The effective Lagrangian for Nambu-Goldstone bosons (NGBs) in systems without Lorentz invariance has a novel feature that some of the NGBs are canonically conjugate to each other, hence describing 1 dynamical degree of freedom by two NGB fields. We develop explicit forms of their effective Lagrangian up to the quadratic order in derivatives. We clarify the counting rules of NGB degrees of freedom and completely classify possibilities of such canonically conjugate pairs based on the topology of the coset spaces. Its consequence on the dispersion relations of the NGBs is clarified. We also present simple scaling arguments to see whether interactions among NGBs are marginal or irrelevant, which justifies a lore in the literature about the possibility of symmetry breaking in $1+1$ dimensions.

High pressure provides a powerful means for exploring unconventional superconductivity which appears mostly on the border of magnetism. Here, we report the discovery of pressure-induced heavy-fermion superconductivity up to 2.5 K in the antiferromanget ${\mathrm{CeAu}}_2{\mathrm{Si}}_2$ ($T_N\approx 10\mathrm{K}$). Remarkably, the magnetic and superconducting phases are found to overlap across an unprecedentedly wide pressure interval from 11.8 to 22.3 GPa. Moreover, both the bulk $T_c$ and $T_M$ are strongly enhanced when increasing the pressure from 16.7 to 20.2 GPa. $T_c$ reaches a maximum at a pressure slightly below $p_c\approx 22.5\mathrm{GPa}$, at which magnetic order disappears. Furthermore, the scaling behavior of the resistivity provides evidence for a continuous delocalization of the Ce $4f$ electrons associated with a critical end point lying just above $p_c$. We show that the maximum $T_c$ of ${\mathrm{CeAu}}_2{\mathrm{Si}}_2$ actually occurs at almost the same unit-cell volume as that of ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$ and ${\mathrm{CeCu}}_2{\mathrm{Ge}}_2$, and when the Kondo and crystal-field splitting energies become comparable. Dynamical mean-filed theory calculations suggest that the peculiar behavior in pressurized ${\mathrm{CeAu}}_2{\mathrm{Si}}_2$ might be related to its $\mathrm{Ce}\text{−}4f$ orbital occupancy. Our results not only provide a unique example of the interplay between superconductivity and magnetism, but also underline the role of orbital physics in understanding Ce-based heavy-fermion systems.

A theoretical study describing the coherence properties of near-field Raman scattering in two- and one-dimensional systems is presented. The model is applied to the Raman modes of pristine graphene and graphene edges. Our analysis is based on the tip-enhanced Raman scheme, in which a sharp metal tip located near the sample surface acts as a broadband optical antenna that transfers the information contained in the spatially correlated (but nonpropagating) near field to the far field. The dependence of the scattered signal on the tip-sample separation is explored, and the theory predicts that the signal enhancement depends on the particular symmetry of a vibrational mode. The model can be applied to extract the correlation length $L_{\mathrm{c}}$ of optical phonons from experimentally recorded near-field Raman measurements. The coherence properties of optical phonons have been broadly explored in the time and frequency domains, and the spatially resolved approach presented here provides a complementary methodology for the study of local material properties at the nanoscale.

A distinct electronic structure was observed in the single-layer FeSe which shows surprisingly high-temperature superconductivity over 65 K. Here, we demonstrate that the electronic structure can be explained by the effective strain effect due to substrates. More importantly, we find that this electronic structure can be tuned into robust topological phases from a topologically trivial metallic phase by the spin-orbital interaction and couplings to substrates. The topological phase is robust against any perturbations that preserve the time-reversal symmetry. Our study suggests that nontrivial topology and high-$T_c$ superconductivity can be intertwined in the single FeSe layer to search novel physics.

Weak connections between superconductors or superfluids can differ from classical links due to quantum coherence, which allows flow without resistance. Transport properties through such weak links can be described with a single function, the current-phase relationship, which serves as the quantum analog of the current-voltage relationship. Here, we present a technique for inteferometrically measuring the current-phase relationship of superfluid weak links. We interferometrically measure the phase gradient around a ring-shaped superfluid Bose-Einstein condensate containing a rotating weak link, allowing us to identify the current flowing around the ring. While our Bose-Einstein condensate weak link operates in the hydrodynamic regime, this technique can be extended to all types of weak links (including tunnel junctions) in any phase-coherent quantum gas. Moreover, it can also measure the current-phase relationships of excitations. Such measurements may open new avenues of research in quantum transport.

