The chiral edge modes of a topological superconductor can transport fermionic quasiparticles with Abelian exchange statistics, but they can also transport non-Abelian anyons: edge vortices bound to a $\pi$-phase domain wall that propagates along the boundary. A pair of such edge vortices is injected by the application of an $h/2e$ flux bias over a Josephson junction. Existing descriptions of the injection process rely on the instantaneous scattering approximation of the adiabatic regime [Beenakker et al., Phys. Rev. Lett. 122, 146803 (2019)], where the internal dynamics of the Josephson junction is ignored. Here, we go beyond that approximation in a time-dependent many-body simulation of the injection process, followed by a braiding of mobile edge vortices with a pair of immobile Abrikosov vortices in the bulk of the superconductor. Our simulation sheds light on the properties of the Josephson junction needed for a successful implementation of a flying topological qubit.

We derive an effective spin-Hamiltonian accounting for the exciton fine structure in quasi-spherical zinc-blende semiconductor nanocrystals within the $\mathbf{k}·\mathbf{p}$ formalism explicitly taking into account the spin-orbit split-off valence band. It is shown that, for excitons in nanocrystals made of III-V and II-VI semiconductors with fairly small spin-orbit splitting, the scaling of the electron-hole exchange interaction with the nanocrystal size insignificantly differs from the inverse nanocrystal volume law predicted within the model neglecting the spin-orbit split-off band. Numerical calculations are performed for InP nanocrystals.

As representative semiconducting hexagonal carbon-boron-nitride lattices, ${\mathrm{C}}_6\mathrm{BN}$ and ${\mathrm{C}}_2\mathrm{BN}$ are experimentally realized two-dimensional (2D) plane materials and have recently become the focus of research. Herein, combining first-principles calculations with the Boltzmann transport equation, we performed a comprehensive study on the phonon interaction and thermal conductivity in ${\mathrm{C}}_6\mathrm{BN}$ and ${\mathrm{C}}_2\mathrm{BN}$ monolayers. It is found that the thermal conductivities of ${\mathrm{C}}_6\mathrm{BN}$ and ${\mathrm{C}}_2\mathrm{BN}$ monolayers at room temperature are reduced by 79% and 73%, respectively, due to four-phonon scattering, compared with the results including three-phonon scattering only. We can attribute this phenomenon to giant four-phonon scattering exclusive for the heat-carrying out-of-plane acoustic (ZA) phonons, because the reflection symmetry allows four-ZA processes much higher than three-ZA processes, and the quasiparallel behavior between the ZA and low-lying out-of-plane optical (ZO) branches contribute to a broad phase space for four-phonon scattering as well. Moreover, ${\mathrm{C}}_6\mathrm{BN}$ monolayer exhibits unusual behavior that optical phonons contribute about ∼60% to the overall thermal conductivity under the four-phonon picture, which differs from the traditional case that acoustic phonons dominate thermal conductivity. Unexpectedly, two low-lying ZO modes have as high as 38% contributions to the thermal transport at 300 K under the four-phonon picture, causing 60% contribution of optical phonon modes, apparently larger than that of the three-phonon case (15%) and many other 2D materials, also indicating the four-phonon scattering has a more significant effect on acoustic phonons than on optical phonons. This finding not only highlights insight into the nature of phonon transport, but also provides a promising strategy for manipulation of heat transport based on optical phonon modes.

Recent theoretical works on two-dimensional molybdenum disulfide (${\mathrm{MoS}}_2$) with sulfur vacancies predict that the suppression of thermal transport in ${\mathrm{MoS}}_2$ by point defects is more prominent in monolayers and becomes negligible as the layer number increases. Here, we investigate experimentally the thermal transport properties of two-dimensional (2D) molybdenum disulfide crystals with inherent sulfur vacancies. We study the first-order temperature coefficients of interlayer and intralayer Raman modes of ${\mathrm{MoS}}_2$ crystals with different layer numbers and stacking orders. The in-plane thermal conductivity ($\kappa$) and total interface conductance per unit area ($g$) across the 2D material-substrate interface of mono-, bi-, and trilayer ${\mathrm{MoS}}_2$ samples are measured using micro-Raman thermometry. Our results clearly demonstrate that the thermal conductivity is significantly suppressed by sulfur vacancies in monolayer ${\mathrm{MoS}}_2$. However, this reduction in $\kappa$ becomes less evident as the layer number increases, confirming the theoretical predictions. No significant variation is observed in the $\kappa$ and $g$ values of $2H$ and $3R$ stacked bilayer ${\mathrm{MoS}}_2$ samples.

