We propose a new type of quantum liquids, dubbed Stiefel liquids, based on ($2+1$)-dimensional nonlinear sigma models on target space $SO(N)/SO(4)$, supplemented with Wess-Zumino-Witten terms. We argue that the Stiefel liquids form a class of critical quantum liquids with extraordinary properties, such as large emergent symmetries, a cascade structure, and nontrivial quantum anomalies. We show that the well-known deconfined quantum critical point and $U(1)$ Dirac spin liquid are unified as two special examples of Stiefel liquids, $N=5$ and $N=6$, respectively. Furthermore, we conjecture that Stiefel liquids with $N>6$ are non-Lagrangian, in the sense that under renormalization group they flow to infrared (conformally invariant) fixed points that cannot be described by any renormalizable continuum Lagrangian. Such non-Lagrangian states are beyond the paradigm of parton gauge mean-field theory familiar in the study of exotic quantum liquids in condensed matter physics. The intrinsic absence of (conventional or partonlike) mean-field construction also means that, within the traditional approaches, will be difficult to decide whether a non-Lagrangian state can actually emerge from a specific UV system (such as a lattice spin system). For this purpose we hypothesize that a quantum state is emergible from a lattice system if its quantum anomalies match with the constraints from the (generalized) Lieb-Schultz-Mattis theorems. Based on this hypothesis, we find that some of the non-Lagrangian Stiefel liquids can indeed be realized in frustrated quantum spin systems, for example, on triangular or kagome lattice, through the intertwinement between noncoplanar magnetic orders and valence-bond-solid orders.

Quasi-one-dimensional (1D) materials provide a superior platform for characterizing and tuning topological phases for two reasons: (i) existence for multiple cleavable surfaces that enables better experimental identification of topological classification and (ii) stronger response to perturbations such as strain for tuning topological phases compared to higher dimensional crystal structures. In this paper, we present experimental evidence for a room-temperature topological phase transition in the quasi-1D material ${\mathrm{Bi}}_4{\mathrm{I}}_4$, mediated via a first-order structural transition between two distinct stacking orders of the weakly coupled chains. Using high-resolution angle-resolved photoemission spectroscopy on the two natural cleavable surfaces, we identify the high-temperature $\beta$ phase to be the first weak topological insulator with two gapless Dirac cones on the (100) surface and no Dirac crossing on the (001) surface, while in the low-temperature $\alpha$ phase, the topological surface state on the (100) surface opens a gap, consistent with a recent theoretical prediction of a higher-order topological insulator beyond the scope of the established topological materials databases that hosts gapless hinge states. Our results not only identify a rare topological phase transition between first-order and second-order topological insulators but also establish a novel quasi-1D material platform for exploring unprecedented physics.

Low-magnetic-field scanning tunneling spectroscopy of individual Abrikosov vortices in heavily overdoped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ unveils a clear $d$-wave electronic structure of the vortex core, with a zero-bias conductance peak at the vortex center that splits with increasing distance from the core. We show that previously reported unconventional electronic structures, including the low-energy checkerboard charge order in the vortex halo and the absence of a zero-bias conductance peak at the vortex center, are direct consequences of short intervortex distance and consequent vortex-vortex interactions prevailing in earlier experiments.

Electron spins are amongst the most coherent solid-state systems known. However, to be used in devices for quantum sensing and information processing applications, they must typically be placed near interfaces. Understanding and mitigating the impacts of such interfaces on the coherence and spectral properties of electron spins is critical to realizing such applications, but it is also challenging: Inferring such data from single-spin studies requires many measurements to obtain meaningful results, while ensemble measurements typically give averaged results that hide critical information. Here, we report a comprehensive study of the coherence of near-surface bismuth donor spins in 28-silicon at millikelvin temperatures. In particular, we use strain-induced frequency shifts caused by a metallic electrode to infer spatial maps of spin coherence as a function of position relative to the electrode. By measuring magnetic-field-insensitive clock transitions, we separate magnetic noise caused by surface spins from charge noise. Our results include quantitative models of the strain-split spin resonance spectra and extraction of paramagnetic impurity concentrations at the silicon surface. The interplay of these decoherence mechanisms for such near-surface electron spins is critical for their application in quantum technologies, while the combination of the strain splitting and clock transition extends the coherence lifetimes by up to 2 orders of magnitude, reaching up to 300 ms at a mean depth of only 100 nm. The technique we introduce here to spatially map coherence in near-surface ensembles is directly applicable to other spin systems of active interest, such as defects in diamond, silicon carbide, and rare earth ions in optical crystals.

