We present theoretical results for the radiative rates and doping-dependent photoluminescence spectrum of interlayer excitonic complexes localized by donor impurities in ${\mathrm{MoSe}}_2/{\mathrm{WSe}}_2$ twisted heterobilayers, supported by quantum Monte Carlo calculations of binding energies and wave-function overlap integrals. For closely aligned layers, radiative decay is made possible by the momentum spread of the localized complexes' wave functions, resulting in radiative rates of a few $\mu {\mathrm{s}}^{-1}$. For strongly misaligned layers, the short-range interaction between the carriers and impurity provides a finite radiative rate with a strong asymptotic twist angle dependence $\propto {\theta }^{-8}$. Finally, phonon-assisted recombination is considered, with emission of optical phonons in both layers resulting in additional, weaker emission lines, redshifted by the phonon energy.

Anisotropy of superconductivity is one of the fundamental physical parameters for understanding layered iron-based superconductors (IBSs). Here we investigated the anisotropic response of resistive transition as a function of thickness $\left(d\right)$ in iron selenide (FeSe) based electric-double-layer transistors (EDLTs) on $\mathrm{SrTi}{\mathrm{O}}_3$, which exhibit superconducting transition temperatures $T_{\mathrm{c}}$ as high as 40 K below $d=10\mathrm{nm}$. According to the analyses of the in-plane $\left(H_{\mathrm{c}2}^{//}\right)$ and out-of-plane $\left(H_{\mathrm{c}2}^{\perp }\right)$ upper critical fields $\left(H_{\mathrm{c}2}\right)$ and the magnetic field angle dependence of the resistance $\left(R_{\mathrm{s}}-\theta \right)$ in ultrathin condition, we found that the anisotropy factor ${\varepsilon }_0=H_{\mathrm{c}2}^{//}/H_{\mathrm{c}2}^{\perp }$ is 7.4 in the thin limit of $d\sim 1\mathrm{nm}$, which is larger than that of bulk IBSs. In addition, we observed the shorter out-of-plane coherence length ${\xi }_{\mathrm{c}}$ of 0.19 nm compared to the $c$-axis lattice constant, which implies the confinement of the order parameter in the one unit cell FeSe. These findings suggest that high-$T_{\mathrm{c}}$ superconductivity in the ultrathin FeSe-EDLT exhibits an anisotropic three-dimensional (3D) or quasi-two-dimensional (2D) nature rather than the pure 2D one, leading to the robust superconductivity. Moreover, we carried out the systematic evaluation of the anisotropic $H_{\mathrm{c}2}$ against thickness reduction in the FeSe channel. The in-plane $H_{\mathrm{c}2}$ as a function of normalized temperature $T/T_{\mathrm{c}}$ is almost independent of $d$ until the thin limit condition. On the other hand, the out-of-plane $H_{\mathrm{c}2}$ near $T/T_{\mathrm{c}}\sim 1$ decreases with increasing $d$, resulting in the increase of ${\varepsilon }_0$ at around $T_{\mathrm{c}}$ to 32.0 at the thick condition of $d=9.3\mathrm{nm}$, which is also confirmed by $R_{\mathrm{s}}-\theta$ measurements. The counterintuitive behavior can be attributed to the degree of coupling strength between two electron-rich layers possessing a high superconducting order parameter induced by electrostatic gating at the top interface and charge transfer from $\mathrm{SrTi}{\mathrm{O}}_3$ substrates at the bottom interface. Besides a large $H_{\mathrm{c}2}^{\perp }$ for $d=9.3\mathrm{nm}$ exceeding 20 T even at $T=0.8T_{\mathrm{c}}$, we observe the decoupling crossover of the two superconducting layers at low temperature, which is a unique feature for the high-$T_{\mathrm{c}}$ FeSe-EDLT on $\mathrm{SrTi}{\mathrm{O}}_3$.

In Levin-Wen (LW) models, a wide class of exactly solvable discrete models, for two-dimensional topological phases, it is relatively easy to describe only single-fluxon excitations, but not the charge and dyonic as well as many-fluxon excitations. To incorporate charged and dyonic excitations in (doubled) topological phases, an extension of the LW models is proposed in this paper. We first enlarge the Hilbert space with adding a tail on one of the edges of each trivalent vertex to describe the internal charge degrees of freedom at the vertex. Then, we study the full dyon spectrum of the extended LW models, including both quantum numbers and wave functions for dyonic quasiparticle excitations. The local operators associated with the dyonic excitations are shown to form the so-called tube algebra, whose representations (modules) form the quantum double (categoric center) of the input data (unitary fusion category). In physically relevant cases, the input data are from a finite or quantum group (with braiding $R$ matrices), and we find that the elementary excitations (or dyon species), as well as any localized/isolated excited states, are characterized by three quantum numbers: charge, fluxon type, and twist. They provide a “complete basis” for many-body states in the enlarged Hilbert space. Concrete examples are presented and the relevance of our results to the electric-magnetic duality existing in the models is addressed.

