A quantum spin-$\frac{1}{2}$ chain with an axial symmetry is normally described by quasiparticles associated with the spins oriented along the axis of rotation. Kinetic constraints can enrich such a description by setting apart different species of quasiparticles, which can get stuck at high enough density, realizing the quantum analog of jamming. We identify a family of interactions satisfying simple kinetic constraints and consider generic translationally invariant models built up from them. We study dynamics following a local unjamming perturbation in a jammed state. We show that they can be mapped into dynamics of ordinary unconstrained systems, but the nonlocality of the mapping changes the scales at which the phenomena manifest themselves. Scattering of quasiparticles, formation of bound states, and eigenstate localization become all visible at macroscopic scales. Depending on whether a symmetry is present or not, the microscopic details of the jammed state turn out to have either a marginal or a strong effect. In the former case or when the initial state is almost homogeneous, we show that even a product state is turned into a macroscopic quantum state.

We propose multilayer moiré structures in strong external magnetic fields as a novel platform for realizing highly tunable, frustrated Hubbard physics with topological order. Identifying the layer degree of freedom as a pseudospin allows us to retain SU(2) symmetry while controlling ring-exchange processes and concurrently quenching the kinetic energy by large external magnetic fields. This way, a broad class of interacting Hubbard-Hofstadter states and their transitions can be studied. Remarkably, in the limit of strong interactions the system becomes Mott insulating and we find chiral pseudospin-liquid phases which are induced by the magnetic field. We find that this topologically ordered state remains exceptionally stable toward relevant perturbations. We discuss how layer pseudospin can be probed in near-term experiments. As the magnetic flux can be easily tuned in moiré systems, our approach provides a promising route toward the experimental realization and control of topologically ordered phases of matter.

The thermoelectric Nernst effect of solids converts heat flow to beneficial electronic voltages. Here, using a correlated topological semimetal with high carrier mobility $\mu$ in the presence of magnetic fluctuations, we demonstrate an enhancement of the Nernst effect close to a magnetic phase transition. A magnetic instability in NdAlSi modifies the carrier relaxation time on “hot spots” in momentum space, causing a strong band filling dependence of $\mu$. We quantitatively derive electronic band parameters from a novel two-band analysis of the Nernst effect $S_{xy}$, in good agreement with quantum oscillation measurements and band calculations. While the Nernst response of NdAlSi behaves much like conventional semimetals at high temperatures, an additional contribution $\mathrm{\Delta }{S}_{\mathrm{xy}}$ from electronic correlations appears just above the magnetic transition. Our work demonstrates the engineering of the relaxation time, or the momentum-dependent self-energy, to generate a large Nernst response independent of a material’s carrier density, i.e., for metals, semimetals, and semiconductors with large $\mu$.

The non-Hermitian skin effect dramatically reshapes the energy bands of non-Hermitian systems, meaning that the usual Bloch band theory is fundamentally inadequate as their characterization. The non-Bloch band theory, in which the concept of Brillouin zone is generalized, has been widely applied to investigate non-Hermitian systems in one spatial dimension. However, its generalization to higher dimensions has been challenging. Here, we develop a formulation of the non-Hermitian skin effect and non-Bloch band theory in arbitrary spatial dimensions, which is based on a natural geometrical object known as the amoeba. Our theory provides a general framework for studying non-Hermitian bands beyond one dimension. Key quantities of non-Hermitian bands, including the energy spectrum, eigenstates profiles, and the generalized Brillouin zone, can be efficiently obtained from this approach.