We study theoretically the nonlinear optical response of Tomonaga-Luttinger spin liquid in the context of terahertz (THz) two-dimensional coherent spectroscopy (2DCS). Using the gapless phase of the $XXZ$-type spin chain as an example, we show that its third-order nonlinear magnetic susceptibilities ${\chi }_{+--+}^{(3)}$ and ${\chi }_{-++-}^{(3)}$ exhibit photon echo, where $\pm$ refers to the left- or right-hand circular polarization with respect to the $S^z$ axis. The photon echo arises from a “lensing” phenomenon in which the wave packets of fractional excitations move apart and then come back toward each other, amounting to a refocusing of the excitations’ world lines. Renormalization-group-irrelevant corrections to the fixed-point Hamiltonian result in dispersion and/or damping of the wave packets, which can be sensitively detected by lensing and consequently the photon echo. Our results thus unveil the strength of THz 2DCS in probing the dynamical properties of the collective excitations in a prototypical gapless many-body system.

Transition-metal dichalcogenide heterobilayers offer attractive opportunities to realize lattices of interacting bosons with several degrees of freedom. Such heterobilayers can feature moiré patterns that modulate their electronic band structure, leading to spatial confinement of single interlayer excitons (IXs) that act as quantum emitters with $C_3$ symmetry. However, the narrow emission linewidths of the quantum emitters contrast with a broad ensemble IX emission observed in nominally identical heterobilayers, opening a debate regarding the origin of IX emission. Here we report the continuous evolution from a few trapped IXs to an ensemble of IXs with both triplet- and singlet-spin configurations in a gate-tunable $2H\text{−}{\mathrm{MoSe}}_2/{\mathrm{WSe}}_2$ heterobilayer. We observe signatures of dipolar interactions in the IX ensemble regime which, when combined with magneto-optical spectroscopy, reveal that the narrow quantum-dot-like and broad ensemble emission originate from IXs trapped in moiré potentials with the same atomic registry. Finally, electron doping leads to the formation of three different species of localized negative trions with contrasting spin-valley configurations, among which we observe both intervalley and intravalley IX trions with spin-triplet optical transitions. Our results identify the origin of IX emission in ${\mathrm{MoSe}}_2/{\mathrm{WSe}}_2$ heterobilayers and highlight the important role of exciton-exciton interactions and Fermi-level control in these highly tunable quantum materials.

The discovery of Weyl semimetals (WSMs) has fueled tremendous interest in condensed matter physics. The realization of WSMs requires the breaking of either inversion symmetry (IS) or time-reversal symmetry (TRS). WSMs can be categorized into type-I and type-II WSMs, which are characterized by untilted and strongly tilted Weyl cones, respectively. Type-I WSMs with breaking of either IS or TRS and type-II WSMs with solely broken IS have been realized experimentally, but a TRS-breaking type-II WSM still remains elusive. In this article, we report transport evidence for a TRS-breaking type-II WSM observed in the intrinsic antiferromagnetic topological insulator $\mathrm{Mn}{({\mathrm{Bi}}_{1-x}{\mathrm{Sb}}_x)}_2{\mathrm{Te}}_4$ under magnetic fields. This state is manifested by the electronic structure transition caused by the spin-flop transition. The transition results in an intrinsic anomalous Hall effect and negative $c$-axis longitudinal magnetoresistance attributable to the chiral anomaly in the ferromagnetic phases of lightly hole-doped samples. Our results establish a promising platform for exploring the underlying physics of the long-sought, ideal TRS-breaking type-II WSM.