We study the properties of a quantum dot coupled to a topological superconductor and a normal lead and discuss the interplay between Kondo-and Majorana-induced couplings in quantum dots. The latter appears due to the presence of Majorana zero-energy modes localized, for example, at the ends of the one-dimensional superconductor. We investigate the phase diagram of the system as a function of Kondo and Majorana interactions using a renormalization-group analysis, a slave-boson mean-field theory, and numerical simulations using the density-matrix renormalization-group method. We show that, in addition to the well-known Kondo fixed point, the system may flow to a new fixed point controlled by the Majorana-induced coupling, which is characterized by nontrivial correlations between a localized spin on the dot and the fermion parity of the topological superconductor and the normal lead. We compute several measurable quantities, such as differential tunneling conductance and impurity-spin susceptibility, which highlight some peculiar features characteristic to the Majorana fixed point.

We propose a construction of a cholesteric pitch axis for an arbitrary nematic director field as an eigenvalue problem. Our definition leads to a Frenet-Serret description of an orthonormal triad determined by this axis, the director, and the mutually perpendicular direction. With this tool, we are able to compare defect structures in cholesterics, biaxial nematics, and smectics. Though they all have similar ground state manifolds, the defect structures are different and cannot, in general, be translated from one phase to the other.

In topologically ordered quantum states of matter in $(2+1)\mathrm{D}$ (spacetime dimensions), the braiding statistics of anyonic quasiparticle excitations is a fundamental characterizing property that is directly related to global transformations of the ground-state wave functions on a torus (the modular transformations). On the other hand, there are theoretical descriptions of various topologically ordered states in $(3+1)\mathrm{D}$, which exhibit both pointlike and looplike excitations, but systematic understanding of the fundamental physical distinctions between phases, and how these distinctions are connected to quantum statistics of excitations, is still lacking. One main result of this work is that the three-dimensional generalization of modular transformations, when applied to topologically ordered ground states, is directly related to a certain braiding process of looplike excitations. This specific braiding surprisingly involves three loops simultaneously, and can distinguish different topologically ordered states. Our second main result is the identification of the three-loop braiding as a process in which the worldsheets of the three loops have a nontrivial triple linking number, which is a topological invariant characterizing closed two-dimensional surfaces in four dimensions. In this work, we consider realizations of topological order in $(3+1)\mathrm{D}$ using cohomological gauge theory in which the loops have Abelian statistics and explicitly demonstrate our results on examples with $Z_2\times Z_2$ topological order.

Recent developments have led to an explosion of activity on skyrmions in three-dimensional (3D) chiral magnets. Experiments have directly probed these topological spin textures, revealed their nontrivial properties, and led to suggestions for novel applications. However, in 3D the skyrmion crystal phase is observed only in a narrow region of the temperature-field phase diagram. We show here, using a general analysis based on symmetry, that skyrmions are much more readily stabilized in two-dimensional (2D) systems with Rashba spin-orbit coupling. This enhanced stability arises from the competition between field and easy-plane magnetic anisotropy and results in a nontrivial structure in the topological charge density in the core of the skyrmions. We further show that, in a variety of microscopic models for magnetic exchange, the required easy-plane anisotropy naturally arises from the same spin-orbit coupling that is responsible for the chiral Dzyaloshinskii-Moriya interactions. Our results are of particular interest for 2D materials like thin films, surfaces, and oxide interfaces, where broken surface-inversion symmetry and Rashba spin-orbit coupling naturally lead to chiral exchange and easy-plane compass anisotropy. Our theory gives a clear direction for experimental studies of 2D magnetic materials to stabilize skyrmions over a large range of magnetic fields down to $T=0$.

Impurities and defects frequently govern materials properties, with the most prominent example being the doping of bulk semiconductors where a minute amount of foreign atoms can be responsible for the operation of the electronic devices. Several computational schemes based on a supercell approach have been developed to get insights into types and equilibrium concentrations of point defects, which successfully work in bulk materials. Here, we show that many of these schemes cannot directly be applied to two-dimensional (2D) systems, as formation energies of charged point defects are dominated by large spurious electrostatic interactions between defects in inhomogeneous environments. We suggest two approaches that solve this problem and give accurate formation energies of charged defects in 2D systems in the dilute limit. Our methods, which are applicable to all kinds of charged defects in any 2D system, are benchmarked for impurities in technologically important $h$-BN and ${\mathrm{MoS}}_2$ 2D materials, and they are found to perform equally well for substitutional and adatom impurities.

