In classes of Weyl semimetals where the symmetry protects nodes with higher than unit charge, the nematic Weyl liquid appears as interactions destroy this underlying symmetry. In the symmetry-broken phase, the multiple-charge nodes are split into objects of unit charge, the position of which in momentum space is determined by the nematic order parameter. We examine the phenomenology of this phase, focusing on topological edge states and Landau levels. We find that the symmetry-broken phase itself, as well as the orientation of the nematic order are identifiable from the resulting edge states. We also find that the nematic order couples to an in-plane magnetic field, indicating that it can be controlled in situ via an external field. Finally, we provide an estimate for the critical coupling where spontaneous symmetry breaking occurs for contact interaction.

${\mathrm{Nb}}_3\mathrm{Sn}$ film coatings have the potential to drastically improve the accelerating performance of Nb superconducting radiofrequency (SRF) cavities in next-generation linear particle accelerators. Unfortunately, persistent ${\mathrm{Nb}}_3\mathrm{Sn}$ stoichiometric material defects formed during fabrication limit the cryogenic operating temperature and accelerating gradient by nucleating magnetic vortices that lead to premature cavity quenching. The SRF community currently lacks a predictive model that can explain the impact of chemical and morphological properties of ${\mathrm{Nb}}_3\mathrm{Sn}$ defects on vortex nucleation and maximum accelerating gradients. Both experimental and theoretical studies of the material and superconducting properties of the first 100 nm of ${\mathrm{Nb}}_3\mathrm{Sn}$ surfaces are complicated by significant variations in the volume distribution and topography of stoichiometric defects. This work contains a coordinated experimental study with supporting simulations to identify how the observed chemical composition and morphology of certain Sn-rich and Sn-deficient surface defects can impact the SRF performance. ${\mathrm{Nb}}_3\mathrm{Sn}$ films were prepared with varying degrees of stoichiometric defects, and the film surface morphologies were characterized. Both Sn-rich and Sn-deficient regions were identified in these samples. For Sn-rich defects, we focus on elemental Sn islands that are partially embedded into the ${\mathrm{Nb}}_3\mathrm{Sn}$ film. Using finite element simulations of the time-dependent Ginzburg-Landau equations, we estimate vortex nucleation field thresholds at Sn islands of varying size, geometry, and embedment. We find that these islands can lead to significant SRF performance degradation that could not have been predicted from the ensemble stoichiometry alone. For Sn-deficient ${\mathrm{Nb}}_3\mathrm{Sn}$ surfaces, we experimentally identify a periodic nanoscale surface corrugation that likely forms because of extensive Sn loss from the surface. Simulation results show that the surface corrugations contribute to the already substantial drop in the vortex nucleation field of Sn-deficient ${\mathrm{Nb}}_3\mathrm{Sn}$ surfaces. This work provides a systematic approach for future studies to further detail the relationship between experimental ${\mathrm{Nb}}_3\mathrm{Sn}$ growth conditions, stoichiometric defects, geometry, and vortex nucleation. These findings have technical implications that will help guide improvements to ${\mathrm{Nb}}_3\mathrm{Sn}$ fabrication procedures. Our outlined experiment-informed theoretical methods can assist future studies in making additional key insights about ${\mathrm{Nb}}_3\mathrm{Sn}$ stoichiometric defects that will help build the next generation of SRF cavities and support related superconducting materials development efforts.

The saddle point (Van Hove singularity) exhibits a divergent density of states in two-dimensional systems, leading to fascinating phenomena such as strong correlations and unconventional superconductivity, yet it is seldom observed in three-dimensional (3D) systems. In this work we find two types of 3D higher-order saddle points (HOSPs) in emerging 3D kagome metals ${\mathrm{YbCo}}_6{\mathrm{Ge}}_6$ and ${\mathrm{MgCo}}_6{\mathrm{Ge}}_6$. Both HOSPs exhibit a singularity in their density of states, which is significantly enhanced compared to the ordinary saddle point. The HOSP near the Fermi energy generates a flatband extending a large area in the Brillouin zone, potentially amplifying the correlation effect and fostering electronic instabilities. Two types of HOSPs exhibit distinct robustness upon element substitution and lattice distortions in these kagome compounds. Our work paves the way for engineering exotic band structures, such as saddle points and flatbands, and exploring interesting phenomena in Co-based kagome materials.