We control the electronic structure of the silicon-vacancy (SiV) color-center in diamond by changing its static strain environment with a nano-electro-mechanical system. This allows deterministic and local tuning of SiV optical and spin transition frequencies over a wide range, an essential step towards multiqubit networks. In the process, we infer the strain Hamiltonian of the SiV revealing large strain susceptibilities of order 1 PHz/strain for the electronic orbital states. We identify regimes where the spin-orbit interaction results in a large strain susceptibility of order 100 THz/strain for spin transitions, and propose an experiment where the SiV spin is strongly coupled to a nanomechanical resonator.

A two-dimensional second-order topological superconductor exhibits a finite gap in both bulk and edges, with the nontrivial topology manifesting itself through Majorana zero modes localized at the corners, i.e., Majorana corner states. We investigate a time-reversal-invariant topological superconductor in two dimensions and demonstrate that an in-plane magnetic field could transform it into a second-order topological superconductor. A detailed analysis reveals that the magnetic field gives rise to mass terms which take distinct values among the edges, and Majorana corner states naturally emerge at the intersection of two adjacent edges with opposite masses. With the rotation of the magnetic field, Majorana corner states localized around the boundary may hop from one corner to a neighboring one and eventually make a full circle around the system when the field rotates by $2\pi$. In the end, we briefly discuss physical realizations of this system.

Second-order topological insulators and superconductors have a gapped excitation spectrum in bulk and along boundaries, but protected zero modes at corners of a two-dimensional crystal or protected gapless modes at hinges of a three-dimensional crystal. A second-order topological phase can be induced by the presence of a bulk crystalline symmetry. Building on Shiozaki and Sato's complete classification of bulk crystalline phases with an order-two crystalline symmetry [Phys. Rev. B 90, 165114 (2014)], such as mirror reflection, twofold rotation, or inversion symmetry, we classify all corresponding second-order topological insulators and superconductors. The classification also includes antiunitary symmetries and antisymmetries.

We study surface states of topological crystalline insulators and superconductors protected by inversion symmetry. These fall into the category of “higher-order” topological insulators and superconductors which possess surface states that propagate along one-dimensional curves (hinges) or are localized at some points (corners) on the surface. We provide a complete classification of inversion-protected higher-order topological insulators and superconductors in any spatial dimension for the 10 symmetry classes by means of a layer construction. We discuss possible physical realizations of such states starting with a time-reversal-invariant topological insulator (class AII) in three dimensions or a time-reversal-invariant topological superconductor (class DIII) in two or three dimensions. The former exhibits one-dimensional chiral or helical modes propagating along opposite edges, whereas the latter hosts Majorana zero modes localized to two opposite corners. Being protected by inversion, such states are not pinned to a specific pair of edges or corners, thus offering the possibility of controlling their location by applying inversion-symmetric perturbations such as magnetic field.

We study the high-temperature transport behavior of the Aubry-André-Harper (AAH) model, both in an isolated thermodynamic limit and in an open system. At the critical point of the AAH model, we find hints of superdiffusive behavior from the scaling of spread of an initially localized wave packet. On the other hand, when connected to two baths with different chemical potentials at the two ends, we find that the critical point shows clear subdiffusive scaling of current with system size. We provide an explanation for this by showing that the current scaling with system size is entirely governed by the behavior of the single-particle eigenfunctions at the boundary sites where the baths are attached. We also look at the particle density profile in the nonequilibrium steady state of the open system when the two baths are at different chemical potentials. We find that the particle density profile has distinctly different behavior in the delocalized, critical, and localized phases of the AAH model.

We provide a definition and explicit expressions for $n$-body Gaussian process (GP) kernels, which can learn any interatomic interaction occurring in a physical system, up to $n$-body contributions, for any value of $n$. The series is complete, as it can be shown that the “universal approximator” squared exponential kernel can be written as a sum of $n$-body kernels. These recipes enable the choice of optimally efficient force models for each target system, as confirmed by extensive testing on various materials. We furthermore describe how the $n$-body kernels can be “mapped” on equivalent representations that provide database-size-independent predictions and are thus crucially more efficient. We explicitly carry out this mapping procedure for the first nontrivial (three-body) kernel of the series, and we show that this reproduces the GP-predicted forces with $\mathrm{meV}/\AA$ accuracy while being orders of magnitude faster. These results pave the way to using novel force models (here named “M-FFs”) that are computationally as fast as their corresponding standard parametrized $n$-body force fields, while retaining the nonparametric character, the ease of training and validation, and the accuracy of the best recently proposed machine-learning potentials.

