We investigate the leading area-law contribution to entanglement entropy in a system described by a general Lagrangian with $O\left(2\right)$ symmetry containing first- and second-order time derivatives, namely, breaking the Lorentz invariance. We establish a connection between the Higgs gap present in a symmetry-broken phase and the area-law term for the entanglement entropy in the general nonrelativistic case. Our predictions for the entanglement entropy and correlation length are successfully compared to numerical results in two paradigmatic systems: the Mott insulator to the superfluid transition for ultracold lattice bosons and the ground state of ferrimagnetic systems.

Multipolar magnetism is an emerging field of quantum materials research. The building blocks of multipolar phenomena are magnetic ions with a non-Kramers doublet, where the orbital and spin degrees of freedom are inextricably intertwined, leading to unusual spin-orbital entangled states. The detection of such subtle forms of matter has, however, been difficult due to a limited number of appropriate experimental tools. In this work, motivated by a recent magnetostriction experiment on ${\mathrm{Pr}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$, we theoretically investigate how multipolar quantum spin ice, an elusive three-dimensional quantum spin liquid, can be detected using magnetostriction, by examining the characteristic signatures of its magnetic-field descendent multipolar kagome ice phase, as well as that of the neighboring multipolar ordered phases in the pyrochlore materials. We provide theoretical results based on classical and/or quantum studies of non-Kramers and Kramers magnetic ions, and contrast the behaviors of distinct phases in both systems. Our work paves an important avenue for future identification of exotic ground states in multipolar systems.

We argue that several empirical constraints strongly restrict parameters of the effective microscopic spin model describing $\alpha \text{−}{\mathrm{RuCl}}_3$. In particular, such constraints dictate a substantial positive off-diagonal anisotropic coupling ${\mathrm{\Gamma }}^{\prime }>0$, not anticipated previously. The renormalization by quantum fluctuations allows to reconcile larger values of the advocated bare parameters with their earlier assessments and provides a consistent description of the field evolution of spin excitations in the paramagnetic phase. We assert that large anisotropic terms inevitably result in strong anharmonic coupling of magnons, necessarily leading to broad features in their spectra due to decays, in accord with the observations in $\alpha \text{−}{\mathrm{RuCl}}_3$. Using duality transformations, we explain the origin of the pseudo-Goldstone mode that is ubiquitous to the studied parameter space and is present in $\alpha \text{−}{\mathrm{RuCl}}_3$. Our analysis offers a description of $\alpha \text{−}{\mathrm{RuCl}}_3$ as an easy-plane ferromagnet with antiferromagnetic further-neighbor and strong off-diagonal couplings, which is in a fluctuating zigzag ground state proximate to an incommensurate phase that is continuously connected to a ferromagnetic one.

How the ground-state nature can be dramatically changed by the distinct underlying spin correlation is a central issue of doped Mott insulators. The two-leg XXZ ladder provides a prototypical spin background, which can be tuned from a long-range Néel order to a short-range spin liquid via the superexchange anisotropy, giving rise to a complex phase diagram at finite doping. By density matrix renormalization group method, we show that although the charge is always self-localized in the Néel ordered phase, a second insulating phase emerges in which the doped holes become paired but remain localized while the transverse spin-spin correlation reduces to short-ranged one to make the Néel order classical. Only when the Néel order totally disappears by further reducing anisotropy does the pairing become truly coherent as characterized by a Luther-Emery state. In sharp contrast, the pairing is totally absent in the in-plane ferromagnetic XXZ regime, where a direct transition from the charge self-localization in the Néel ordered phase to a Fermi-gas-like state in the spin liquid phase is found. A consistent physical picture is briefly discussed.

