We extend the previous results of exact bosonization, mapping from fermionic operators to Pauli matrices, in 2D and 3D to arbitrary dimensions. This bosonization map gives a duality between any fermionic system in arbitrary $n$ spatial dimensions and a class of $(n-1)$-form ${\mathbb{Z}}_2$ gauge theories in $n$ dimensions with a modified Gauss's law. This map preserves locality and has an explicit dependence on the second Stiefel-Whitney class and a choice of spin structure on the spatial manifold. A formula for Stiefel-Whitney homology classes on lattices is derived. In the Euclidean path integral, this exact bosonization map is equivalent to introducing a topological Steenrod square term to the space-time action.

We predict that the Lee-Huang-Yang effect makes it possible to create stable quantum droplets (QDs) in binary Bose-Einstein condensates with a heterosymmetric or heteromultipole structure, i.e., different vorticities or multipolarities in their components. The QDs feature flat-top shapes when either chemical potential, ${\mu }_{1,2}$, of the droplet approaches an edge of a triangular existence domain in the $({\mu }_1,{\mu }_2)$ plane. QDs with different vorticities of their components are stable against azimuthal perturbations, provided that the norm of one component is large. We also present multipole states in which the interaction with a strong fundamental component balances the repulsion between poles with opposite signs in the other component, leading to the formation of stable bound states. Extended stability domains are obtained for dipole QDs; tripole ones exist but are unstable, while quadrupoles are stable in a narrow region. The results uncover the existence of much richer families of stable binary QDs in comparison to states with identical components.

Disorder effects on three-dimensional second-order topological insulators (3DSOTIs) are investigated numerically and analytically. The study is based on a tight-binding Hamiltonian for noninteracting electrons on a cubic lattice with a reflection symmetry that supports a 3DSOTI in the absence of disorder. Interestingly, unlike the disorder effects on a topological trivial system that can only be either a diffusive metal (DM) or an Anderson insulator (AI), disorders can sequentially induce four phases of 3DSOTIs, three-dimensional first-order topological insulators (3DFOTIs), DMs, and AIs. At a weak disorder when the on-site random potential of strength $W$ is below a low critical value $W_{c1}$ at which the gap of surface states closes while the bulk sates are still gapped, the system is a disordered 3DSOTI characterized by a constant density of states and a quantized integer conductance of $e^2/h$ through its chiral hinge states. The gap of the bulk states closes at a higher critical disorder $W_{c2}$, and the system is a disordered 3DFOTI in a lower intermediate disorder between $W_{c1}$ and $W_{c2}$ in which electron conduction is through the topological surface states. The system becomes a DM in a higher intermediate disorder between $W_{c2}$ and $W_{c3}$ above which the states at the Fermi level are localized. It undergoes a normal three-dimensional metal-to-insulator transition at $W_{c3}$ and becomes the conventional AI for $W>W_{c3}$. The self-consistent Born approximation allows one to see how the density of bulk states and the Dirac mass are modified by the on-site disorders.

The Josephson current is investigated in a superconducting graphene bilayer where pristine graphene sheets can make in-plane or out-of-plane displacements with respect to each other. The superconductivity can be of an intrinsic nature, or due to a proximity effect. The results demonstrate that the supercurrent responds qualitatively differently to relative displacement if the superconductivity is due to either intralayer or interlayer spin-singlet electron-electron pairing, thus providing a tool to distinguish between the two mechanisms. Specifically, both the AA and AB stacking orders are studied with antiferromagnetic spin alignment. For the AA stacking order with intralayer and on-site pairing no current reversal is found. In contrast, the supercurrent may switch its direction as a function of the in-plane displacement and out-of-plane interlayer coupling for the cases of AA ordering with interlayer pairing and AB ordering with either intralayer or interlayer pairing. In addition to sign reversal, the Josephson signal displays many characteristic fingerprints which derive directly from the pairing mechanism. Thus, measurements of the Josephson current as a function of the graphene bilayer displacement open up the means to achieve deeper insights into the superconducting pairing mechanism.