Here, we report the experimental observation of a dynamical quantum phase transition in a strongly interacting open photonic system. The system studied, comprising a Jaynes-Cummings dimer realized on a superconducting circuit platform, exhibits a dissipation-driven localization transition. Signatures of the transition in the homodyne signal and photon number reveal this transition to be from a regime of classical oscillations into a macroscopically self-trapped state manifesting revivals, a fundamentally quantum phenomenon. This experiment also demonstrates a small-scale realization of a new class of quantum simulator, whose well-controlled coherent and dissipative dynamics is suited to the study of quantum many-body phenomena out of equilibrium.

Recently, two interesting candidate quantum phases—the chiral spin-density wave state featuring anomalous quantum Hall effect and the $d+id$ superconductor—were proposed for the Hubbard model on the honeycomb lattice at $1/4$ doping. Using a combination of exact diagonalization, density matrix renormalization group, the variational Monte Carlo method, and quantum field theories, we study the quantum phase diagrams of both the Hubbard model and the $t\text{−}J$ model on the honeycomb lattice at $1/4$ doping. The main advantage of our approach is the use of symmetry quantum numbers of ground-state wave functions on finite-size systems (up to 32 sites) to sharply distinguish different quantum phases. Our results show that for $1\lesssim U/t<40$ in the Hubbard model and for $0.1<J/t<0.80(2)$ in the $t\text{−}J$ model, the quantum ground state is either a chiral spin-density wave state or a spin-charge-Chern liquid, but not a $d+id$ superconductor. However, in the $t\text{−}J$ model, upon increasing $J$, the system goes through a first-order phase transition at $J/t=0.80(2)$ into the $d+id$ superconductor. Here, the spin-charge-Chern liquid state is a new type of topologically ordered quantum phase with Abelian anyons and fractionalized excitations. Experimental signatures of these quantum phases, such as tunneling conductance, are calculated. These results are discussed in the context of $1/4$-doped graphene systems and other correlated electronic materials on the honeycomb lattice.

The diversities in crystal structures and ways of doping result in extremely diversified phase diagrams for iron-based superconductors. With angle-resolved photoemission spectroscopy, we have systematically studied the effects of chemical substitution on the electronic structure of various series of iron-based superconductors. Beyond the Fermi-surface alteration that has been reported most often in the past, we found two more extraordinary effects of doping: (1) the site and band dependencies of quasiparticle scattering and, more importantly, (2) the ubiquitous and significant change of electronic correlation by both isovalent and heterovalent dopants in the iron-anion layer. Moreover, we found that the electronic correlation could be suppressed by applying either the chemical pressure or doping electrons but not by doping holes. Together with other findings provided here, these results complete the microscopic picture of the electronic effects of dopants, which facilitates a unified understanding of the diversified phase diagrams and resolutions to many open issues of various iron-based superconductors.

We show how off-resonant light scattering can provide quantitative information on antiferromagnetic ordering of a two-species fermionic atomic gas in a tightly-confined two-dimensional optical lattice. We analyze the emerging magnetic ordering of atoms in the mean-field and in random phase approximations and show how the many-body static and dynamic correlations, evaluated in the standard Feynman-Dyson perturbation series, can be detected in the scattered light signal. The staggered magnetization reveals itself in the magnetic Bragg peaks of the individual spin components. These magnetic peaks, however, can be considerably suppressed in the absence of a true long-range antiferromagnetic order. The light scattered outside the diffraction orders can be collected by a lens with highly improved signal-to-shot-noise ratio when the diffraction maxima are blocked. The collective and single-particle excitations are identified in the spectrum of the scattered light. We find that the spin-conserving and spin-exchanging atomic transitions convey information on density, longitudinal spin, and transverse spin correlations. The different correlations and scattering processes exhibit characteristic angular distribution profiles for the scattered light, and e.g., the diagnostic signal of transverse spin correlations could be separated from the optical response by the scattering direction, frequency, or polarization. We also analyze the detection accuracy by estimating the number of required measurements, constrained by the heating rate that is determined by inelastic light-scattering events. The imaging technique could be extended to the two-species fermionic states in other regions of the phase diagram where the ground-state properties are still not fully understood.