Skyrmionic textures are being extensively investigated due to the occurrence of novel topological magnetic phenomena, and their promising applications in a new generation of spintronic devices take advantage of the robust topological stability of their spin structures. The development of practical devices relies on a detailed understanding of how skyrmionic structures can be formed, transferred, detected, and annihilated. In this work our considerations go beyond static skyrmions and theoretically show that the formation/annihilation of both skyrmions and antiskyrmions is enabled by the transient creation and propagation of topological singularities (magnetic monopolelike Bloch points). Critically, our results predict that during the winding/unwinding of skyrmionic textures, the Bloch-point propagation will give rise to an emergent electric field with a substantial amplitude and in the terahertz frequency range. We also demonstrate ways for controlling Bloch-point dynamics, which directly enable the tunablility on generation of this signal, as well as its frequency and amplitude. Our studies provide a concept of directly exploiting topological singularities for terahertz skyrmion-based electronic devices.

The protected surface states of topological insulators (TIs) form gapless Dirac cones corresponding nondegenerate eigenstates with helical spin polarization. The presence of a warping term deforms the isotropic cone of the most simple model into snowflake Fermi surfaces as in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ and ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. Their features have been identified in STM quasiparticle interference (QPI) experiments on isolated surfaces. Here we investigate the QPI spectrum for the TI thin film geometry with a finite tunneling between the surface states. This leads to a dramatic change of spectrum due to gapping and a change in spin texture that should leave distinct signatures in the QPI pattern. We consider both normal and magnetic exchange scattering from the surface impurities and obtain the scattering $t$ matrix in Born approximation as well as the general closed solution. We show the expected systematic variation of QPI snowflake intensity features by varying film thickness and study, in particular, the influence on backscattering processes. We predict the variation of QPI spectrum for ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ thin films using the observed gap dependence from ARPES results.

The discovery of intrinsic two-dimensional magnetism has ignited intense research interest due to the several and attractive applications in spintronics. ${\mathrm{Nb}}_3{\mathrm{I}}_8$ is a recently investigated van der Waals material, exhibiting ferromagnetism and extraordinary visible light-harvesting ability in monolayer form, besides useful remarkable features for the realization of future high-performance nanodevices. Here we use density functional theory and classical Monte Carlo simulations to investigate the electronic and magnetic properties of ${\mathrm{Nb}}_3{\mathrm{I}}_8$ in bulk, monolayer, and some multilayer (bilayer and trilayer) forms. Two suitable vdW exchange-correlation functionals, $\mathsf{vdW-DF2-C09}$ and $\mathsf{rev-vdW-DF2}$, have been chosen to compare the first-principles calculation predictions. The layer number directly influences the ground-state magnetism, indicating the possibility of using the thickness as a parameter to control the magnetic response of the material. In particular, it is possible to switch on the antiferromagnetism by adding one or two layers to the ferromagnetic monolayer. This makes ${\mathrm{Nb}}_3{\mathrm{I}}_8$ an excellent platform for spintronics applications. Monte Carlo simulations based on a third-nearest-neighbor Ising model provide a Curie temperature close to room temperature ($\sim 307$ K) for the monolayer. The results on the electronic and magnetic properties render the two-dimensional ${\mathrm{Nb}}_3{\mathrm{I}}_8$ an ideal and promising candidate for future research and applications.

We introduce a Ramsey pulse scheme which extracts the non-Hermitian Hamiltonian associated with an arbitrary Lindblad dynamics. We propose a related protocol to measure via interferometry a generalized Loschmidt echo of a generic state evolving in time with the non-Hermitian Hamiltonian itself, and we apply the scheme to a one-dimensional weakly interacting Bose gas coupled to a stochastic atomic impurity. The Loschmidt echo is mapped into a functional integral from which we calculate the long-time decohering dynamics at arbitrary impurity strengths. For strong dissipation we uncover the phenomenology of a quantum many-body Zeno effect: Corrections to the decoherence exponent resulting from the impurity self-energy become purely imaginary, in contrast to the regime of small dissipation where they instead enhance the decay of quantum coherences. Our results illustrate the prospects for experiments employing Ramsey interferometry to study dissipative quantum impurities in condensed matter and cold-atom systems.