The chemical bonding within the transition-metal carbide materials MAX phase ${\mathrm{Ti}}_3\mathrm{Al}{\mathrm{C}}_2$ and MXene ${\mathrm{Ti}}_3{\mathrm{C}}_2{T}_x$ is investigated by x-ray absorption near-edge structure (XANES) and extended x-ray absorption fine-structure (EXAFS) spectroscopies. MAX phases are inherently nanolaminated materials that consist of alternating layers of $M_{n+1}{X}_n$ and monolayers of an A-element from the IIIA or IVA group in the Periodic Table, where M is a transition metal and X is either carbon or nitrogen. Replacing the A-element with surface termination species $T_x$ will separate the $M_{n+1}{X}_n$-layers forming two-dimensional (2D) flakes of $M_{n+1}{X}_n{T}_x$. For ${\mathrm{Ti}}_3{\mathrm{C}}_2{T}_x$ the $T_x$ corresponds to fluorine (F) and oxygen (O) covering both sides of every single 2D $M_{n+1}{X}_n$-flake. The Ti K-edge ($1s$) XANES of both ${\mathrm{Ti}}_3\mathrm{Al}{\mathrm{C}}_2$ and ${\mathrm{Ti}}_3{\mathrm{C}}_2{T}_x$ exhibit characteristic preedge absorption regions of C $2p\text{−}\mathrm{Ti}3d$ hybridization with clear crystal-field splitting while the main-edge absorption features originate from the Ti $1s\to 4p$ excitation, where only the latter shows sensitivity toward the fcc-site occupation of the termination species. The coordination numbers obtained from EXAFS show that ${\mathrm{Ti}}_3\mathrm{Al}{\mathrm{C}}_2$ and ${\mathrm{Ti}}_3{\mathrm{C}}_2{T}_x$ are highly anisotropic with a strong in-plane contribution for Ti and with a dynamic out-of-plane contribution from the Al monolayers and termination species, respectively. As shown in the temperature-dependent measurements, the O contribution shifts to shorter bond length while the F diminishes as the temperature is raised from room temperature up to 750 °C.

The sign problem is a widespread numerical hurdle preventing us from simulating the equilibrium behavior of various problems at the forefront of physics. Focusing on an important subclass of such problems, bosonic $(2+1)$-dimensional topological quantum field theories, here we provide a simple criterion to diagnose intrinsic sign problems—that is, sign problems that are inherent to that phase of matter and cannot be removed by any local unitary transformation. Explicitly, if the exchange statistics of the anyonic excitations do not form complete sets of roots of unity, then the model has an intrinsic sign problem. This establishes a concrete connection between the statistics of anyons, contained in the modular $S$ and $T$ matrices, and the presence of a sign problem in a microscopic Hamiltonian. Furthermore, it places constraints on the phases that can be realized by stoquastic Hamiltonians. We prove this and a more restrictive criterion for the large set of gapped bosonic models described by an Abelian topological quantum field theory at low-energy, and we offer evidence that it applies more generally with analogous results for non-Abelian and chiral theories.

Weyl metals host relativistic chiral quasiparticles, which display quantum anomalies in the presence of external electromagnetic fields. Here, we study the manifestations of chiral anomalies in the longitudinal and planar magnetotransport coefficients of Weyl metals, in the presence of a quantizing magnetic field. We present a general framework for calculating all the transport coefficients in the regime where multiple Landau levels are occupied. We explicitly show that all the longitudinal and planar transport coefficients show quantum oscillations which are periodic in $1/B$. Our calculations recover the quadratic-$B$ dependence in the semiclassical regime and predict a linear-$B$ dependence in the ultraquantum limit for all the transport coefficients.

Linear-in-wave-vector $K$ terms of an electron Hamiltonian play an important role in topological insulators and spintronic devices. Here we demonstrate how an external electric field can control the magnitude of a linear-in-$K$ term in the exciton Hamiltonian. The effect of the electric field on interference of exciton polaritons in a high-quality structure with a wide GaAs quantum well was experimentally studied by means of the differential reflection spectroscopy. It is found that the interference pattern is strongly suppressed at certain electric field and then it is reinstalled, but with an inverted phase, at the further increase of the field. This behavior of the pattern is successfully explained by the electric-field-induced linear-in-$K$ terms in the Hamiltonian of the exciton propagating across the quantum well. An excellent agreement between the experimental data and the results of calculations using semiclassical nonlocal dielectric response model confirms the validity of the method and paves the way for the realization of excitonic Datta-Das transistors. In full analogy with the spin-orbit transistor proposed by Datta and Das [Appl. Phys. Lett. 56, 665 (1990)], the switch between positive and negative interference of exciton polaritons propagating forward and backward in a GaAs film is achieved by application of an electric field having a nonzero component in the plane of the quantum well layer.