Weyl semimetals are three-dimensional crystalline systems where pairs of bands touch at points in momentum space, termed Weyl nodes, that are characterized by a definite topological charge: the chirality. Consequently, they exhibit the Adler-Bell-Jackiw anomaly, which in this condensed-matter realization implies that the application of parallel electric ($\mathbf{E}$) and magnetic ($\mathbf{B}$) fields pumps electrons between nodes of opposite chirality at a rate proportional to $\mathbf{E}·\mathbf{B}$. We argue that this pumping is measurable via nonlocal transport experiments, in the limit of weak internode scattering. Specifically, we show that as a consequence of the anomaly, applying a local magnetic field parallel to an injected current induces a valley imbalance that diffuses over long distances. A probe magnetic field can then convert this imbalance into a measurable voltage drop far from source and drain. Such nonlocal transport vanishes when the injected current and magnetic field are orthogonal and therefore serves as a test of the chiral anomaly. We further demonstrate that a similar effect should also characterize Dirac semimetals—recently reported to have been observed in experiments—where the coexistence of a pair of Weyl nodes at a single point in the Brillouin zone is protected by a crystal symmetry. Since the nodes are analogous to valley degrees of freedom in semiconductors, the existence of the anomaly suggests that valley currents in three-dimensional topological semimetals can be controlled using electric fields, which has potential practical “valleytronic” applications.

We study the ground state of $N$ weakly interacting electrons (with $N\le 10$) in a two-dimensional parabolic quantum dot with strong Rashba spin-orbit coupling. Using dimensionless parameters for the Coulomb interaction $\lambda \lesssim 1$ and the Rashba coupling $\alpha \gg 1$, the low-energy physics is characterized by an almost flat single-particle dispersion. From an analytical approach for $\alpha \to \infty$ and $N=2$, and from numerical exact-diagonalization and Hartree-Fock calculations, we find a transition from a conventional unmagnetized ground state (for $\lambda <{\lambda }_c$) to an orbital ferromagnet (for $\lambda >{\lambda }_c$), with a large magnetization and a circulating charge current. We show that the critical interaction strength ${\lambda }_c={\lambda }_c(\alpha ,N)$ vanishes in the limit $\alpha \to \infty$.

On theoretical grounds, we show that orbital domain walls (ODWs), which are known to exist in the charge and orbital ordered layered manganite ${\mathrm{LaSr}}_2{\mathrm{Mn}}_2{\mathrm{O}}_7$, should be partially charged as a result of competition between orbital-induced strain and Coulomb repulsion. This unexpected result provides the necessary condition for the known thermodynamic stability of these ODWs, which are unlike the more typical domain walls that arise only from an external field. We offer experimental data consistent with this theoretical framework through a combined transport and x-ray-diffraction study. In particular, our transport data on this charge and orbital ordered manganite exhibit abrupt transformations to higher conductance at a threshold electric field. As transport phenomena closely resemble effects found for sliding charge-density waves (SCDWs) in pseudo-one-dimensional (1D) materials, a SCDW along such pseudo-1D ODWs provides a natural explanation of our data. Importantly, x-ray-diffraction data eliminate heating and melting of charge order as tenable alternative explanations of our data.

Inspired by the recent demonstration that ${\mathrm{Ca}}_2\mathrm{N}$ is a two-dimensional electride in which electrons near the Fermi level float between ionic layers, we have conducted a systematic search for 2D electrides by an approach combining crystal structure databases and ab initio electronic structure calculations. Starting from a set of working hypotheses, we have identified six 2D metallic electrides, of which one is nonmagnetic and five are nearly ferromagnetic ferrimagnets with a distinct spin texture. The latter five materials are the first magnetic electrides reported at ambient pressure.

Physics and information are intimately connected, and the ultimate information processing devices will be those that harness the principles of quantum mechanics. Many physical systems have been identified as candidates for quantum information processing, but none of them are immune from errors. The challenge remains to find a path from the experiments of today to a reliable and scalable quantum computer. Here, we develop an architecture based on a simple module comprising an optical cavity containing a single negatively charged nitrogen vacancy center in diamond. Modules are connected by photons propagating in a fiber-optical network and collectively used to generate a topological cluster state, a robust substrate for quantum information processing. In principle, all processes in the architecture can be deterministic, but current limitations lead to processes that are probabilistic but heralded. We find that the architecture enables large-scale quantum information processing with existing technology.