, the nonreciprocity can be dynamically tuned by varying the voltage at the port, an aspect that may enable reconfigurable passive routing of microwave signals on chip.

Topological solitons are knots in continuous physical fields classified by nonzero Hopf index values. Despite arising in theories that span many branches of physics, from elementary particles to condensed matter and cosmology, they remain experimentally elusive and poorly understood. We introduce a method of experimental and numerical analysis of such localized structures in liquid crystals that, similar to the mathematical Hopf maps, relates all points of the medium’s order parameter space to their closed-loop preimages within the three-dimensional solitons. We uncover a surprisingly large diversity of naturally occurring and laser-generated topologically nontrivial solitons with differently knotted nematic fields, which previously have not been realized in theories and experiments alike. We discuss the implications of the liquid crystal’s nonpolar nature on the knot soliton topology and how the medium’s chirality, confinement, and elastic anisotropy help to overcome the constraints of the Hobart-Derrick theorem, yielding static three-dimensional solitons without or with additional defects. Our findings will establish chiral nematics as a model system for experimental exploration of topological solitons and may impinge on understanding of such nonsingular field configurations in other branches of physics, as well as may lead to technological applications.

Electronic heating of cold crystal lattices in nonlinear multiphoton excitation can transiently alter their physical and chemical properties. In metals where free electron densities are high and the relative fraction of photoexcited hot electrons is low, the effects are small, but in semimetals, where the free electron densities are low and the photoexcited densities can overwhelm them, the intense femtosecond laser excitation can induce profound changes. In semimetal graphite and its derivatives, strong optical absorption, weak screening of the Coulomb potential, and high cohesive energy enable extreme hot electron generation and thermalization to be realized under femtosecond laser excitation. We investigate the nonlinear interactions within a hot electron gas in graphite through multiphoton-induced thermionic emission. Unlike the conventional photoelectric effect, within about 25 fs, the memory of the excitation process, where resonant dipole transitions absorb up to eight quanta of light, is erased to produce statistical Boltzmann electron distributions with temperatures exceeding 5000 K; this ultrafast electronic heating causes thermionic emission to occur from the interlayer band of graphite. The nearly instantaneous thermalization of the photoexcited carriers through Coulomb scattering to extreme electronic temperatures characterized by separate electron and hole chemical potentials can enhance hot electron surface femtochemistry, photovoltaic energy conversion, and incandescence, and drive graphite-to-diamond electronic phase transition.

We construct and classify chiral topological phases in driven (Floquet) systems of strongly interacting bosons, with finite-dimensional site Hilbert spaces, in two spatial dimensions. The construction proceeds by introducing exactly soluble models with chiral edges, which in the presence of many-body localization (MBL) in the bulk are argued to lead to stable chiral phases. These chiral phases do not require any symmetry and in fact owe their existence to the absence of energy conservation in driven systems. Surprisingly, we show that they are classified by a quantized many-body index, which is well defined for any MBL Floquet system. The value of this index, which is always the logarithm of a positive rational number, can be interpreted as the entropy per Floquet cycle pumped along the edge, formalizing the notion of quantum-information flow. We explicitly compute this index for specific models and show that the nontrivial topology leads to edge thermalization, which provides an interesting link between bulk topology and chaos at the edge. We also discuss chiral Floquet phases in interacting fermionic systems and their relation to chiral bosonic phases.