Majorana zero modes (MZMs), fundamental building blocks for realizing topological quantum computers, can appear at the interface between a superconductor and a topological material. One of the experimental signatures that has been widely pursued to confirm the existence of MZMs is the observation of a large, quantized zero-bias conductance peak (ZBCP) in the differential conductance measurements. In this Letter, we report observation of such a large ZBCP in junction structures of normal metal (titanium/gold Ti/Au)—Dirac semimetal (cadmium-arsenide $\mathrm{C}{\mathrm{d}}_3\mathrm{A}{\mathrm{s}}_2$)—conventional superconductor (aluminum Al), with a value close to four times that of the normal state conductance. Our detailed analyses suggest that this large ZBCP is most likely not caused by MZMs. We attribute the ZBCP, instead, to the existence of a supercurrent between two far-separated superconducting Al electrodes, which shows up as a zero-bias peak because of the circuitry and thermal fluctuations of the supercurrent phase, a mechanism conceived by Ivanchenko and Zil'berman more than 50 years ago [Ivanchenko and Zil’berman, JETP 28, 1272 (1969)]. Our results thus call for extreme caution when assigning the origin of a large ZBCP to MZMs in a multiterminal semiconductor or topological insulator/semimetal setup. We thus provide criteria for identifying when the ZBCP is definitely not caused by an MZM. Furthermore, we present several remarkable experimental results of a supercurrent effect occurring over unusually long distances and clean perfect Andreev reflection features.

We present an investigation of the influence of low levels of chemical substitution on the magnetic ground state and Néel skyrmion lattice (SkL) state in ${\mathrm{GaV}}_4{\mathrm{S}}_{8\text{−}y}{\mathrm{Se}}_y$, where $y=0,0.1,7.9$, and 8. Muon-spin spectroscopy ($\mu \mathrm{SR}$) measurements on $y=0$ and 0.1 materials reveal the magnetic ground state consists of microscopically coexisting incommensurate cycloidal and ferromagnetic environments, whereas chemical substitution leads to the growth of localized regions of increased spin density. $\mu \mathrm{SR}$ measurements of emergent low-frequency skyrmion dynamics show that the SkL exists under low levels of substitution at both ends of the series. Skyrmionic excitations persist to temperatures below the equilibrium SkL in substituted samples, suggesting the presence of skyrmion precursors over a wide range of temperatures.

The Haldane state is a typical quantum and topological state of matter, which exhibits an edge state corresponding to symmetry-protected topological order in a one-dimensional integer spin chain. Here we propose a concept to design the Haldane state with one-half spins by making use of a chain composed of one-half spin clusters. If the clusters contain two spins, the ground state of a chain corresponds to the Affleck-Kennedy-Lieb-Tasaki state. We thus extend this knowledge to general clusters consisting of not only even, but odd numbers of one-half spins. In the case of an odd number of spins in the clusters, we present a concrete procedure to construct a field-induced Haldane state, and demonstrate the Haldane state in a five-spin cluster chain. Our concept is useful to understand quantum magnetism in real materials such as Fedotovite, consisting of six-spin clusters aligned in one dimension. Furthermore, the edge state designed by our flexible scheme can be utilized for a processing unit of quantum computation with recent progress on intended synthesis of organic materials, quantum dots, and optical lattices.

Quasiparticle interference (QPI) of the electronic states has been widely applied in scanning tunneling microscopy to analyze the electronic band structure of materials. Single-defect-induced QPI reveals defect-dependent interaction between a single atomic defect and electronic states, which deserves special attention. Due to the weak signal of single-defect-induced QPI, the signal-to-noise ratio is relatively low in a standard two-dimensional QPI measurement. In this paper, we introduce a projective quasiparticle interference (PQPI) method in which a one-dimensional measurement is taken along high-symmetry directions centered on a specified defect. We apply the PQPI method to the topological nodal-line semimetal ZrSiS. We focus on two special types of atomic defects that scatter the surface and bulk electronic bands. With an enhanced signal-to-noise ratio in PQPI, the energy dispersions are clearly resolved along high-symmetry directions. We discuss the defect-dependent scattering of bulk bands with the nonsymmorphic symmetry-enforced selection rules. Furthermore, an energy shift of the surface floating band is observed, and a branch of energy dispersion (${\mathit{q}}_6$) is resolved. This PQPI method can be applied to other complex materials to explore defect-dependent interactions in the future.