Two-dimensional (2D) materials offer a large variety of optical properties, from transparency to plasmonic excitation. They can be structured and combined to form heterostructures that expand the realm of possibility to manipulate light interactions at the nanoscale. Appropriate and numerically efficient models accounting for the high intrinsic anisotropy of 2D materials and heterostructures are needed. In this article, we retrieve the relevant intrinsic parameters that describe the optical response of a homogeneous 2D material from a microscopic approach. Well-known effective models for vertical heterostructure (stacking of different layers) are retrieved. We found that the effective optical response model of horizontal heterostructures (alternating nanoribbons) depends on the thickness. In the thin layer model, well adapted for 2D materials, a counterintuitive in-plane isotropic behavior is predicted. We confront the effective model formulation with exact reference calculations such as ab initio calculations for graphene, hexagonal boron nitride (hBN), as well as corrugated graphene with larger thickness but also with classical electrodynamics calculations that exactly account for the lateral structuration.

$1T\text{−}\mathrm{Nb}{\mathrm{Se}}_2$ is a $d^1$ transition metal dichalcogenide, featuring a $\text{low-}T \sqrt{13}\times \sqrt{13}$ commensurate charge-density-wave (CCDW) phase with the formation of a star of David (SD) pattern. Here, we investigate the temperature dependence of the lattice and electronic structures of the $1T\text{−}\mathrm{Nb}{\mathrm{Se}}_2$ monolayer using ab initio molecular dynamics simulations, which predicts that the CCDW phase transition can persist up to 350 K. Before melting, an unprecedented enhancement of CCDW order is revealed at $\sim 50$ K, characterized by two order parameters which respectively indicate the in-plane negative thermal expansion and out-of-plane buckling of the SDs. Such lattice distortion takes place in each SD individually via a detailed balance kinetic process, and the induced sharp variation of the charge gap size and the local density of states are consistent with recent scanning tunneling microscopy observations. This unique phenomenon, which is absent in the more extensively studied $d^1$ transition metal dichalcogenide $1T\text{−}\mathrm{Ta}{\mathrm{S}}_2$, is explained by the delicate competition between lattice energy and entropy.

According to the Kibble-Zurek mechanism, there is a universal power-law relationship between the defect density and the quench rate during a slow linear quench through a critical point. It is generally accepted that a fast quench results in a deviation from the Kibble-Zurek scaling law and leads to the formation of a saturated plateau in the defect density. By adjusting the quench rate from slow to very fast limits, we observe the varying quench dynamics and identify a presaturated regime that lies between the saturated and Kibble-Zurek regimes. This significant result is first elucidated through the adiabatic-impulse approximation, then verified by a rigorous analysis on the transverse Ising chain as well. As we approach the turning point from the saturated to presaturated regimes, we notice a change in scaling laws and, with an increase in the initial transverse field, a shrinking of the saturated regime until it disappears. During another turning point from the Kibble-Zurek to presaturated regimes, we observe an attenuation of the dephasing effect and a change in the behavior of the kink-kink correlation function from a Gaussian decay to an exponential decay. Finally, the coherent many-body oscillation after quench exhibits different behaviors in the three regimes and shows a significant change of scaling behavior between the S and PS regimes.

Biasing a three-terminal Josephson junction (TTJ) with symmetrical voltages $0,V,-V$ leads to new kinds of DC currents, namely quartet Josephson currents and phase-dependent multiple Andreev reflection (MAR) currents. We study these currents in a system where a normal diffusive metallic node $N$ is connected to three terminals $S_{0,1,2}$ by barriers of arbitrary transparency. We use the quantum circuit theory to calculate the current in each terminal, including decoherence. In addition to the stationary combination ${\phi }_Q={\phi }_1+{\phi }_2-2{\phi }_0$ of the terminal phases ${\phi }_i$, the bias voltage $V$ appears as a new and unusual control variable for a DC Josephson current. A general feature is the sign changes of the current-phase characteristics, manifesting in minima of the quartet “critical current”. Those sign changes can be triggered by the voltage, by the junction transparency or by decoherence. We study the possible separation of quartet currents from MAR currents in different regimes of parameters, including a “funnel” regime with very asymmetric couplings to $S_{0,1,2}$. In the regime of low transparency and asymmetric couplings, we provide an analytic perturbative expression for the currents, which shows an excellent agreement with the full numerical results.

We study mesoscopic signatures of the topological Anderson transitions in topological disordered chains. To this end we introduce an integer-valued sample-specific definition of the topological index in finite-size systems. Its phase diagram exhibits a fascinating structure of intermittent topological phases, dubbed topological islands. Their existence is rooted in the real zeros of the underlying random polynomial. Their statistics exhibits finite-size scaling, pointing to the location of the bulk topological Anderson transition. While the average theories in AIII and BDI symmetry classes are rather similar, the corresponding patterns of topological islands and their statistics are qualitatively different. We also discuss observable signatures of sharp topological transitions in mesoscopic systems, such as persistent currents and entanglement spectra.