Transverse electromagnetic plane waves are fundamental solutions of Maxwells equations. It is less known that a radically different type of solutions has been described theoretically, but has never been realized experimentally, that exist only in the form of short bursts of electromagnetic energy propagating in free space at the speed of light. They are distinguished from transverse waves by a doughnutlike configuration of electric and magnetic fields with a strong field component along the propagation direction. Here, we demonstrate numerically that such flying doughnuts can be generated from conventional pulses using a singular metamaterial converter designed to manipulate both the spatial and spectral structure of the input pulse. The ability to generate flying doughnuts is of fundamental interest, as they shall interact with matter in unique ways, including nontrivial field transformations upon reflection from interfaces and the excitation of toroidal response and anapole modes in matter, hence offering opportunities for telecommunications, sensing, and spectroscopy.

Motivated by recent progress in applying techniques from the field of artificial neural networks (ANNs) to quantum many-body physics, we investigate to what extent the flexibility of ANNs can be used to efficiently study systems that host chiral topological phases such as fractional quantum Hall (FQH) phases. With benchmark examples, we demonstrate that training ANNs of restricted Boltzmann machine type in the framework of variational Monte Carlo can numerically solve FQH problems to good approximation. Furthermore, we show by explicit construction how $n$-body correlations can be kept at an exact level with ANN wave functions exhibiting polynomial scaling with power $n$ in system size. Using this construction, we analytically represent the paradigmatic Laughlin wave function as an ANN state.

We study the equivalence of four different approaches to calculate the excitonic linear and nonlinear optical response of multiband semiconductors. These four methods derive from two choices of gauge, i.e., length and velocity gauges, and two ways of computing the current density, i.e., direct evaluation and evaluation via the time-derivative of the polarization density. The linear and quadratic response functions are obtained for all methods by employing a perturbative density-matrix approach within the mean-field approximation. The equivalence of all four methods is shown rigorously, when a correct interaction Hamiltonian is employed for the velocity gauge approaches. The correct interaction is written as a series of commutators containing the unperturbed Hamiltonian and position operators, which becomes equivalent to the conventional velocity gauge interaction in the limit of infinite Coulomb screening and infinitely many bands. As a case study, the theory is applied to hexagonal boron nitride monolayers, and the linear and nonlinear optical response found in different approaches are compared.

A scanning tunneling microscope is used to explore the evolution of electron and Cooper-pair transport across single Mn-phthalocyanine molecules adsorbed on Pb(111) from tunneling to contact ranges. Normal-metal as well as superconducting tips give rise to a gradual transition of the Bardeen-Cooper-Schrieffer energy gap in the tunneling range into a zero-energy resonance close to and at contact. Supporting transport calculations show that in the normal-metal–superconductor junctions this resonance reflects the merging of in-gap Yu-Shiba-Rusinov states as well as the onset of Andreev reflection. For the superconductor-superconductor contacts, the zero-energy resonance is rationalized in terms of a finite Josephson current that is carried by phase-dependent Andreev and Yu-Shiba-Rusinov levels.

We study geometric aspects of the Laughlin fractional quantum Hall (FQH) states using a description of these states in terms of a matrix quantum mechanics model known as the Chern-Simons matrix model (CSMM). This model was proposed by Polychronakos as a regularization of the noncommutative Chern-Simons theory description of the Laughlin states proposed earlier by Susskind. Both models can be understood as describing the electrons in a FQH state as forming a noncommutative fluid, i.e., a fluid occupying a noncommutative space. Here, we revisit the CSMM in light of recent work on geometric response in the FQH effect, with the goal of determining whether the CSMM captures this aspect of the physics of the Laughlin states. For this model, we compute the Hall viscosity, Hall conductance in a nonuniform electric field, and the Hall viscosity in the presence of anisotropy (or intrinsic geometry). Our calculations show that the CSMM captures the guiding center contribution to the known values of these quantities in the Laughlin states, but lacks the Landau orbit contribution. The interesting correlations in a Laughlin state are contained entirely in the guiding center part of the state/wave function, and so we conclude that the CSMM accurately describes the most important aspects of the physics of the Laughlin FQH states, including the Hall viscosity and other geometric properties of these states, which are of current interest.

In a recent report, sum-frequency excitation of a Raman-active phonon was experimentally demonstrated. This mechanism is the sibling of impulsive stimulated Raman scattering, in which the difference-frequency components of a light field excite a Raman-active mode. Here, we propose that also ionic Raman scattering analogously has a sum-frequency counterpart. We compare the four Raman mechanisms, photonic and ionic difference- and sum-frequency excitation, for three different example materials using a generalized oscillator model for which we calculate the parameters with density functional theory. Sum-frequency ionic Raman scattering completes the toolkit for controlling material properties by means of selective excitation of lattice vibrations.