Weakly coupled ferroelectric/dielectric superlattice thin-film heterostructures exhibit complex nanoscale polarization configurations that arise from a balance of competing electrostatic, elastic, and domain-wall contributions to the free energy. A key feature of these configurations is that the polarization can locally have a significant component that is along the thin-film surface normal direction with an overall configuration maintaining zero net in-plane polarization. ${\mathrm{PbTiO}}_3/{\mathrm{SrTiO}}_3$ thin-film superlattice heterostructures on a conducting ${\mathrm{SrRuO}}_3$ bottom electrode on ${\mathrm{SrTiO}}_3$ have a room-temperature stripe nanodomain pattern with a nanometer-scale lateral period. Ultrafast time-resolved x-ray free electron laser diffraction and scattering experiments reveal that above-bandgap optical pulses induce propagating acoustic pulses and a perturbation of the domain diffuse scattering intensity arising from the nanoscale stripe domain configuration. With 400-nm optical excitation, two separate acoustic pulses are observed: a high-amplitude pulse resulting from strong optical absorption in the bottom electrode and a weaker pulse arising from the depolarization-field-screening effect due to absorption directly within the superlattice. The picosecond scale variation of the nanodomain diffuse scattering intensity is consistent with a larger polarization change than would be expected due to the polarization-tetragonality coupling of uniformly polarized ferroelectrics. The polarization change is consistent, instead, with polarization rotation facilitated by the reorientation of the in-plane component of the polarization at the domain boundaries of the striped polarization structure. The complex steady-state configuration within these ferroelectric heterostructures leads to ultrafast polarization rotation phenomena that have previously been available only through the selection of bulk crystal composition.

Fluid dynamics is one of the cornerstones of modern physics and has recently found applications in the transport of electrons in solids. In most solids, electron transport is dominated by extrinsic factors, such as sample geometry and scattering from impurities. However, in the hydrodynamic regime, Coulomb interactions transform the electron motion from independent particles to the collective motion of a viscous “electron fluid.” The fluid viscosity is an intrinsic property of the electron system, determined solely by the electron-electron interactions. Resolving the universal intrinsic viscosity is challenging, as it affects the resistance only through interactions with the sample boundaries, whose roughness not only is unknown but also varies from device to device. Here, we eliminate all unknown parameters by fabricating samples with smooth sidewalls to achieve the perfect slip boundary condition, which has been elusive in both molecular fluids and electronic systems. We engineer the device geometry to create viscous dissipation and reveal the true intrinsic hydrodynamic properties of a 2D system. We observe a clear transition from ballistic to hydrodynamic electron motion, driven by both temperature and magnetic field. We directly measure the viscosity and electron-electron scattering lifetime (the Fermi quasiparticle lifetime) over a wide temperature range without fitting parameters and show they have a strong dependence on electron density that cannot be explained by conventional theories based on the random phase approximation.

Mechanical oscillators have been demonstrated with very high quality factors over a wide range of frequencies. They also couple to a wide variety of fields and forces, making them ideal as sensors. The realization of a mechanically based quantum bit could therefore provide an important new platform for quantum computation and sensing. Here, we show that by coupling one of the flexural modes of a suspended carbon nanotube to the charge states of a double quantum dot defined in the nanotube, it is possible to induce sufficient anharmonicity in the mechanical oscillator so that the coupled system can be used as a mechanical quantum bit. However, these results can only be achieved when the device enters the ultrastrong coupling regime. We discuss the conditions for the anharmonicity to appear, and we show that the Hamiltonian can be mapped onto an anharmonic oscillator, allowing us to work out the energy level structure and find how decoherence from the quantum dot and the mechanical oscillator is inherited by the qubit. Remarkably, the dephasing due to the quantum dot is expected to be reduced by several orders of magnitude in the coupled system. We outline qubit control, readout protocols, the realization of a CNOT gate by coupling two qubits to a microwave cavity, and finally how the qubit can be used as a static-force quantum sensor.