Controlling the flow of energy and heat at the microscale is crucial to achieve energy-efficient quantum technologies, for on-chip thermal management, and to realize quantum heat engines and refrigerators. Yet, the efficiency of current quantum technologies is affected by thermal noise, and efficient cooling of quantum devices remains challenging in various solid-state implementations such as superconducting circuits. Collective effects, such as the Dicke superradiant emission, have been exploited to enhance the performance of quantum devices. However, the inherently transient nature of Dicke superradiant emission raises questions about its impact on steady-state properties. Here, we study how to enhance the steady-state heat current flowing between a hot bath and a cold bath through an ensemble of $N$ qubits, that are collectively coupled to the thermal baths. Remarkably, we find a regime where the heat current scales quadratically with $N$ in a finite-size scenario. Conversely, when approaching the thermodynamic limit, we prove that the collective scenario exhibits a parametric enhancement over the noncollective case. We then consider the presence of a third uncontrolled parasitic bath, interacting locally with each qubit, that models unavoidable couplings to the external environment. Despite having a nonperturbative effect on the steady-state currents, we show that the collective enhancement is robust to such an addition. Finally, we discuss the feasibility of realizing such a Dicke heat valve with superconducting circuits. Our findings indicate that in a minimal realistic experimental setting with two superconducting qubits, the collective advantage offers an enhancement of approximately $10\%$ compared to the noncollective scenario.

Isospectrality is a general fundamental concept often involving whether various operators can have identical spectra, i.e., the same set of eigenvalues. In the context of the Laplacian operator, the famous question “Can one hear the shape of a drum?” concerns whether different shaped drums can have the same vibrational modes. The isospectrality of a lattice in $d$-dimensional Euclidean space ${\mathbb{R}}^d$ is a tantamount to whether it is uniquely determined by its theta series, i.e., the radial distribution function $g_2\left(r\right)$. While much is known about the isospectrality of Bravais lattices across dimensions, little is known about this question of more general crystal (periodic) structures with an $n$-particle basis ($n\ge 2$). Here, we ask what is $n_{\text{min}}\left(d\right)$, the minimum value of $n$ for inequivalent (i.e., unrelated by isometric symmetries) crystals with the same theta function in space dimension $d$? To answer these questions, we use rigorous methods as well as a precise numerical algorithm that enables us to determine the minimum multiparticle basis of inequivalent isospectral crystals. Our algorithm identifies isospectral four-, three- and two-particle bases in one, two, and three spatial dimensions, respectively. For many of these isospectral crystals, we rigorously show that they indeed possess identically the same $g_2\left(r\right)$'s for all values of $r$. Based on our analyses, we conjecture that $n_{\text{min}}\left(d\right)=4$, 3, 2 for $d=1$, 2, 3, respectively. The identification of isospectral crystals enables one to study the degeneracy of the ground-state under the action of isotropic pair potentials. Indeed, using inverse statistical-mechanical techniques, we find an isotropic pair potential whose low-temperature configurations in two dimensions obtained via simulated annealing can lead to both of two isospectral crystal structures with $n=3$, the proportion of which can be controlled by the cooling rate. Our findings provide general insights into the structural and ground-state degeneracies of crystal structures as determined by radial pair information.

We perform an extended numerical search for practical fermion-to-qubit encodings with error-correcting properties. Ideally, encodings should strike a balance between a number of the seemingly incompatible attributes, such as having a high minimum distance, low-weight fermionic logical operators, a small qubit to fermionic mode ratio and a simple qubit connectivity graph including ancilla qubits for the measurement of stabilizers. Our strategy consists of a three-step procedure in which we: First generate encodings with code distances up to $d\le 4$ by a brute-force enumeration technique; subsequently, we use these encodings as starting points and apply Clifford deformations to them which allows us to identify higher-distance codes with $d\le 7$; finally, we optimize the hardware connectivity graphs of resulting encodings in terms of the graph thickness and the number of connections per qubit. We report multiple promising high-distance encodings which significantly improve the weights of stabilizers and logical operators compared to previously reported alternatives.