Neutron scattering, specific-heat, and magnetization measurements on both powders and single crystals reveal that ${\mathrm{Dy}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ realizes the fragmented monopole crystal state in which antiferromagnetic order and a Coulomb phase spin liquid coinhabit. The measured residual entropy is that of a hard-core dimer liquid, as predicted. Inclusion of Coulomb interactions allows for a quantitative description of both the thermodynamic data and the magnetization dynamics, with the energy scale given by deconfined defects in the emergent ionic crystal. Our data reveal low-energy excitations, as well as a large distribution of energy barriers down to low temperatures, while the magnetic response to an applied field suggests that domain wall pinning is important, results that call for further theoretical modeling.

The anisotropy and magnetic ground state of hyperkagome dysprosium gallium garnet ${\mathrm{Dy}}_3{\mathrm{Ga}}_5{\mathrm{O}}_{12}$ are investigated, along with that of its closest structural analog and archetypal Ising multiaxis antiferromagnet, dysprosium aluminum garnet ${\mathrm{Dy}}_3{\mathrm{Al}}_5{\mathrm{O}}_{12}$, using a combination of neutron scattering techniques, including polarized neutron powder diffraction. Results show a dramatic change from an Ising-like anisotropy in ${\mathrm{Dy}}_3{\mathrm{Al}}_5{\mathrm{O}}_{12}$, to a quasiplanar one in ${\mathrm{Dy}}_3{\mathrm{Ga}}_5{\mathrm{O}}_{12}$. According to a point charge modeling, this is due to small variations of the oxygen positions surrounding ${\mathrm{Dy}}^{3+}$ ions. The magnetic ground state of ${\mathrm{Dy}}_3{\mathrm{Ga}}_5{\mathrm{O}}_{12}$ is investigated for the first time and is found to be similar to that of ${\mathrm{Dy}}_3{\mathrm{Al}}_5{\mathrm{O}}_{12}$, yet with a much lower $T_{\mathrm{N}}$. Mean-field calculations show that the dipolar interaction favors distinct magnetic ground states, depending on the anisotropy tensor: a multiaxis antiferromagnetic state is favored in the case of strong Ising-like anisotropy, like in ${\mathrm{Dy}}_3{\mathrm{Al}}_5{\mathrm{O}}_{12}$, whereas a complex ferrimagnetic state is stabilized in the case of planar anisotropy. The ${\mathrm{Dy}}_3{\mathrm{Ga}}_5{\mathrm{O}}_{12}$ crystal field parameters locate the latter close to the boundary between those two ground states, which, alongside competition between dipolar and a small but finite magnetic exchange, may explain its low $T_{\mathrm{N}}$. To widen the scope of these experimental results, we performed mean-field calculations to generate the magnetic phase diagram of an effective anisotropic pseudospin $S=1/2$, characterized by general $g_{xx}$, $g_{yy}$, and $g_{zz}$ Landé factors. A very rich magnetic phase diagram, encompassing complex phases, likely disordered, is evidenced when magnetic anisotropy departs from the strong Ising case. With magnetic anisotropy being controllable through appropriate tuning of the rare-earth oxygen environment, these results emphasize the potential of rare-earth hyperkagome networks for the exploration of new magnetic phases.

The main feature of amorphous materials is the presence of excess vibrational modes at low energies, giving rise to the so-called “boson peak” in neutron and optical spectroscopies. These same modes manifest themselves as two-level systems (TLSs) causing noise and decoherence in qubits and other sensitive devices. Here, we present an experiment that uses the spin relaxation of dangling bonds at the $\mathrm{Si}/\left(\mathrm{amorphous}\right){\mathrm{SiO}}_2$ interface as a probe of TLSs. We introduce a model that is able to explain the observed nonexponential electron spin inversion recovery and provides a measure of the degree of spatial localization and concentration of the TLSs close to the interface, their maximum energy, and its temperature dependence.