The transition-metal-based kagome metals provide a versatile platform for correlated topological phases hosting various electronic instabilities. While superconductivity is rare in layered kagome compounds, its interplay with nontrivial topology could offer an engaging space to realize exotic excitations of quasiparticles. Here, we use scanning tunneling microscopy to study a newly discovered $Z_2$ topological kagome metal ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ with a superconducting ground state. We observe charge modulation associated with the opening of an energy gap near the Fermi level. When across single-unit-cell surface step edges, the intensity of this charge modulation exhibits a $\pi$-phase shift, suggesting a three-dimensional $2\times 2\times 2$ charge density wave ordering. Interestingly, while conventional Caroli–de Gennes–Matricon bound states are observed inside the superconducting vortex on the Sb surfaces, a robust zero-bias conductance peak emerges that does not split in a large distance when moving away from the vortex center on the Cs $2\times 2$ surfaces, resembling the Majorana bound states arising from the superconducting Dirac surface states in ${\mathrm{Bi}}_2{\mathrm{Te}}_3/{\mathrm{NbSe}}_2$ heterostructures. Our findings establish ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ as a promising candidate for realizing exotic excitations at the confluence of nontrivial lattice geometry, topology and multiple electronic orders.

Hydrodynamics provides a universal description of interacting quantum field theories at sufficiently long times and wavelengths, but breaks down at scales dependent on microscopic details of the theory. In the vicinity of a quantum critical point, it is expected that some aspects of the dynamics are universal and dictated by properties of the critical point. We use gauge-gravity duality to investigate the breakdown of diffusive hydrodynamics in two low-temperature states dual to black holes with ${\mathrm{AdS}}_2$ horizons, which exhibit quantum critical dynamics with an emergent scaling symmetry in time. We find that the breakdown is characterized by a collision between the diffusive pole of the retarded Green’s function with a pole associated to the ${\mathrm{AdS}}_2$ region of the geometry, such that the local equilibration time is set by infrared properties of the theory. The absolute values of the frequency and wave vector at the collision (${\omega }_{\mathrm{eq}}$ and $k_{\mathrm{eq}}$) provide a natural characterization of all the low-temperature diffusivities $D$ of the states via $D={\omega }_{\mathrm{eq}}/k_{\mathrm{eq}}^2$, where ${\omega }_{\mathrm{eq}}=2\pi \mathrm{\Delta }T$ is set by the temperature $T$ and the scaling dimension $\mathrm{\Delta }$ of an operator of the infrared quantum critical theory. We confirm that these relations are also satisfied in a Sachdev-Ye-Kitaev chain model in the limit of strong interactions. Our work paves the way toward a deeper understanding of transport in quantum critical phases.

A number of experimental platforms relevant for quantum simulations, ranging from arrays of superconducting circuits hosting correlated states of light to ultracold atoms in optical lattices in the presence of controlled dissipative processes, are described as open quantum many-body systems. Their theoretical understanding is hampered by the exponential scaling of their Hilbert space and by their intrinsic nonequilibrium nature, limiting the applicability of many traditional approaches. In this work, we extend the nonequilibrium bosonic dynamical mean-field theory (DMFT) to Markovian open quantum systems. Within DMFT, a Lindblad master equation describing a lattice of dissipative bosonic particles is mapped onto an impurity problem describing a single site embedded in its Markovian environment and coupled to a self-consistent field and to a non-Markovian bath, where the latter accounts for fluctuations beyond Gutzwiller mean-field theory due to the finite lattice connectivity. We develop a nonperturbative approach to solve this bosonic impurity problem, which dresses the impurity, featuring Markovian dissipative channels, with the non-Markovian bath, in a self-consistent scheme based on a resummation of noncrossing diagrams. As a first application of our approach, we address the steady state of a driven-dissipative Bose-Hubbard model with two-body losses and incoherent pump. We show that DMFT captures hopping-induced dissipative processes, completely missed in Gutzwiller mean-field theory, which crucially determine the properties of the normal phase, including the redistribution of steady-state populations, the suppression of local gain, and the emergence of a stationary quantum-Zeno regime. We argue that these processes compete with coherent hopping to determine the phase transition toward a nonequilibrium superfluid, leading to a strong renormalization of the phase boundary at finite connectivity. We show that this transition occurs as a finite-frequency instability, leading to an oscillating-in-time order parameter, that we connect with a quantum many-body synchronization transition of an array of quantum van der Pol oscillators.

