The noninteracting and non-Hermitian, parity-time $\left(\mathcal{PT}\right)$ symmetric Anderson model exhibits an exceptional point (EP) at a non-Hermitian coupling $g=1$, which remains unrenormalized in the presence of interactions [J. A. S. Lourenço et al., Phys. Rev. B 98, 085126 (2018)], where the EP was shown to coincide with the quantum critical point for Kondo destruction. In this work, we consider a quantum dot hybridizing with metallic leads having Rashba spin-orbit coupling $\left(\lambda \right)$. We show that for a non-Hermitian hybridization, $\lambda$ can renormalize the exceptional point even in the noninteracting case, stabilizing $\mathcal{PT}$ symmetry beyond $g=1$. Through exact diagonalization of a zero-bandwidth, three-site model, we show that the quantum critical point and the exceptional point bifurcate, with the critical point for Kondo destruction at $g_c=1$, and the exceptional coupling being $g_{EP}>1$ for all $U\ne 0$ and $\lambda \ge 0;\lambda \ne U/2$. On the line $\lambda =U/2$, the critical point and the EP again coincide at $g_c=g_{EP}=1$. The full model with finite-bandwidth leads is investigated through the slave-boson approach, using which we show that, in the strong-coupling regime, $\lambda$ and interactions cooperate in strongly reducing the critical point associated with Kondo destruction, below the $\lambda =0$ value.

While the growth of germanene has been extensively claimed on many substrates, their exact crystal structures remain controversial. Herein, we systematically explore the surface structures of Ge deposition onto the Al(111) surface by theoretical calculations combined with available scanning tunneling microscopy (STM) and low-energy electron diffraction data. We show that the formation of germanene on Al(111) is energetically unfavorable by $abinitio$ evolutionary simulations and high-level random-phase approximation calculations, and the two experimental phases are identified as honeycomb alloys ${\mathrm{Al}}_3{\mathrm{Ge}}_3/\mathrm{Al}\left(\sqrt{7}\times \sqrt{7}\right)$ and ${\mathrm{Al}}_3{\mathrm{Ge}}_4/\mathrm{Al}\left(3\times 3\right)$. It is interesting to find a vacancy at the interface of ${\mathrm{Al}}_3{\mathrm{Ge}}_4/\mathrm{Al}\left(3\times 3\right)$, which is responsible for the dark clover pattern in STM experiments. Our results clarify the structural controversy of the Ge/Al(111) system and indicate that the fabrication of germanene on Al(111) remains challenging.

Alloy engineering is a well-established approach to tune various materials’ properties, but its application to topological alloys remains rudimentary. Of special interest is the band gap, the most defining property of topological materials; however, the concentration dependence of energy gaps in topological alloys remains unknown. Here we systematically investigate the band gap evolution of a topological alloy as a function of alloy concentration, using $\mathrm{KZn}{\mathrm{Sb}}_{1-\mathrm{x}}{\mathrm{Bi}}_{\mathrm{x}}$ as a prototype, based on first-principles calculations. In contrast to the well-established smooth bowing curve for a trivial gap in semiconductor alloys, we found that the topological gap evolves generally with a complex fragmented pattern due to topological phase transitions, and most strikingly a linear dependence on concentration locally in each distinct phase. Such gap linearization is fundamentally rooted in the linear dependence on alloy concentration of spin-orbit coupling (SOC) that predominantly determines a topological gap. Furthermore, we demonstrate topological alloy engineering as a general approach to tune the topological order by modulating the band edge composition and degeneracy through the alloying-induced interplay of SOC and atomic orbital on-site energy, while the linear gap dependence on alloy concentration remains independent of the degree of topological order.