We present a method for calculating Rényi entanglement entropies for fermionic field theories originating from microscopic Hamiltonians. The method builds on an operator identity, which leads to the representation of traces of operator products, and thus Rényi entropies of a subsystem, in terms of fermionic-displacement operators. This allows for a very transparent path-integral formulation, both in and out of equilibrium, having a simple boundary condition on the fermionic fields. The method is validated by reproducing well-known expressions for entanglement entropy in terms of the correlation matrix for noninteracting fermions. We demonstrate the effectiveness of the method by explicitly formulating the field theory for Rényi entropy in a few zero- and higher dimensional large-$N$ interacting models akin to the Sachdev-Ye-Kitaev (SYK) model and for the Hubbard model within the dynamical mean field theory (DMFT) approximation. We use the formulation to compute Rényi entanglement entropy of interacting Fermi liquid (FL) and non-Fermi liquid (NFL) states in the large-$N$ models and compare the results successfully with those obtained via exact diagonalization for finite $N$. We elucidate the connection between Rényi entanglement entropy and residual entropy of the NFL ground state in the SYK model and extract sharp signatures of quantum phase transition in the entanglement entropy across an NFL to FL transition. Furthermore, we employ the method to obtain nontrivial system-size scaling of entanglement in an interacting diffusive metal described by a chain of SYK dots.

The orbital degree of freedom of electrons greatly influences the physical properties of materials such as magnetic order and unconventional superconductivity. An orbital is a minimal unit of “shape,” and the orbital state can be unraveled by observing the spatial anisotropic distribution of electrons. However, it is difficult to experimentally extract the orbital information in a crystal because of various technical problems. Here, the $\mathrm{Ti}\text{−}3d$ orbital state in perovskite-type oxides $R\mathrm{Ti}{\mathrm{O}}_3$ ($R=\mathrm{Y}$, Sm, and La) is directly determined by a core differential Fourier synthesis (CDFS) method using synchrotron x-ray diffraction. The valence electron-density distribution, including information on the anisotropy and the hybridization between atomic orbitals, can be extracted from the CDFS analysis. Our study not only demonstrates the relationship between the magnetic- and orbital-ordered states called the Kugel-Khomskii model, but also provides a nontrivial picture of the orbital state reconstructed by the orbital hybridization.

Most of our quantitative understanding of disorder-induced metal-insulator transitions comes from numerical studies of simple noninteracting tight-binding models, like the Anderson model in three dimensions. An important outstanding problem is the fate of the Anderson transition in the presence of additional Hubbard interactions of strength $U$ between particles. Based on large-scale numerics, we compute the position of the mobility edge for a system of two identical bosons or two fermions with opposite spin components. The resulting phase diagram in the interaction-energy-disorder space possesses a remarkably rich and counterintuitive structure, with multiple metallic and insulating phases. We show that this phenomenon originates from the molecular or scatteringlike nature of the pair states available at given energy $E$ and disorder strength $W$. The disorder-averaged density of states of the effective model for the pair is also investigated. Finally, we discuss the implications of our results for ongoing research on many-body localization.

Artificially fabricated $3d/5d$ superlattices (SLs) involve both strong electron correlation and spin-orbit coupling in one material by means of interfacial $3d\text{−}5d$ coupling, whose mechanism remains mostly unexplored. In this work we investigated the mechanism of interfacial coupling in ${\mathrm{LaMnO}}_3\text{/}{\mathrm{SrIrO}}_3$ SLs by several spectroscopic approaches. Hard x-ray absorption, magnetic circular dichroism and photoemission spectra evidence the systematic modulation of the Ir ferromagnetism and the electronic structure with the change of the SL repetition period. First-principles calculations further reveal the mechanism of the SL-period dependence of the interfacial electronic structure and the local properties of the Ir moments, confirming that the formation of Ir-Mn molecular orbital is responsible for the interfacial coupling effects. The SL-period dependence of the ratio between orbital and spin components of the Ir magnetic moments can be attributed to the realignment of electron spin during the formation of the interfacial molecular orbital. Our results clarify the nature of interfacial coupling in this prototypical $3d/5d$ SL system and the conclusion will shed light on the study of other strongly correlated and spin-orbit coupled oxide heterointerfaces.