Quantum electrodynamics in $2+1$ dimensions (${\mathrm{QED}}_3$) has been proposed as a critical field theory describing the low-energy effective theory of a putative algebraic Dirac spin liquid or of quantum phase transitions in two-dimensional frustrated magnets. We provide compelling evidence that the intricate spectrum of excitations of the elementary but strongly frustrated $J_1\text{−}{J}_2$ Heisenberg model on the triangular lattice is in one-to-one correspondence to a zoo of excitations from ${\mathrm{QED}}_3$, in the quantum spin liquid regime. This evidence includes a large manifold of explicitly constructed monopole and bilinear excitations of ${\mathrm{QED}}_3$, which is thus shown to serve as an organizing principle of phases of matter in triangular lattice antiferromagnets and their low-lying excitations. Moreover, we observe signatures of emergent valence-bond solid (VBS) correlations, which can be interpreted either as evidence of critical VBS fluctuations of an emergent Dirac spin liquid or as a transition from the 120° Néel order to a VBS whose quantum critical point is described by ${\mathrm{QED}}_3$. Our results are obtained by comparing ansatz wave functions from a parton construction to exact eigenstates obtained using large-scale exact diagonalization up to $N=48$ sites.

Given a renormalization scheme, we show how to formulate a tractable convex relaxation of the set of feasible local density matrices of a many-body quantum system. The relaxation is obtained by introducing a hierarchy of constraints between the reduced states of ever-growing sets of lattice sites. The coarse-graining maps of the underlying renormalization procedure serve to eliminate a vast number of those constraints, such that the remaining ones can be enforced with reasonable computational means. This process can be used to obtain rigorous lower bounds on the ground-state energy of arbitrary local Hamiltonians by performing a linear optimization over the resulting convex relaxation of reduced quantum states. The quality of the bounds crucially depends on the particular renormalization scheme, which must be tailored to the target Hamiltonian. We apply our method to 1D translation-invariant spin models, obtaining energy bounds comparable to those attained by optimizing over locally translation-invariant states of $n\gtrsim 100$ spins. Beyond this demonstration, the general method can be applied to a wide range of other problems, such as spin systems in higher spatial dimensions, electronic structure problems, and various other many-body optimization problems, such as entanglement and nonlocality detection.

Nonlinear electromagnetic response functions have reemerged as a crucial tool for studying quantum materials, due to recently appreciated connections between optical response functions, quantum geometry, and band topology. Most attention has been paid to responses to spatially uniform electric fields, relevant to low-energy optical experiments in conventional solid state materials. However, magnetic and magnetoelectric phenomena are naturally connected by responses to spatially varying electric fields due to Maxwell’s equations. Furthermore, in the emerging field of moiré materials, characteristic lattice scales are much longer, allowing spatial variation of optical electric fields to potentially have a measurable effect in experiments. In order to address these issues, we develop a formalism for computing linear and nonlinear responses to spatially inhomogeneous electromagnetic fields. Starting with the continuity equation, we derive an expression for the second-quantized current operator that is manifestly conserved and model independent. Crucially, our formalism makes no assumptions on the form of the microscopic Hamiltonian and so is applicable to model Hamiltonians derived from tight-binding or ab initio calculations. We then develop a diagrammatic Kubo formalism for computing the wave vector dependence of linear and nonlinear conductivities, using Ward identities to fix the value of the diamagnetic current order by order in the vector potential. We apply our formula to compute the magnitude of the Kerr effect at oblique incidence for a model of a moiré-Chern insulator and demonstrate the experimental relevance of spatially inhomogeneous fields in these systems. We further show how our formalism allows us to compute the (orbital) magnetic multipole moments and magnetic susceptibilities in insulators. Turning to nonlinear response, we use our formalism to compute the second-order transverse response to spatially varying transverse electric fields in our moiré-Chern insulator model, with an eye toward the next generation of experiments in these systems.