We expand the phase diagram of two-dimensional, nonsymmorphic crystals at integer fillings that do not guarantee gaplessness. In addition to the trivial, gapped phase that is expected, we find that band inversion leads to a class of topological, gapless phases. These topological phases are exemplified by the monolayers of $M{\mathrm{Te}}_2$ ($M=\mathrm{W},\mathrm{Mo}$) if spin-orbit coupling is neglected. We characterize the Dirac band touching of these topological metals by the Wilson loop of the non-Abelian Berry gauge field. Furthermore, we develop a criterion for the proximity of these topological metals to 2D and 3D ${\mathbb{Z}}_2$ topological insulators when spin-orbit coupling is included; our criterion is based on nonsymmorphic symmetry eigenvalues, and may be used to identify topological materials without inversion symmetry. An additional feature of the Dirac cone in monolayer $M{\mathrm{Te}}_2$ is that it tilts over in a Lifshitz transition to produce electron and hole pockets—a type-II Dirac cone. These pockets, together with the pseudospin structure of the Dirac electrons, suggest a unified, topological explanation for the recently reported, nonsaturating magnetoresistance in ${\mathrm{WTe}}_2$, as well as its circular dichroism in photoemission. We complement our analysis and first-principles band structure calculations with an ab-initio-derived tight-binding model for the ${\mathrm{WTe}}_2$ monolayer.

The Lieb-Schultz-Mattis theorem and its higher-dimensional generalizations by Oshikawa and Hastings require that translationally invariant 2D spin systems with a half-integer spin per unit cell must either have a continuum of low energy excitations, spontaneously break some symmetries, or exhibit topological order with anyonic excitations. We establish a connection between these constraints and a remarkably similar set of constraints at the surface of a 3D interacting topological insulator. This, combined with recent work on symmetry-enriched topological phases with on-site unitary symmetries, enables us to develop a framework for understanding the structure of symmetry-enriched topological phases with both translational and on-site unitary symmetries, including the effective theory of symmetry defects. This framework places stringent constraints on the possible types of symmetry fractionalization that can occur in 2D systems whose unit cell contains fractional spin, fractional charge, or a projective representation of the symmetry group. As a concrete application, we determine when a topological phase must possess a “spinon” excitation, even in cases when spin rotational invariance is broken down to a discrete subgroup by the crystal structure. We also describe the phenomena of “anyonic spin-orbit coupling,” which may arise from the interplay of translational and on-site symmetries. These include the possibility of on-site symmetry defect branch lines carrying topological charge per unit length and lattice dislocations inducing degeneracies protected by on-site symmetry.

Unveiling the identity, spatial configuration, and microscopic structure of point defects is one of the key challenges in materials science. Here, we demonstrate that quantitative scanning transmission electron microscopy (STEM) can be used to directly observe Sr vacancies in ${\mathrm{SrTiO}}_3$ and to determine the atom column relaxations around them. By combining recent advances in quantitative STEM, including variable-angle, high-angle annular dark-field imaging and rigid registration methods, with frozen phonon multislice image simulations, we identify which Sr columns contain vacancies and quantify the number of vacancies in them. Picometer precision measurements of the surrounding atom column positions show that the nearest-neighbor Ti atoms are displaced away from the Sr vacancies. The results open up a new methodology for studying the microscopic mechanisms by which point defects control materials properties.

The appearance of spin-density-wave (SDW) magnetic order in the low-temperature and high-field corner of the superconducting phase diagram of ${\mathrm{CeCoIn}}_5$ is unique among unconventional superconductors. The nature of this magnetic $Q$ phase is a matter of current debate. Here, we present the thermal conductivity of ${\mathrm{CeCoIn}}_5$ in a rotating magnetic field, which reveals the presence of an additional order inside the $Q$ phase that is intimately intertwined with the superconducting $d$-wave and SDW orders. A discontinuous change of the thermal conductivity within the $Q$ phase, when the magnetic field is rotated about antinodes of the superconducting $d$-wave order parameter, demands that the additional order must change abruptly, together with the recently observed switching of the SDW. A combination of interactions, where spin-orbit coupling orients the SDW, which then selects the secondary $p$-wave pair-density-wave component (with an average amplitude of 20% of the primary $d$-wave order parameter), accounts for the observed behavior.