The multiferroic and the rotating magnetocaloric properties of ${\mathrm{Nd}}_{0.8}{\mathrm{Tb}}_{0.2}{\mathrm{Mn}}_2{\mathrm{O}}_5$ are investigated by microscopic optical probes and macroscopic magnetic measurements. Raman-active phonons as a function of temperature, and ${\mathrm{Nd}}^{3+}$ and ${\mathrm{Tb}}^{3+}$ infrared active crystal-field (CF) excitations as a function of temperature and under magnetic fields up to 11 T have been studied in ${\mathrm{Nd}}_{0.8}{\mathrm{Tb}}_{0.2}{\mathrm{Mn}}_2{\mathrm{O}}_5$. The obtained results are compared to those of ${\mathrm{NdMn}}_2{\mathrm{O}}_5$ and ${\mathrm{TbMn}}_2{\mathrm{O}}_5$ reference compounds. The observation of one set of Raman-active phonons and CF excitations rule out possible twinning while their energy positions and thermal evolutions indicate noticeable changes of Mn1-O3-Mn1 and ${\mathrm{TbO}}_8$ structural units. This would explain the nature of separated magnetic phases in ${\mathrm{Nd}}_{0.8}{\mathrm{Tb}}_{0.2}{\mathrm{Mn}}_2{\mathrm{O}}_5$. The degeneracy of the ground-state Kramers doublet is lifted $({\mathrm{\Delta }}_0\sim 9\mathrm{c}{\mathrm{m}}^{\text{–}1})$, indicating that the ${\mathrm{Nd}}^{3+}\text{–}{\mathrm{Mn}}^{3+}$ interaction impacts the magnetic and ferroelectric properties of ${\mathrm{Nd}}_{0.8}{\mathrm{Tb}}_{0.2}{\mathrm{Mn}}_2{\mathrm{O}}_5$. The Zeeman splitting of excited crystal-field levels of the ${\mathrm{Nd}}^{3+}$ ions at low temperatures shows that $\mathrm{the}{g}_z$ factor is weak compared to that in ${\mathrm{NdMn}}_2{\mathrm{O}}_5$. This indicates that the $R^{3+}$ spins in ${\mathrm{Nd}}_{0.8}{\mathrm{Tb}}_{0.2}{\mathrm{Mn}}_2{\mathrm{O}}_5$ are mostly aligned within the $ab$-plane. The nature of magnetocrystalline anisotropy in ${\mathrm{Nd}}_{0.8}{\mathrm{Tb}}_{0.2}{\mathrm{Mn}}_2{\mathrm{O}}_5$ as well as in all $R{\mathrm{Mn}}_2{\mathrm{O}}_5$ compounds is quantitatively investigated by studying the anisotropy of paramagnetic Curie temperatures along (${\theta }_{\left|\right|}$) and perpendicular (${\theta }_{\perp }$) to the $c$ axis, $\left({\theta }_{\left|\right|}-{\theta }_{\perp }\right)$, as a function of the rare-earth atomic number. It is particularly found that the magnetocrystalline anisotropy is mainly determined by the quadrupolar charge distribution of $4f$ shells. The rotating magnetocaloric effect in ${\mathrm{Nd}}_{0.8}{\mathrm{Tb}}_{0.2}{\mathrm{Mn}}_2{\mathrm{O}}_5$ is also evaluated and compared to that in ${\mathrm{NdMn}}_2{\mathrm{O}}_5$ and ${\mathrm{TbMn}}_2{\mathrm{O}}_5$. Our findings show that Nd- and Tb- separated magnetic phases independently contribute to the magnetocaloric effect of ${\mathrm{Nd}}_{0.8}{\mathrm{Tb}}_{0.2}{\mathrm{Mn}}_2{\mathrm{O}}_5$.

Edge states of two-dimensional topological insulators are helical and single-particle backscattering is prohibited by time-reversal symmetry. In this paper, we show that an isotropic exchange coupling of helical edge states (HES) to a spin 1/2 impurity subjected to a magnetic field results in characteristic backscattering current noise (BCN) as a function of bias voltage and tilt angle between the direction of the magnetic field and the quantization axis of the HES. In particular, we find transitions from sub-Poissonian (antibunching) to super-Poissonian (bunching) behavior as a direct consequence of the helicity of the edge state electrons. We use the method of full counting statistics within a master equation approach treating the exchange coupling between the spin-1/2 impurity and the HES perturbatively. We express the BCN via coincidence correlation functions of scattering processes between the HES, which gives a precise interpretation of the Fano factor in terms of bunching and antibunching behavior of electron jump events. We also investigate the effect of electron-electron interactions in the HES in terms of the Tomonaga-Luttinger liquid theory.