Topological superconductivity in multiband systems has received much attention due to a variety of possible exotic superconducting order parameters as well as nontrivial bulk and surface states. While the impact of coexisting magnetic order on superconductivity, such as ferromagnetic superconductors, has been studied for many years, the implication of coexisting multipolar order has not been explored much despite the possibility of multipolar hidden order in a number of $f$-electron materials. In this work, we investigate topological properties of multipolar superconductors that may arise when quadrupolar local moments are coupled to conduction electrons in the multiband Luttinger semimetal. We show that the multipolar ordering of local moments leads to various multipolar superconductors with distinct topological properties. We apply these results to the quadrupolar Kondo semimetal system, PrBi, by deriving the microscopic multipolar Kondo model and examining the possible superconducting order parameters.

We consider a Josephson bijunction consisting of a thin $SIS\pi$-Josephson junction sandwiched between two-dimensional semiconducting layers with strong Rashba spin-orbit interaction. Each of these layers forms an $SNS$ junction due to proximity-induced superconductivity. The $SIS$ junction is assumed to be thin enough such that the two Rashba layers are tunnel coupled. We show that, by tuning external gates, this system can be controllably brought into a time-reversal invariant topological superconducting phase with a Kramers pair of Majorana bound states being localized at the end of the normal region for a large parameter phase space. In particular, in the strong spin-orbit interaction limit, the topological phase can be accessed already in the regime of small tunneling amplitudes.

We theoretically study the low-energy electromagnetic response of Bardeen-Cooper-Schrieffer–type superconductors focusing on propagating collective modes that are observable with terahertz near-field optics. The interesting frequency and momentum range is $\omega <2\mathrm{\Delta }$ and $q<1/\xi$, where $\mathrm{\Delta }$ is the gap and $\xi$ is the coherence length. We show that it is possible to observe the superfluid plasmons, amplitude (Higgs) modes, Bardasis-Schrieffer modes, and Carlson-Goldman modes using the terahertz near-field technique, although none of these modes couple linearly to far-field radiation. Coupling of terahertz near-field radiation to the amplitude mode requires particle-hole symmetry breaking, while coupling to the Bardasis-Schrieffer mode does not and is typically stronger. For parameters appropriate to layered superconductors of current interest, the Carlson-Goldman mode appears in the near-field reflection coefficient as a weak feature in the subterahertz frequency range. In a system of two superconducting layers with nanometer-scale separation, an acoustic phase mode appears as the antisymmetric density fluctuation mode of the system. This mode produces well-defined resonance peaks in the near-field terahertz response and has strong anticrossings with the Bardasis-Schrieffer and amplitude modes, enhancing their response. In a slab consisting of many layers of quasi-two-dimensional superconductors, realized for example in samples of high-$T_c$ cuprate compounds, many branches of propagating Josephson plasmon modes are found to couple to the terahertz near-field radiation.

In planar tilted Dirac cone systems, the tilt parameter can be made space-dependent by either a perpendicular displacement field or by chemical substitution in certain systems. We show that the symmetric partial derivative of the tilt parameter generates non-Abelian synthetic gauge fields in these systems. The small velocity limit of these gauge forces corresponds to Rashba and Dresselhaus spin-orbit couplings. At the classical level, new forms of forces from conservative and Lorentz-type to (anti-)friction-like forces emerge from the effective spacetime structure in these materials. The velocity-dependent forces are odd with respect to tilt and therefore have opposite signs in the two valleys when the system is inversion symmetric. Furthermore, toggling the chemical potential between the valence and conduction bands by a gate voltage reverses the sign of the all these classical forces, which indicates these forces couple to the electric charge of the carriers. As such, these “gravitomagnetic” forces are natural extensions of the electric and magnetic forces that appear in the particular geometry of the tilted Dirac cone systems.