Electrons with large kinetic energy have a superconducting instability for infinitesimal attractive interactions. Quenching the kinetic energy and creating a flat band renders an infinitesimal repulsive interaction the relevant perturbation. Thus, flat-band systems are an ideal platform to study the competition of superconductivity and magnetism and their possible coexistence. Recent advances in the field of twisted bilayer graphene highlight this in the context of two-dimensional materials. Two dimensions, however, put severe restrictions on the stability of the low-temperature phases due to enhanced fluctuations. Only three-dimensional flat bands can solve the conundrum of combining the exotic flat-band phases with stable order existing at high temperatures. Here, we present a way to generate such flat bands through strain engineering in topological nodal-line semimetals. We present analytical and numerical evidence for this scenario and study the competition of the arising superconducting and magnetic orders as a function of externally controlled parameters. We show that the order parameter is rigid because the three-dimensional quantum geometry of the Bloch wave functions leads to a large superfluid stiffness in all three directions. Using density-functional theory and numerical tight-binding calculations, we further apply our theory to strained rhombohedral graphite and CaAgP materials.

We present an optimal protocol for encoding an unknown qubit state into a multiqubit Greenberger-Horne-Zeilinger-like state and, consequently, transferring quantum information in large systems exhibiting power-law ($1/r^{\alpha }$) interactions. For all power-law exponents $\alpha$ between $d$ and $2d+1$, where $d$ is the dimension of the system, the protocol yields a polynomial speed-up for $\alpha >2d$ and a superpolynomial speed-up for $\alpha \le 2d$, compared to the state of the art. For all $\alpha >d$, the protocol saturates the Lieb-Robinson bounds (up to subpolynomial corrections), thereby establishing the optimality of the protocol and the tightness of the bounds in this regime. The protocol has a wide range of applications, including in quantum sensing, quantum computing, and preparation of topologically ordered states. In addition, the protocol provides a lower bound on the gate count in digital simulations of power-law interacting systems.

Constructing systems that exhibit timescales much longer than those of the underlying components, as well as emergent dynamical and collective behavior, is a key goal in fields such as synthetic biology and materials self-assembly. Inspiration often comes from living systems, in which robust global behavior prevails despite the stochasticity of the underlying processes. Here, we present two-dimensional stochastic networks that consist of minimal motifs representing out-of-equilibrium cycles at the molecular scale and support chiral edge currents in configuration space. These currents arise in the topological phase because of the bulk-boundary correspondence and dominate the system dynamics in the steady state, further proving robust to defects or blockages. We demonstrate the topological properties of these networks and their uniquely non-Hermitian features such as exceptional points and vorticity, while characterizing the edge-state localization. As these emergent edge currents are associated with macroscopic timescales and length scales, simply tuning a small number of parameters enables varied dynamical phenomena, including a global clock, dynamical growth and shrinkage, and synchronization. Our construction provides a novel topological formalism for stochastic systems and fresh insights into non-Hermitian physics, paving the way for the prediction of robust dynamical states in new classical and quantum platforms.

To fully capitalize on the potential and versatility of resonant inelastic x-ray scattering (RIXS), it is essential to develop the capability to interpret different RIXS contributions through calculations, including the dependence on momentum transfer, from first principles for correlated materials. Toward that objective, we present new methodology for calculating the full RIXS response of a correlated metal in an unbiased fashion. Through comparison of measurements and calculations that tune the incident photon energy over a wide portion of the Fe $L_3$ absorption resonance of the benchmark material ${\mathrm{BaFe}}_2{\mathrm{As}}_2$, we show that the RIXS response in ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ is dominated by the direct-channel contribution, including the Raman-like response below threshold. Calculations are initially performed within the first-principles Bethe-Salpeter equation (BSE) framework, which we then significantly improve by invoking a quasiboson model to describe the secondary excitations within the intermediate state. This enhancement allows the many-electron RIXS signal to be approximated as a convolution of BSE-calculated spectra with effective spectral functions. We construct these spectral functions, also from first principles, by employing the cumulant expansion of the Green’s function and performing a real-time time-dependent density functional theory calculation of the response of the electronic system to the perturbation of the intermediate-state excitation. Importantly, this process allows us to evaluate the indirect RIXS response from first principles, accounting for the full periodicity of the crystal structure and with full dependence on the momentum transfer.