Recently, the two-dimensional magnetic semiconductor CrSBr has attracted considerable attention due to its excellent air-stable property and high magnetic critical temperature. Here, we systematically investigate the electronic structure, magnetocrystalline anisotropy energy, first-order magneto-optical effects (Kerr and Faraday effects), and second-order magneto-optical effects (Schäfer-Hubert and Voigt effects) as well as intrinsically anomalous transport properties (anomalous Hall, anomalous Nernst, and anomalous thermal Hall effects) of two-dimensional van der Waals layered magnets $\mathrm{Cr}\mathit{XY} (X=\mathrm{S},\mathrm{Se},\mathrm{Te};Y=\mathrm{Cl},\mathrm{Br},\mathrm{I})$ by using first-principles calculations. Our results show that monolayer and bilayer $\mathrm{Cr}\mathit{XY} (X=\mathrm{S},\mathrm{Se})$ are narrow-band-gap semiconductors, whereas monolayer and bilayer $\mathrm{CrTe}Y$ are multiband metals. The magnetic ground states of bilayer $\mathrm{Cr}\mathit{XY}$ and the easy magnetization axis of monolayer and bilayer $\mathrm{Cr}\mathit{XY}$ are confirmed by the magnetocrystalline anisotropy energy calculations. Utilizing magnetic group theory analysis, the first-order magneto-optical effects as well as anomalous Hall, anomalous Nernst, and anomalous thermal Hall effects are identified to exist in a ferromagnetic state with out-of-plane magnetization. The second-order magneto-optical effects are not restricted by the above symmetry requirements, and therefore they can arise in ferromagnetic and antiferromagnetic states with in-plane magnetization. The calculated results are compared with the available theoretical and experimental data of other two-dimensional magnets and some conventional ferromagnets. The present work reveals that monolayer and bilayer $\mathrm{Cr}\mathit{XY}$ with superior magneto-optical responses and anomalous transport properties provide an excellent material platform for the promising applications of magneto-optical devices, spintronics, and spin caloritronics.

We have explored the dynamic response of in-plane magnetized thin permalloy films excited by microwave fields of high amplitudes (up to 3 Oe) at 1 GHz. The response was detected using a microstrip line by measuring the second harmonic signal generated by the dynamic components of the uniform magnetization. The data measured at ferromagnetic resonance showed the threshold effect of the Suhl parametric instability process. With the increase of the microwave power above the threshold value, the dynamic response revealed an intricate nonlinear behavior, including the emergence of an additional threshold. This second threshold can be explained in terms of the “stage by stage” process of parametric spin wave excitation following the $S$ theory of Zakharov, L’vov, and Starobinets.

In spin-$\frac{1}{2}$ Mott insulators, nonmagnetic quantum liquid phases are often argued to arise when the system shows no magnetic ordering, but identifying positive signatures of these phases or related spinon quasiparticles can be elusive. Here, we use Raman scattering to provide three signatures for spinons in a possible spin-orbit quantum liquid material $\mathrm{Ba}{}_4\mathrm{Ir}{}_3\mathrm{O}{}_{10}$: (1) a broad hump, which we show can arise from Luttinger liquid spinons in Raman with parallel photon polarizations normal to one-dimensional chains; (2) strong phonon damping from phonon-spin coupling via the spin-orbit interaction; and (3) the absence of (1) and (2) in the magnetically ordered phase that is produced when 2% of Ba is substituted by Sr [($\mathrm{Ba}{}_{0.98}\mathrm{Sr}{}_{0.02}){}_4\mathrm{Ir}{}_3\mathrm{O}{}_{10}$]. The phonon damping via itinerant spinons seen in this quantum liquid insulator suggests a mechanism for enhancing thermoelectricity in strongly correlated conductors, through a neutral quantum liquid that need not affect electronic transport.