Higher-order topological materials with topologically protected states at the boundaries of their boundaries (hinges or corners) have attracted attention in recent years. In this paper, we utilize time-periodic driving to generate second-order topological superconductors out of systems which otherwise do not even allow second-order topological characterization. This is made possible by the design of periodic drives which inherently exhibit nontrivial winding in the time domain. Through the interplay of topology in both spatial and temporal dimensions, nonchiral Majorana modes may emerge at the systems' corners and sometimes even coexist with chiral Majorana modes. Our proposal thus presents an opportunity for Floquet engineering with minimal system complexity and its application in quantum information processing.

Motivated by the recent experimental realization of twisted double bilayer graphene (TDBG) samples, we study, both analytically and numerically, the effects of circularly polarized light propagating in free space and confined in a waveguide on the band structure and topological properties of these systems. These two complementary Floquet protocols allow us to selectively tune different parameters of the system by varying the intensity and light frequency. For the drive protocol in free space, in the high-frequency regime, we find that in TDBG with $AB/BA$ stacking, we can selectively close the zone-center quasienergy gaps around one valley while increasing the gaps near the opposite valley by tuning the parameters of the drive. In TDBG with $AB/AB$ stacking, a similar effect can be obtained upon the application of a perpendicular static electric field. Furthermore, we study the topological properties of the driven system in different settings, provide accurate effective Floquet Hamiltonians, and show that relatively strong drives can generate flat bands. On the other hand, longitudinal light confined in a waveguide couples to the components of the interlayer hopping that are perpendicular to the TDBG sheet, allowing for selective engineering of the bandwidth of Floquet zone-center quasienergy bands without breaking the symmetries of the static system.

We show that the microwave (MW) spectra in semiconductor-nanowire-based transmon qubits provide a strong signature of the presence of Majorana bound states in the junction. This occurs as an external magnetic field tunes the wire into the topological regime and the energy splitting of the emergent Majorana modes oscillates around zero energy owing to their wave function spatial overlap in finite-length wires. In particular, we discuss how these Majorana oscillations, and the concomitant fermion parity switches in the ground state of the junction, result in distinct spectroscopic features—in the form of an intermittent visibility of absorption lines—that strongly deviate from standard transmon behavior. In contrast, nonoscillating zero modes, such as topologically trivial Andreev bound states resulting from sufficiently smooth potentials, exhibit an overall standard transmon response. These differences in the MW response could help determine whether the junction contains topological Majoranas or not.

Skyrmion crystals support chiral magnonic edge states akin to electronic quantum Hall edge states. However, magnonic topology relies on the harmonic approximation, neglecting ubiquitous magnon-magnon interactions that yield a finite zero-temperature quantum damping. We demonstrate that spontaneous quasiparticle decay in two-dimensional ferromagnetic skyrmion crystals is a delicate issue, with the quantum damping ranging over several orders of magnitude. Flat magnon bands cause exceptionally strong spontaneous decay at twice their energy. The resulting externally controllable energy-selective magnon breakdown is measurable not only by scattering but also by magnetic resonance experiments, probing the magnetically active anticlockwise, breathing, and clockwise modes. They exhibit distinct decay behavior, with the clockwise (anticlockwise) mode being the least (most) stable mode out of the three. The quantum damping of the topologically nontrivial anticlockwise mode is negligible, establishing the harmonic theory as a trustworthy approximation at low energies, implying excellent prospects of topological magnonics in skyrmion crystals.

Turning a pristine Mott insulator into a correlated metal by chemical doping is a common procedure in strongly correlated materials physics, e.g., underlying the phenomenology of high-$T_c$ cuprates. The ruthenate bilayer compound ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ is a prominent example of a reversed case, namely, a correlated metal at stoichiometry that realizes a transition into an insulating state via Ti doping. We here investigate this puzzling metal-insulator transition (MIT) by first-principles many-body theory and elucidate a challenging interplay between electronic correlations and symmetry breaking on the Ru sublattice. While average effects on the ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ crystal structure are still relevant, the key to the MIT is the cooperation of electronic correlations with the spatial inhomogeneity in the defect regime. Together they give rise to the emergence of site-selective Mott criticality and competing orbital-ordering tendencies.