We present a theoretical analysis of low-energy quantum transport in coupled Majorana box devices. A single Majorana box represents a Coulomb-blockaded mesoscopic superconductor proximitizing two or more long topological nanowires. The box thus harbors at least four Majorana zero modes (MZMs). Setups with several Majorana boxes, where MZMs on different boxes are tunnel coupled via short nanowire segments, are key ingredients to recent Majorana qubit and code network proposals. We construct and study the low-energy theory for multiterminal junctions with normal leads connected to the coupled box device by lead-MZM tunnel contacts. Transport experiments in such setups can test the nonlocality of Majorana-based systems and the integrity of the underlying Majorana qubits. For a single box, we recover the previously described topological Kondo effect which can be captured by a purely bosonic theory. For several coupled boxes, however, nonconserved local fermion parities require the inclusion of additional local sets of Pauli operators. We present a renormalization group analysis and develop a nonperturbative strong-coupling approach to quantum transport in such systems. Our findings are illustrated for several examples, including a loop qubit device and different two-box setups.

We analyze the interplay between a $d$-wave uniform superconducting and a pair-density-wave (PDW) order parameter in the neighborhood of a vortex. We develop a phenomenological nonlinear sigma model, solve the saddle-point equation for the order-parameter configuration, and compute the resulting local density of states in the vortex halo. The intertwining of the two superconducting orders leads to a charge density modulation with the same periodicity as the PDW, which is twice the period of the charge density wave that arises as a second harmonic of the PDW itself. We discuss key features of the charge density modulation that can be directly compared with recent results from scanning tunneling microscopy and speculate on the role PDW order may play in the global phase diagram of the hole-doped cuprates.

A recent scanning tunneling microscopy (STM) experiment reports the observation of a charge-density wave (CDW) with a period of approximately 8a in the halo region surrounding the vortex core, in striking contrast to the approximately 4a period CDWs that are commonly observed in the cuprates. Inspired by this work, we study a model where a bidirectional pair-density wave (PDW) with period 8 is at play. This further divides into two classes: (1) where the PDW is a competing state of the $d$-wave superconductor and can exist only near the vortex core where the $d$-wave order is suppressed and (2) where the PDW is the primary order, the so-called “mother state” that persists with strong phase fluctuations to high temperature and high magnetic field and lies behind the pseudogap phenomenology. We study the charge-density wave structures near the vortex core in these models. We emphasize the importance of the phase winding of the $d$-wave order parameter. The PDW can be pinned by the vortex core due to this winding and become static. Furthermore, the period-8 CDW inherits the properties of this winding, which gives rise to a special feature of the Fourier transform peak, namely, it is split in certain directions. There is also a line of zeros in the inverse Fourier transform of filtered data. We propose that these are key experimental signatures that can distinguish between the PDW-driven scenario from the more mundane option that the period-8 CDW is primary. We discuss the pro's and con's of the options considered above. Finally, we attempt to place the STM experiment in the broader context of pseudogap physics of underdoped cuprates and relate this observation to the unusual properties of x-ray scattering data on CDW carried out to very high magnetic field.

We present an experimental realization of an $S=1/2$ fully frustrated square lattice (FFSL) composed of a verdazyl-based salt $\left(p\text{-MePy-V}\right)\left(\mathrm{TCNQ}\right)·{\left({\mathrm{CH}}_3\right)}_2\mathrm{CO}$. Ab initio molecular orbital calculations indicate that there are four types of competing ferro- and antiferromagnetic nearest-neighbor interactions present in the system, which combine to form an $S=1/2$ FFSL. Below room temperature, the magnetic susceptibility of the material can be considered to arise from the $S=1/2$ FFSL formed by the $p$-MePy-V and indicates that the system forms a quantum valence-bond solid state whose excitation energy is gapped. Furthermore, we also observe semiconducting behavior arising from the one-dimensional chain structure of the TCNQ molecules.

Samarium hexaboride $\left({\mathrm{SmB}}_6\right)$, a Kondo insulator with mixed valence, has recently attracted much attention as a possible host for correlated topological surface states. Here, we use a combination of x-ray absorption and reflectometry techniques, backed up with a theoretical model for the resonant $M_{4,5}$ absorption edge of Sm and photoemission data, to establish laterally averaged chemical and valence depth profiles at the surface of ${\mathrm{SmB}}_6$. We show that upon cleaving, the highly polar (001) surface of ${\mathrm{SmB}}_6$ undergoes substantial chemical and valence reconstruction, resulting in boron termination and a ${\mathrm{Sm}}^{3+}$ dominated subsurface region. Whereas at room temperature, the reconstruction occurs on a timescale of less than 2 h, it takes about 24 h below 50 K. The boron termination is eventually established, irrespective of the initial termination. Our findings reconcile earlier depth resolved photoemission and scanning tunneling spectroscopy studies performed at different temperatures and are important for better control of surface states in this system.