Topological insulators and superconductors support extended surface states protected against the otherwise localizing effects of static disorder. Specifically, in the Wigner-Dyson insulators belonging to the symmetry classes A, AI, and AII, a band of extended surface states is continuously connected to a likewise extended set of bulk states forming a “bridge” between different surfaces via the mechanism of spectral flow. In this work we show that this mechanism is absent in the majority of non-Wigner-Dyson topological superconductors and chiral topological insulators. In these systems, there is precisely one point with granted extended states, the center of the band, $E=0$. Away from it, states are spatially localized, or can be made so by the addition of spatially local potentials. Considering the three-dimensional insulator in class AIII and winding number $\nu =1$ as a paradigmatic case study, we discuss the physical principles behind this phenomenon, and its methodological and applied consequences. In particular, we show that low-energy Dirac approximations in the description of surface states can be treacherous in that they tend to conceal the localizability phenomenon. We also identify markers defined in terms of Berry curvature as measures for the degree of state localization in lattice models, and back our analytical predictions by extensive numerical simulations. A main conclusion of this work is that the surface phenomenology of non-Wigner-Dyson topological insulators is a lot richer than that of their Wigner-Dyson siblings, extreme limits being spectrumwide quantum critical delocalization of all states versus full localization except at the $E=0$ critical point. As part of our study we identify possible experimental signatures distinguishing between these different alternatives in transport or tunnel spectroscopy.

The asymmetric distribution of chiral objects with opposite chirality is of great fundamental interest ranging from molecular biology to particle physics. In quantum materials, chiral states can build on inversion-symmetry-breaking lattice structures or emerge from spontaneous magnetic ordering induced by competing interactions. Although the handedness of a chiral state can be changed through external fields, a spontaneous chirality flipping has yet to be discovered. We present experimental evidence of chirality flipping via changing temperature in a topological magnet ${\mathrm{EuAl}}_4$, which features orthogonal spin density waves (SDW) and charge density waves (CDW). Using circular dichroism of Bragg peaks in the resonant magnetic x-ray scattering, we find that the chirality of the helical SDW flips through a first-order phase transition with modified SDW wavelength. Intriguingly, we observe that the CDW couples strongly with the SDW and displays a rare commensurate-to-incommensurate transition at the chirality flipping temperature. Combining with first-principles calculations and angle-resolved photoemission spectroscopy, our results support a Fermi surface origin of the helical SDW with intertwined spin, charge, and lattice degrees of freedom in ${\mathrm{EuAl}}_4$. Our results reveal an unprecedented spontaneous chirality flipping and lay the groundwork for a new functional manipulation of chirality through momentum-dependent spin-charge-lattice interactions.

We provide a universal tight bound on the energy gap of topological insulators by exploring relationships between topology, quantum geometry, and optical absorption. Applications of our theory to infrared absorption near topological band inversion, magnetic circular dichroism in Chern insulators, and topological gap in moiré materials are demonstrated.

Quantum systems with engineered Hamiltonians can be used to study many-body physics problems to provide insights beyond the capabilities of classical computers. Semiconductor gate-defined quantum dot arrays have emerged as a versatile platform for realizing generalized Fermi-Hubbard physics, one of the richest playgrounds in condensed matter physics. In this work, we employ a germanium $4\times 2$ quantum dot array and show that the naturally occurring long-range Coulomb interaction can lead to exciton formation and transport. We tune the quantum dot ladder into two capacitively coupled channels and exploit Coulomb drag to probe the binding of electrons and holes. Specifically, we shuttle an electron through one leg of the ladder and observe that a hole is dragged along in the second leg under the right conditions. This corresponds to a transition from single-electron transport in one leg to exciton transport along the ladder. Our work paves the way for the study of excitonic states of matter in quantum dot arrays.