We present a Floquet framework for controlling topological features of a one-dimensional optical lattice system with dual-mode resonant driving, in which both the amplitude and phase of the lattice potential are modulated simultaneously. We investigate a three-band model consisting of the three lowest orbitals and elucidate the formation of a crosslinked two-leg ladder through an indirect interband coupling via an off-resonant band. We numerically demonstrate the emergence of topologically nontrivial bands within the driven system, and a topological charge pumping phenomenon with cyclic parameter changes in the dual-mode resonant driving. Finally, we show that the band topology in the driven three-band system is protected by parity-time reversal symmetry.

Among vortex structures identified so far in superfluid ${}^3\mathrm{He}\text{−}\mathrm{B}$, the most common are the A-phase-core and double-core vortices. According to earlier numerical calculations, the double-core vortex is energetically favored nearly everywhere in the $p\text{−}T$ phase diagram. Nevertheless, in experiments, the A-phase-core vortex has been observed down to temperatures of $0.6T_{\mathrm{c}}$ at high pressures. We use the Ginzburg-Landau formalism to calculate the energies of the two vortex structures in the experimentally relevant magnetic field as well as the energy barrier for the transition between the two structures. Assigning vanishing barrier as the boundary of the metastability region of the A-phase-core vortex, we reproduce the experimentally measured vortex phase diagram and provide an explanation for the reappearance of the double-core vortex near the critical temperature $T_{\mathrm{c}}$ at low pressures: the difference in Zeeman energy between the two vortex structures becomes relatively more important close to $T_{\mathrm{c}}$, and the A-phase-core vortex becomes unstable. In contrast to the equilibrium vortex structures, we suggest that the vortex nucleation process favors the A-phase-core vortex over the double-core vortex. Our approach can be used to analyze competition between different vortex structures in other unconventional superfluids and superconductors.

We employ ab initio electronic-structure calculations to investigate the charge-density waves and periodic lattice distortions in bilayer $2\mathrm{H}\text{−}{\mathrm{NbSe}}_2$. We demonstrate that the vertical stacking can give rise to a variety of patterns that may lower the symmetry of the charge-density waves exhibited separately by the two composing $1\mathrm{H}\text{−}{\mathrm{NbSe}}_2$ monolayers. The general tendency to a spontaneous symmetry breaking observed in the ground state and the first excited states is shown to originate from a non-negligible interlayer coupling. Simulated images for scanning tunneling microscopy as well as geometric structure factors show signatures of the different stacking orders. This may not only be useful to reinterpret past experiments on surfaces and thin films, but it may also be exploited to devise ad hoc experiments for the investigation of the stacking order in $2\mathrm{H}\text{−}{\mathrm{NbSe}}_2$. We anticipate that our analysis not only applies to the $2\mathrm{H}\text{−}{\mathrm{NbSe}}_2$, but is also relevant for thin films and bulk, whose smallest centrosymmetric component is indeed the bilayer. Finally, our results illustrate clearly that the vertical stacking is not only important for 1T structures, as exemplified by the metal-to-insulator transition observed in $1\mathrm{T}\text{−}{\mathrm{TaS}}_2$, but seems to be a general feature of metallic layered transition metal dichalcogenides as well.