We present neutron scattering measurements on powder samples of the spinel ${\mathrm{FeSc}}_2{\mathrm{S}}_4$ that reveal a previously unobserved magnetic ordering transition occurring at 11.8(2) K. Magnetic ordering occurs subsequent to a subtle cubic-to-tetragonal structural transition that distorts Fe coordinating sulfur tetrahedra and lifts the orbital degeneracy. The orbital ordering is not truly long ranged, but occurs over finite-sized domains that limit magnetic correlation lengths. The application of 1 GPa hydrostatic pressure appears to destabilize this Néel state, reducing the transition temperature to 8.6(8) K and redistributing magnetic spectral weight to higher energies. The relative magnitudes of ordered $⟨m{⟩}^2=3.1(2)$ ${\mu }_B^2$ and fluctuating moments $⟨\delta m⟩=13(1)$ ${\mu }_B^2$ show that the magnetically ordered state of ${\mathrm{FeSc}}_2{\mathrm{S}}_4$ is drastically renormalized and close to criticality.

The appearance of the light Higgs boson at the LHC is difficult to explain, particularly in light of naturalness arguments in quantum field theory. However, light scalars can appear in condensed matter systems when parameters (like the amount of doping) are tuned to a critical point. At zero temperature these quantum critical points are directly analogous to the finely tuned standard model. In this paper, we explore a class of models with a Higgs near a quantum critical point that exhibits non-mean-field behavior. We discuss the parametrization of the effects of a Higgs emerging from such a critical point in terms of form factors, and present two simple realistic scenarios based on either generalized free fields or a 5D dual in anti–de Sitter space. For both of these models, we consider the processes $gg\to ZZ$ and $gg\to hh$, which can be used to gain information about the Higgs scaling dimension and IR transition scale from the experimental data.

One major change of the future revision of the International System of Units is a new definition of the ampere based on the elementary charge $e$. Replacing the former definition based on Ampère’s force law will allow one to fully benefit from quantum physics to realize the ampere. However, a quantum realization of the ampere from $e$, accurate to within ${10}^{-8}$ in relative value and fulfilling traceability needs, is still missing despite the many efforts made for the development of single-electron tunneling devices. Starting again with Ohm’s law, applied here in a quantum circuit combining the quantum Hall resistance and Josephson voltage standards with a superconducting cryogenic amplifier, we report on a practical and universal programmable quantum current generator. We demonstrate that currents generated in the milliampere range are accurately quantized in terms of $e{f}_{\mathrm{J}}$ ($f_{\mathrm{J}}$ is the Josephson frequency) with measurement uncertainty of ${10}^{-8}$. This new quantum current source, which is able to deliver such accurate currents down to the microampere range, can greatly improve the current measurement traceability, as demonstrated with the calibrations of digital ammeters. In addition, it opens the way to further developments in metrology and in fundamental physics, such as a quantum multimeter or new accurate comparisons to single-electron pumps.

Using quantum Monte Carlo simulations, we study a series of models of fermions coupled to quantum Ising spins on a square lattice with $N$ flavors of fermions per site for $N=1$, 2, and 3. The models have an extensive number of conserved quantities but are not integrable, and they have rather rich phase diagrams consisting of several exotic phases and phase transitions that lie beyond the Landau-Ginzburg paradigm. In particular, one of the prominent phases for $N>1$ corresponds to $2N$ gapless Dirac fermions coupled to an emergent ${\mathbb{Z}}_2$ gauge field in its deconfined phase. However, unlike a conventional ${\mathbb{Z}}_2$ gauge theory, we do not impose “Gauss’s Law” by hand; instead, it emerges because of spontaneous symmetry breaking. Correspondingly, unlike a conventional ${\mathbb{Z}}_2$ gauge theory in two spatial dimensions, our models have a finite-temperature phase transition associated with the melting of the order parameter that dynamically imposes the Gauss’s law constraint at zero temperature. By tuning a parameter, the deconfined phase undergoes a transition into a short-range entangled phase, which corresponds to Néel antiferromagnet or superconductor for $N=2$ and a valence-bond solid for $N=3$. Furthermore, for $N=3$, the valence-bond solid further undergoes a transition to a Néel phase consistent with the deconfined quantum critical phenomenon studied earlier in the context of quantum magnets.