The opening of an energy gap in the electronic structure generally indicates the presence of interactions. In materials with low carrier density and short screening length, long-range Coulomb interaction favors the spontaneous formation of electron-hole pairs, so called excitons, opening an excitonic gap at the Fermi level. Excitonic materials host unique phenomena associated with pair excitations. However, there is still no generally recognized single-crystal material with excitonic order, which is, therefore, awaited in condensed matter physics. Here, we show that excitonic states may exist in the quasi-one-dimensional material ${\mathrm{Ta}}_2{\mathrm{Pd}}_3{\mathrm{Te}}_5$, which has an almost ideal Dirac-like band structure, with the Dirac point located exactly at the Fermi level. We find that an energy gap appears at 350 K, and it grows with decreasing temperature. The spontaneous gap opening is absent in a similar material ${\mathrm{Ta}}_2{\mathrm{Ni}}_3{\mathrm{Te}}_5$. Intriguingly, the gap is destroyed by the potassium deposition on the crystal, likely due to extra-doped carriers. Furthermore, we observe a pair of in-gap flat bands, which is an analog of the impurity states in a superconducting gap. All these observations can be properly explained by an excitonic order, providing ${\mathrm{Ta}}_2{\mathrm{Pd}}_3{\mathrm{Te}}_5$ as a new and promising candidate realizing excitonic states.

The excitonic insulator (EI) is an exotic ground state of narrow-gap semiconductors and semimetals arising from spontaneous condensation of electron-hole pairs bound by attractive Coulomb interaction. Despite research on EIs dating back to half a century ago, their existence in real materials remains a subject of ongoing debate. In this study, through systematic experimental and theoretical investigations, we provide evidence for the existence of an EI ground state in a van der Waals compound ${\mathrm{Ta}}_2{\mathrm{Pd}}_3{\mathrm{Te}}_5$. Density-functional-theory calculations suggest that it is a semimetal with a small band overlap, whereas various experiments exhibit an insulating ground state with a clear band gap. Upon incorporating electron-hole Coulomb interaction into our calculations, we obtain an EI phase where the electronic symmetry breaking opens a many-body gap. Angle-resolved photoemission spectroscopy measurements exhibit that the band gap is closed with a significant change in the dispersions as the number of thermally excited charge carriers becomes sufficiently large in both equilibrium and nonequilibrium states. Structural measurements reveal a slight breaking of crystal symmetry with exceptionally small lattice distortion in the insulating state, which cannot account for the significant gap opening. Therefore, we attribute the insulating ground state with a gap opening in ${\mathrm{Ta}}_2{\mathrm{Pd}}_3{\mathrm{Te}}_5$ to exciton condensation, where the coupling to the symmetry-breaking electronic state induces a subtle change in the crystal structure.

The excitations in the Kitaev spin liquid (KSL) can be described by Majorana fermions, which have characteristic field dependence of bulk gap and topological edge modes. In the high-field state of layered honeycomb magnet $\alpha \text{−}{\mathrm{RuCl}}_3$, experimental results supporting these Majorana features have been reported recently. However, there are challenges due to sample dependence, and the impact of inevitable disorder on the KSL is poorly understood. Here, we study how low-energy excitations are modified by introducing point defects in $\alpha \text{−}{\mathrm{RuCl}}_3$ using electron irradiation, which induces site vacancies and exchange randomness. High-resolution measurements of the temperature dependence of specific heat $C(T)$ under in-plane fields $H$ reveal that, while the field-dependent Majorana gap is almost intact, additional low-energy states with $C/T=A(H)T$ are induced by introduced defects. At low temperatures, we obtain the data collapse of $C/T\sim H^{-\gamma }(T/H)$ expected for a disordered quantum spin system but with an anomalously large exponent $\gamma$. This leads us to find a power-law relationship between the coefficient $A(H)$ and the field-sensitive Majorana gap. These results are consistent with the picture that the disorder induces low-energy linear Majorana excitations, which may be considered as a weak localization effect of Majorana fermions in the KSL.