Quantum phase transitions from the cluster-charge interaction, which is composed of competing short- and long-range interactions, are investigated on a $\pi$-flux lattice by using the mean-field theory and determinant quantum Monte Carlo (DQMC) simulations. Both methods identify a plaquette-dimer phase, which develops from a finite interaction strength. While its signature in DQMC is relatively weak, an obvious antiferromagnetic transition is revealed in the spin structure factor instead. The corresponding critical interaction and exponents are readily obtained by finite-size scalings, with the plaquette-dimer structure factor that can also be well scaled. These results suggest a possible deconfined quantum critical point between the plaquette-dimer and antiferromagnetic phases driven by the cluster-charge interaction on a $\pi$-flux lattice.

The defect levels produced in insulators doped with transition metal (TM) ions are important for a variety of defect-related optical processes and magnetic properties. Here, we performed a systematical first-principles study of the defect levels in the band gap for all the $3d^n$ TM ions occupying octahedral sites in $\alpha \text{−}{\mathrm{Al}}_2{\mathrm{O}}_3, {\mathrm{MgAl}}_2{\mathrm{O}}_4$, MgO, ${\mathrm{KMgF}}_3$, and ${\mathrm{MgF}}_2$ based on density functional theory. The spin-polarized hybrid density functional with a dielectric-dependent Hartree-Fock mixing parameter was adopted to improve the band gap. The defect levels, i.e., the charge transition levels, were obtained by calculating the total energy differences of relaxed geometric structures for various valence states, considering image-charge and potential alignment corrections. These results were rationalized with available experimental optical spectra related to the charge transfer or photoionization transitions. The calculation scheme is appropriate for predicting the valence states of TM ions and their defect levels in insulators. The trends of variation of the defect levels across the $3d$ TM series may help interpreting experimental results and aid in the design and optimization of optical materials.

Graphene on $h$-BN (G/hBN) has a long period moiré superstructure owing to the lattice mismatch between two materials. The long periodic potential caused by the moiré superstructure induces modulation of the electronic properties of the system. In this paper, we numerically calculate the optical conductivity of G/hBN under circularly polarized light irradiation. The lack of spatial inversion symmetry in G/hBN induces valley polarization. Furthermore, valley polarization becomes most pronounced in the infrared and terahertz regions if the twist angle between two materials is close to zero for the nondoping case, however, it is insensitive to the twist angle for the hole-doped case. These results will serve to design valleytronics devices using G/hBN.

We investigate the electron transport and the waiting time distribution (WTD) in a topological superconducting Coulomb island system weakly coupled to two metallic leads. A pair of Majorana bound states are hosted in the island with a finite charging energy. By employing the Markovian master equation, we study the effect of interplay between Majorana energy splitting and the charging energy on the current correlations and the relevant electron WTDs. It is found that the super-Poissonian shot noise could be induced when the Majorana energy splitting is larger than the charging energy. The reason is that the degeneracy of the ground states in the island could be lifted by a finite Majorana energy splitting, which produces the asymmetry between tunneling channels and leads to the dynamical channel blockade effect. We show that the WTD for electron tunneling through two Majorana bound states is equivalent to the WTD in a single-resonant-level device. For comparison, we also discuss the WTD for electron tunneling through a non-Majorana device. It is found that the WTD sensitively depends on the length of the island and indicates oscillation behaviors in the absence of Majorana bound states. The particular behaviors of the WTDs in a Majorana island device can be useful in identifying the existence of Majorana bound states. Furthermore, we study the randomness parameter of the waiting time to describe the fluctuations of waiting times. It is shown that the randomness parameter indicates behavior similar to that indicated by the noise Fano factor, and both of them reflect the information of tunneling dynamics.