We investigate the topological phases and corresponding edge states in silicene with fixed intrinsic and extrinsic Rashba spin-orbit couplings. The results show that silicene can exhibit four distinct topological phases, such as two types of valley-polarized quantum anomalous Hall effect (QAHE) and two types of QAHE that can be effectively controlled by the exchange field and electric field. In addition, these topological phases only correspond to the valley edge states distributed at the boundary of silicene. In particular, when the off-resonant circularly polarized (ORCP) light is further considered, silicene can host richer topological phases that are characterized by the Chern numbers from $C=-3$ to $C=3$, where the corresponding mixed edge states—where the valley and nonvalley edge states could coexist—can remarkably appear. More interestingly, the special higher Chern numbers $C=\pm 3$ determine two valley edge states and one nonvalley edge state, with the right-moving or left-moving direction. These peculiar edge states are attributed to the ORCP light destroying the collapse of the Dirac cones that the valley edge states bridge. Additionally, silicene can experience multiple edge-state transitions for identical Chern numbers $C=\pm 2$ between the valley edge state, nonvalley edge state, and two types of mixed edge state, under the ORCP light. This work may provide a platform and point of view for investigating other forms of topological edge state and is beneficial for designing multifunctional topological devices.

We propose a loop optimization algorithm based on nuclear norm regularization for the tensor network. The key ingredient of this scheme is to introduce a rank penalty term proposed in the context of data processing. Compared to the standard variational periodic matrix product states method, this algorithm can circumvent the local minima related to short-ranged correlation in a simpler fashion. We demonstrate its performance when used as a part of the tensor network renormalization algorithms [S. Yang, Z.-C. Gu, and X.-G. Wen, Phys. Rev. Lett. 118, 110504 (2017)] for the critical two-dimensional Ising model. The scale invariance of the renormalized tensors is attained with higher accuracy while the higher parts of the scaling dimension spectrum are obtained in a more stable fashion.

We simulate the dynamics of Rydberg atoms resonantly exchanging energy via two-, three-, and four-body dipole-dipole interactions in a one-dimensional array. Using simplified models of a realistic experimental system, we study the initial-state survival probability, mean level spacing, spread of entanglement, and properties of the energy eigenstates. By exploring a range of disorders and interaction strengths, we find regions in parameter space where the three- and four-body dynamics either fail to thermalize or do so slowly. The interplay between the stronger hopping and weaker field-tuned interactions gives rise to quantum many-body scar states, which play a critical role in slowing the dynamics of the three- and four-body interactions.

Water ice, an archetypal molecular system, exhibits a complex phase diagram characterized by numerous phase transitions under varying pressure-temperature conditions. However, it remains a significant challenge to theoretical modeling of these transitions owing to the high dimensionality in representing the potential energy landscapes (PEL) of ice crystalline phases. In an attempt to deeply understand the mechanisms of phase transitions between ice VII, VIII, and X, a graph-based stationary-point network was employed to simplify the representation of the PEL and locally constructed the PEL of ice at different pressures by our developed high-index saddle dynamic scheme. The stationary-point networks at 40 and 80 GPa indicate a pronounced flattened PEL of ice over a wide range of pressure (up to at least 80 GPa), where multiple structures (i.e., local minima) are energetically degenerate with phase VIII and separated by low-energy barriers ($\sim 10$ meV/atom at 40 GPa). These features indicate the disordered VII phase is more favorable at finite temperatures, in agreement with previous experimental observations. Additionally, we demonstrated that the PEL topology undergoes a fundamental alteration at higher pressures, with a single funnel emerging at 120 GPa, facilitating the crystallization of phase X. This work serves as a proof of concept for using the stationary-point network to explicitly represent the PEL, highlighting their potential in elucidating complex phase transitions.

The recent discovery of a variety of intricate electronic order in kagome metals has sprouted significant theoretical and experimental interest. From an electronic perspective on the potential microscopic origin of these phases, the most basic model is given by a Hubbard model on the kagome lattice. We employ a functional renormalization group (FRG) to analyze the kagome Hubbard model. Through our methodological refinement of FRG both within its $N$-patch and truncated unity formulation, we resolve previous discrepancies of different FRG approaches [Wang et al., Phys. Rev. B 87, 115135 (2013) vs Kiesel et al., Phys. Rev. Lett. 110, 126405 (2013)], and analyze both the pure ($p$-type) and mixed ($m$-type) van Hove fillings of the kagome lattice.