Spontaneous symmetry breaking—the phenomenon in which an infinitesimal perturbation can cause the system to break the underlying symmetry—is a cornerstone concept in the understanding of interacting solid-state systems. In a typical series of temperature-driven phase transitions, higher-temperature phases are more symmetric due to the stabilizing effect of entropy that becomes dominant as the temperature is increased. However, the opposite is rare but possible when there are multiple degrees of freedom in the system. Here, we present such an example of a symmetry-ascending phenomenon upon cooling in a magnetic kagome metal FeGe by utilizing neutron Larmor diffraction and Raman spectroscopy. FeGe has a kagome lattice structure with simple A-type antiferromagnetic order below Néel temperature $T_N\approx 400\mathrm{K}$ and a charge density wave (CDW) transition at $T_{\mathrm{CDW}}\approx 110\mathrm{K}$, followed by a spin-canting transition at around 60 K. In the paramagnetic state at 460 K, we confirm that the crystal structure is indeed a hexagonal kagome lattice. On cooling to around $T_N$, the crystal structure changes from hexagonal to monoclinic with in-plane lattice distortions on the order of ${10}^{-4}$ and the associated splitting of the double-degenerate phonon mode of the pristine kagome lattice. Upon further cooling to $T_{\mathrm{CDW}}$, the kagome lattice shows a small negative thermal expansion, and the crystal structure gradually becomes more symmetric upon further cooling. A tendency of increasing the crystalline symmetry upon cooling is unusual; it originates from an extremely weak structural instability that coexists and competes with the CDW and magnetic orders. These observations are against the expectations for a simple model with a single order parameter and hence can only be explained by a Landau free energy expansion that takes into account multiple lattice, charge, and spin degrees of freedom. Thus, the determination of the crystalline lattice symmetry as well as the unusual spin-lattice coupling is a first step towards understanding the rich electronic and magnetic properties of the system, and it sheds new light on intertwined orders where the lattice degree of freedom is no longer dominant.

In conventional ab initio methodologies, phonons are calculated by solving equations of motion involving static interatomic force constants and atomic masses. The Born-Oppenheimer approximation, where all electronic degrees of freedom are assumed to adiabatically follow the nuclear dynamics, is also adopted. This approach does not fully account for the effects of broken time-reversal symmetry in systems with magnetic order. Recent attempts to rectify this involve the inclusion of the velocity dependence of the interatomic forces in the equations of motion, which accounts for time-reversal symmetry breaking, and can result in chiral phonon modes with nonzero angular momentum even at the zone center. However, since the energy ranges of phonons and magnons typically overlap, the spins cannot be treated as adiabatically following the lattice degrees of freedom. Instead, phonon and spins must be treated on a similar footing. Focusing on zone-center modes, we propose a method involving Hessian matrices and Berry curvature tensors in terms of both phonon and spin degrees of freedom, and describe a first-principles methodology for calculating these. We then solve Lagrange’s equations of motion to determine the energies and characters of the mixed excitations, allowing us to quantify, for example, the energy splittings between chiral pairs of phonons in some cases, and the degree of magnetically induced mixing between infrared and Raman modes in others. The approach is general and can be applied to determine the adiabatic dynamics of any mixed set of slow variables.

We synthesized polycrystalline ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_{7-\delta }$ ($\delta \approx 0.07$) samples by using the sol-gel method without postannealing under high oxygen pressure, and then measured temperature-dependent resistivity under various hydrostatic pressures up to 18 GPa by using the cubic anvil and two-stage multianvil apparatus. We find that the density-wave-like anomaly in resistivity is progressively suppressed with increasing pressure and the resistivity drop corresponding to the onset of superconductivity emerges at pressure as low as $\sim 6\mathrm{GPa}$. Zero resistivity is achieved at 9 GPa below $T_{\mathrm{c}}^{\mathrm{zero}}\approx 6.6\mathrm{K}$, which increases quickly with pressure to 41 K at 18 GPa. However, the diamagnetic response was not detected in the ac magnetic susceptibility measurements up to 15 GPa, indicating a filamentary nature of the observed superconductivity in the studied pressure range. The constructed $T\text{−}P$ phase diagram reveals an intimate relationship between superconductivity, density-wave-like order, and the strange-metal-like behaviors. The observation of zero-resistance state in the polycrystalline ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_{7-\delta }$ samples under high pressures not only corroborates the recent report of superconductivity in the pressurized ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ crystals but also facilitates further studies on this emerging family of nickelate high-$T_{\mathrm{c}}$ superconductors.