We consider the details of the near-surface electronic band structure of a prototypical ferromagnet, Fe(001). Using high-resolution angle-resolved photoemission spectroscopy, we demonstrate openings of the spin-orbit-induced electronic band gaps near the Fermi level. The band gaps, and thus the Fermi surface, can be manipulated by changing the remanent magnetization direction. The effect is of the order of $\mathrm{\Delta }E=100\mathrm{meV}$ and $\mathrm{\Delta }k=0.1{\AA }^{-1}$. We show that the observed dispersions are dominated by the bulk band structure. First-principles calculations and one-step photoemission calculations suggest that the effect is related to changes in the electronic ground state and not caused by the photoemission process itself. The symmetry of the effect indicates that the observed electronic bulk states are influenced by the presence of the surface, which might be understood as related to a Rashba-type effect. By pinpointing the regions in the electronic band structure where the switchable band gaps occur, we demonstrate the significance of spin-orbit interaction even for elements as light as $3d$ ferromagnets. These results set a new paradigm for the investigations of spin-orbit effects in the spintronic materials. The same methodology could be used in the bottom-up design of the devices based on the switching of spin-orbit gaps such as electric-field control of magnetic anisotropy or tunneling anisotropic magnetoresistance.

Topological Dirac and Weyl semimetals have an energy spectrum that hosts Weyl nodes appearing in pairs of opposite chirality. Topological stability is ensured when the nodes are separated in momentum space and unique spectral and transport properties follow. In this work, we study the effect of a space-dependent Weyl node separation, which we interpret as an emergent background axial-vector potential, on the electromagnetic response and the energy spectrum of Weyl and Dirac semimetals. This situation can arise in the solid state either from inhomogeneous strain or nonuniform magnetization and can also be engineered in cold atomic systems. Using a semiclassical approach, we show that the resulting axial magnetic field ${\mathbf{B}}_5$ is observable through an enhancement of the conductivity as $\sigma \sim {\mathbf{B}}_5^2$ due to an underlying chiral pseudomagnetic effect. We then use two lattice models to analyze the effect of ${\mathbf{B}}_5$ on the spectral properties of topological semimetals. We describe the emergent pseudo-Landau-level structure for different spatial profiles of ${\mathbf{B}}_5$, revealing that (i) the celebrated surface states of Weyl semimetals, the Fermi arcs, can be reinterpreted as $n=0$ pseudo-Landau levels resulting from a ${\mathbf{B}}_5$ confined to the surface, (ii) as a consequence of position-momentum locking, a bulk ${\mathbf{B}}_5$ creates pseudo-Landau levels interpolating in real space between Fermi arcs at opposite surfaces, and (iii) there are equilibrium bound currents proportional to ${\mathbf{B}}_5$ that average to zero over the sample, which are the analogs of bound currents in magnetic materials. We conclude by discussing how our findings can be probed experimentally.

Magnetism and nematic order are the two nonsuperconducting orders observed in iron-based superconductors. To elucidate the interplay between them and ultimately unveil the pairing mechanism, several models have been investigated. In models with quenched orbital degrees of freedom, magnetic fluctuations promote stripe magnetism, which induces orbital order. In models with quenched spin degrees of freedom, charge fluctuations promote spontaneous orbital order, which induces stripe magnetism. Here, we develop an unbiased approach, in which we treat magnetic and orbital fluctuations on equal footing. Key to our approach is the inclusion of the orbital character of the low-energy electronic states into renormalization group (RG) analysis. We analyze the RG flow of the couplings and argue that the same magnetic fluctuations, which are known to promote $s^{+-}$ superconductivity, also promote an attraction in the orbital channel, even if the bare orbital interaction is repulsive. We next analyze the RG flow of the susceptibilities and show that, if all Fermi pockets are small, the system first develops a spontaneous orbital order, then $s^{+-}$ superconductivity, and magnetic order does not develop down to $T=0$. We argue that this scenario applies to FeSe. In systems with larger pockets, such as ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ and LaFeAsO, we find that the leading instability is either towards a spin-density wave or superconductivity. We argue that in this situation nematic order is caused by composite spin fluctuations and is vestigial to stripe magnetism. Our results provide a unifying description of different iron-based materials.