The two main classes of liquid-crystal (LC) phases of rodlike molecules are nematics, where the rods align in the same direction (the nematic director $\mathbf{n}$), and smectics, where the rods not only are aligned but also form layers. The electro-optic effects in LC devices that are a backbone in today’s display industry mainly use the Fréedericksz transition, which is the bulk reorientation of a surface-anchored nematic by an electric field. Conventional (uniaxial) smectics do not present a Fréedericksz transition, because, due to their layered structure, the director reorientation would distort the layers, which would cost too much energy. In a worldwide ongoing effort to extend the variety of LC compounds suitable for applications in the display industry, bent-shaped molecules have recently raised much attention, since they present multiple new LC phases with unusual properties. In this paper, we report on a structural and electro-optic study of the LC phases of a bent-shaped dimer. On cooling from the isotropic liquid, this compound shows a usual nematic ($N$), a twist-bend nematic ($N_{\mathrm{TB}}$), and a biaxial smectic-$A$ phase ($\mathrm{Sm}{A}_b$). Quite surprisingly, contrary to usual smectics, $\mathrm{Sm}{A}_b$ presents a remarkable electro-optic response, with low ($<4\mathrm{V}$) voltage threshold, no reorganization of the smectic layers, and low ($<1\mathrm{ms}$) response time (i.e., 30 times faster than the $N$ phase at higher temperature). We interpret this unexpected electro-optic effect as a Fréedericksz transition affecting the secondary director $\mathbf{m}$ of the $\mathrm{Sm}{A}_b$, and we model it by analogy with the usual Fréedericksz transition of the $\mathbf{n}$ director of the uniaxial $N$ phase. Indeed, a Fréedericksz transition affecting only $\mathbf{m}$ in this biaxial fluid smectic does not alter its layered structure and costs little energy. From the point of view of applications, thanks to its low relaxation time, this “biaxial” Fréedericksz transition could be exploited in electro-optic devices that require fast switching.

Since the discovery of high-temperature superconductivity in cuprates, Josephson junction based phase-sensitive experiments are believed and used to provide the most convincing evidence for determining the pairing symmetry. Regardless of different junction materials and geometries used, quantum tunneling involved in these experiments is essentially a nanoscale process, and thus, actual experimental results are extremely sensitive to atomic details of the junction structures. The situation has led to controversial results as to the nature of the pairing symmetry of cuprates: while in-plane junction experiments generally support $d$-wave pairing symmetry, those based on out-of-plane ($c$-axis) Josephson junctions between two rotated cuprate blocks favor $s$-wave pairing. In this work, we revisit the $c$-axis experiment by fabricating Josephson junctions with atomic-level control in their interface structure. We fabricate over 90 junctions of ultrathin ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+x}$ (BSCCO) flakes by state-of-the-art exfoliation technique and obtain atomically flat junction interfaces in the whole junction regions as characterized by high-resolution transmission electron microscopy. Notably, the resultant uniform junctions at various twist angles all exhibit a single tunneling branch behavior, suggesting that only the first half of a unit cell on both sides of the twisted flakes is involved in the Josephson tunneling process. With such well-defined geometry and structure and the characteristic single tunneling branch, we repeatedly observe Josephson tunneling at a nominal twist angle of 45°, which is against the expectation from a purely $d$-wave pairing scenario. Our results strongly favor the scenario of a persistent $s$-wave order parameter in the junction.

The interplay between thermal and quantum fluctuations controls the competition between phases of matter in strongly correlated electron systems. We study finite-temperature properties of the strongly coupled two-dimensional doped Hubbard model using the minimally entangled typical thermal states method on width-four cylinders. We discover that a phase characterized by commensurate short-range antiferromagnetic correlations and no charge ordering occurs at temperatures above the half-filled stripe phase extending to zero temperature. The transition from the antiferromagnetic phase to the stripe phase takes place at temperature $T/t\approx 0.05$ and is accompanied by a steplike feature of the specific heat. We find the single-particle gap to be smallest close to the nodal point at $\mathit{k}=(\pi /2,\pi /2)$ and detect a maximum in the magnetic susceptibility. These features bear a strong resemblance to the pseudogap phase of high-temperature cuprate superconductors. The simulations are verified using a variety of different unbiased numerical methods in the three limiting cases of zero temperature, small lattice sizes, and half filling. Moreover, we compare to and confirm previous determinantal quantum Monte Carlo results on incommensurate spin-density waves at finite doping and temperature.