Micromechanical and nanomechanical systems with exceptionally low dissipation rates are enabling the next-generation technologies of ultrasensitive detectors and quantum information systems. New techniques and methods for lowering the dissipation rate have in recent years been discovered and allowed for the engineering of mechanical oscillators with phononic modes that are extremely well isolated from the environment and thus possess quality factors close to and beyond $1\times {10}^9$. A powerful strategy for isolating and controlling a single phononic mode is based on phononic crystal engineering. Here we propose a new method for phononic crystal engineering of nanomechanical oscillators that is based on a periodic variation of the material density. To circumvent the introduction of additional bending losses resulting from the variation of material density, the added mass constitutes an array of nanopillars in which the losses will be diluted. Using this novel technique for phononic crystal engineering, we design and fabricate corrugated mechanical oscillators with quality factors approaching $1\times {10}^9$ in a room temperature environment. The flexibility space of these new phononic crystals is large and further advancement can be attained through optimized phononic crystal patterning and strain engineering via topology optimization. This will allow for the engineering of mechanical membranes with quality factors beyond $1\times {10}^9$ at room temperature. Such extremely low mechanical dissipation rates will enable the development of radically new technologies such as quantum-limited atomic force microscopy at room temperature, ultrasensitive detectors of dark matter, spontaneous waveform collapses, gravity, and high-efficiency quantum information transducers.

The ultrafast manipulation of quantum material has led to many novel and significant discoveries. Among them, the light-induced transient superconductivity in cuprates achieved by melting competing stripe orders represents a highly appealing accomplishment. However, recent investigations have shown that the notion of photoinduced superconductivity remains a topic of controversy, and its elucidation solely through $c$-axis time-resolved terahertz spectroscopy remains an arduous task. Here, we measure the in-plane and out-of-plane transient terahertz responses simultaneously in the stripe-ordered nonsuperconducting ${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x{\mathrm{CuO}}_4$ after near-infrared excitations. We find that although a pump-induced reflectivity edge appears in the $c$-axis reflectance spectrum, the reflectivity along the ${\mathrm{CuO}}_2$ planes decreases simultaneously, indicating an enhancement in the scattering rate of quasiparticles. This in-plane transient response is clearly distinct from the features associated with superconducting condensation. Therefore, we conclude the out-of-plane transient responses cannot be explained by an equivalent of Josephson tunneling. Notably, those pump-induced terahertz responses remain consistent even when we vary the near-infrared optical pump wavelengths and hole concentrations. Our results provide critical evidence that transient three-dimensional superconductivity cannot be induced by melting the competing stripe orders with pump pulses whose photon energy is much higher than the superconducting gap of cuprates.

We study two-dimensional (2D) droplets of noninteracting electrons in a strong magnetic field, placed in a confining potential with arbitrary shape. Using semiclassical methods adapted to the lowest Landau level, we obtain near-Gaussian energy eigenstates that are localized on level curves of the potential and have a position-dependent height. This one-particle insight allows us to deduce explicit formulas for expectation values of local many-body observables, such as density and current, in the thermodynamic limit. In particular, correlations along the edge are long-ranged and inhomogeneous. As we show, this is consistent with the system’s universal low-energy description as a free 1D chiral conformal field theory of edge modes, known from earlier works in simple geometries. A delicate interplay between radial and angular dependencies of eigenfunctions ultimately ensures that the theory is homogeneous in terms of the canonical angle variable of the potential, despite its apparent inhomogeneity in terms of more naïve angular coordinates. Finally, we propose a scheme to measure the anisotropy by subjecting the droplet to microwave radiation; we compute the corresponding absorption rate and show that it depends on the droplet’s shape and the waves’ polarization. These results, both local and global, are likely to be observable in solid-state systems or quantum simulators of 2D electron gases with a high degree of control on the confining potential.