A superconductor subject to electromagnetic irradiation in the terahertz range can show amplitude oscillations of its order parameter. However, coupling this so-called Higgs mode to the charge current is notoriously difficult. We propose to achieve such a coupling in a particle-hole-asymmetric configuration using a DC-voltage-biased normal-metal–superconductor tunnel junction. Using the quasiclassical Green's function formalism, we demonstrate three characteristic signatures of the Higgs mode: (i) The AC charge current exhibits a pronounced resonant behavior and is maximal when the radiation frequency coincides with the order parameter. (ii) The AC charge current amplitude exhibits a characteristic nonmonotonic behavior with increasing voltage bias. (iii) At resonance for large voltage bias, the AC current vanishes inversely proportional to the bias. These signatures provide an electric detection scheme for the Higgs mode.

Experiments are reported, which allow us to quantify the near-surface cation diffusion in (001) oriented ${\mathrm{Fe}}_3{\mathrm{O}}_4$ single crystals at temperatures between 470 and 770 K. Thin homoepitaxial films of magnetite, grown using isotopically labeled ${}^{57}\mathrm{Fe}$, were investigated by neutron reflectivity and time-of-flight secondary ion mass spectrometry. By heating the thin films in high vacuum to different temperatures for a well-defined time and determining the ${}^{57}\mathrm{Fe}$ distribution along the surface normal, the diffusion lengths are obtained. For the investigated temperature range, diffusion constants of the order of ${10}^{-20}$ ${\mathrm{m}}^2$/s are deduced. These results are important in view of near-surface mass transport induced by oxygen chemical potential differences occurring when magnetite is exposed to different gas atmospheres or by adsorbates.

We study the properties of Bose polarons in two dimensions using quantum Monte Carlo techniques. Results for the binding energy, the effective mass, and the quasiparticle residue are reported for a typical strength of interactions in the gas and for a wide range of impurity-gas coupling strengths. A lower and an upper branch of the quasiparticle exist. The lower branch corresponds to an attractive polaron and spans from the regime of weak coupling where the impurity acts as a small density perturbation of the surrounding medium to deep bound states which involve many particles from the bath and extend as far as the healing length. The upper branch corresponds to an excited state where due to repulsion a low-density bubble forms around the impurity but might be unstable against decay into many-body bound states. Interaction effects strongly affect the quasiparticle properties of the polaron. In particular, in the strongly correlated regime, the impurity features a vanishing quasiparticle residue, signaling the transition from an almost free quasiparticle to a bound state involving many atoms from the bath.

Three-dimensional strontium ruthenate (${\mathrm{SrRuO}}_3$) is an itinerant ferromagnet that features Weyl points acting as sources of emergent magnetic fields, anomalous Hall conductivity, and unconventional spin dynamics. Integrating ${\mathrm{SrRuO}}_3$ in oxide heterostructures is potentially a novel route to engineer emergent electrodynamics, but its electronic band topology in the two-dimensional limit remains unknown. Here we show that ultrathin ${\mathrm{SrRuO}}_3$ exhibits spin-polarized topologically nontrivial bands at the Fermi energy. Their band anticrossings show an enhanced Berry curvature and act as competing sources of emergent magnetic fields. We control their balance by designing heterostructures with symmetric (${\mathrm{SrTiO}}_3$/${\mathrm{SrRuO}}_3$/${\mathrm{SrTiO}}_3$ and ${\mathrm{SrIrO}}_3$/${\mathrm{SrRuO}}_3$/${\mathrm{SrIrO}}_3$) and asymmetric interfaces (${\mathrm{SrTiO}}_3$/${\mathrm{SrRuO}}_3$/${\mathrm{SrIrO}}_3$). Symmetric structures exhibit an interface-tunable single-channel anomalous Hall effect, while ultrathin ${\mathrm{SrRuO}}_3$ embedded in asymmetric structures shows humplike features consistent with multiple Hall contributions. The band topology of two-dimensional ${\mathrm{SrRuO}}_3$ proposed here naturally accounts for these observations and harmonizes a large body of experimental results.