The fractionalization of global symmetry charges is a striking hallmark of topological quantum order. Here, we discuss the fractionalization of subsystem symmetries in two-dimensional topological phases. In line with previous no-go arguments, we show that subsystem symmetry fractionalization is not possible in many cases due to the additional rigid geometric structure of the symmetries. However, we identify a mechanism that allows fractionalization, involving global relations between macroscopically many symmetry generators. We find that anyons can fractionalize such relations, meaning that the total charge carried under all generators involved in the global relation is nontrivial, despite the fact that these generators multiply to the identity. We first discuss the general algebraic framework needed to characterize this type of fractionalization, and then explore this framework using a number of exactly solvable models with ${\mathbb{Z}}_2$ topological order, including models having line and fractal symmetries. These models all showcase another necessary property of subsystem symmetry fractionalization: Fractionalized anyons must have restricted mobility when the symmetry is enforced, such that they are confined to a single line or point in the case of line and fractal symmetries, respectively. Looking forward, we expect that our identification of the importance of global relations in fractionalization will hold significance for the classification of phases with subsystem symmetries in all dimensions.

The understanding and modeling of heat transport across nanometer and subnanometer gaps, where the distinction between thermal radiation and conduction becomes blurred, remains an open question. In this work, we present a three-dimensional atomistic simulation framework by combining the molecular dynamics (MD) and phonon nonequilibrium Green's function (NEGF) methods. The relaxed atomic configuration and interaction force constants of metallic vacuum nanogaps are generated from MD as inputs into harmonic phonon NEGF. Phonon tunneling across gold-gold and copper-copper nanogaps is quantified, and is shown to be a significant heat transport channel below a gap size of 1 nm. We demonstrate that lattice anharmonicity contributes to within 20%–30% of phonon tunneling depending on gap size, whereas electrostatic interactions turn out to have a weak effect for the small bias voltage typically used in experimental measurements. This work provides detailed information of the heat current spectrum and interprets the recent experimental determination of thermal conductance across gold-gold nanogaps. Our study contributes to deeper insight into heat transport in the extremely near-field regime, as well as hints for future experimental investigation.

We consider square and equilateral triangular open acoustic resonators with the $C_{4v}$ and $C_{3v}$ symmetries, respectively. There is a unique property of square and triangular resonators of accidental number fourfold degeneracy of eigenstates that gives rise to twofold-degenerate Friedrich-Wintgen (FW) bound states in the continuum (BICs). Compared to usual FW BICs, the degenerate FW BICs maintain high $Q$ factor in wide range of the size of resonators. That removes the fabrication difficulties of the proper choice of resonator. The presence of degenerate BICs in triangular resonators is extremely sensitive to switch output flows by small perturbations with $100\%$ efficiency.

We use the nonequilibrium bosonization technique to study the effects of Coulomb interactions in mesoscopic electron colliders based on quantum Hall edge states at filling factor $\nu =2$. The current cross correlations and Fano factor, which carry the information about the exclusion statistics, are calculated. It is shown that both these quantities have a nonanalytical dependence on the source transparency, which scales as $log(1/T_s)$ at small $T_s\ll 1$. This is a consequence of electron-electron interactions in the outgoing nonequilibrium states of the collider.

Quantifying entanglement of multiple subsystems is a challenging open problem in interacting quantum systems. Here, we focus on two subsystems of length $\ell$ separated by a distance $r=\alpha \ell$ and quantify their entanglement negativity ($\mathcal{E}$) and mutual information ($\mathcal{I}$) in critical random Ising chains. We find universal constant $\mathcal{E}\left(\alpha \right)$ and $\mathcal{I}\left(\alpha \right)$ over any distances, using the asymptotically exact strong disorder renormalization group method. Our results are qualitatively different from both those in the clean Ising model and random spin chains of a singlet ground state, like the spin-$\frac{1}{2}$ random Heisenberg chain and the random XX chain. While for random singlet states $\mathcal{I}\left(\alpha \right)/\mathcal{E}\left(\alpha \right)=2$, in the random Ising chain this universal ratio is strongly $\alpha$ dependent. This deviation between systems contrasts with the behavior of the entanglement entropy of a single subsystem, for which the various random critical chains and clean models give the same qualitative behavior. The reason is that $\mathcal{E}$ and $\mathcal{I}$ are sensitive to higher order correlations in the ground-state structure. Therefore, studying multipartite entanglement provides additional universal information in random quantum systems, beyond what we can learn from a single subsystem.