We carry out a theoretical study of unconventional superconductivity in twisted bilayer cuprates (TBCs) as a function of electron density and layer twist angle. The bilayer $t\text{−}J\text{−}U$ model is employed and analyzed within the framework of a generalized variational wave function approach in the statistically consistent Gutzwiller formulation. The constructed phase diagram encompasses both a gapless $d$-wave state (reflecting the pairing symmetry of untwisted copper-oxides) and gapped $d+{\mathrm{e}}^{i\phi }d$ phase that breaks spontaneously time reversal symmetry (TRS) and is characterized by a nontrivial Chern number. We find that the $d+{\mathrm{e}}^{i\phi }d$ state occupies a nonconvex butterfly-shaped region in the doping versus twist-angle plane and demonstrate the presence of a reentrant TRS-breaking phase on the underdoped side of the phase diagram. This circumstance supports the emergence of topological superconductivity for fine-tuned twist angles in TBC away from ${45}^{\circ }$. Our analysis of the microscopically derived Landau free-energy functional points toward sensitivity of the superconducting order parameter to small perturbations close to the topological state boundary.

Understanding the role of lattice geometry in shaping topological states and their properties is of fundamental importance to condensed matter and device physics. Here, we demonstrate how an anisotropic crystal lattice drives a topological hybrid nodal line in transition metal tetraphosphides $M{\mathrm{P}}_4$ ($M$ = transition metal). $M{\mathrm{P}}_4$ constitutes a unique class of black phosphorus materials formed by intercalating transition metal ions between the phosphorus layers without destroying the characteristic anisotropic band structure of the black phosphorous. Based on the first-principles calculations and $k·p$ theory, we show that $M{\mathrm{P}}_4$ harbors a single hybrid nodal line formed between anisotropic $Md$ and P states with oppositely oriented effective masses. The nodal line consists of both type-I and type-II nodal band crossings whose nature and location are determined by the effective mass anisotropies of the intersecting bands. We further discuss a possible topological phase transition to exemplify the formation of the hybrid nodal-line state in $M{\mathrm{P}}_4$. Our results offer a comprehensive study for understanding the interplay between structural motifs-driven mass anisotropies and topology in anisotropic lattice materials to realize hybrid semimetal states.

We investigate interaction-driven integer quantum Hall states realized in Landau levels of monolayer graphene when two out of its four nearly degenerate spin-valley flavors are filled. By employing a model that accounts for interactions beyond pure $\delta$-functions as well as Zeeman and substrate-induced valley potentials, we demonstrate the existence of a delicate competition of several phases with spontaneous generation of spin-valley entanglement, akin to the spontaneous appearance of spin-orbit coupling driven by interactions. We encounter a particular phase that we term the entangled-Kekulé-antiferromagnet (E-KD-AF) which only becomes spin-valley entangled under the simultaneous presence of Zeeman and substrate potentials, because it gains energy by simultaneously canting in the spin and valley spaces, by combining features of a canted antiferromagnet and a canted Kekulé state. We quantify the degree of spin-valley entanglement of the many competing phases by computing their bipartite concurrence.

The electronic structure of nickel dichalcogenides, ${\mathrm{NiS}}_2$ and ${\mathrm{NiSe}}_2$, in monolayer form, is studied employing first-principles methods. We assess the importance of band ordering, covalency, and Coulomb interactions in the ground state of these systems. Hybrid functional results are compared with standard functionals and also with Hubbard-corrected functionals to systematically address the role of electronic interactions and localization. Using empirical as well as linear response derived and modified parameters, we found that mean-field correlations realized by intersite Hubbard interactions are directly linked to the magnitude of the energy band gap. This gives compelling evidence that the $\mathrm{DFT}+U+V$ method is suitable to describe the charge transfer insulating phase in these materials.

We explore the Kardar-Parisi-Zhang (KPZ) scaling in the one-dimensional Hubbard model, which exhibits global $S{U}_c\left(2\right)\otimes S{U}_s\left(2\right)$ symmetry at half filling, for the pseudocharge and the total spin. We analyze dynamical scaling properties of high-temperature charge and spin correlations and transport. At half filling, we observe a clear KPZ scaling in both charge and spin sectors. Away from half filling, the $S{U}_c\left(2\right)$ charge symmetry is reduced to $U_c\left(1\right)$, while the $S{U}_s\left(2\right)$ symmetry for the total spin is retained. Consequently, transport in the charge sector becomes ballistic, while KPZ scaling is preserved in the spin sector. These findings confirm the link between non-Abelian symmetries and KPZ scaling in the presence of integrability. We study two settings of the model: one involving a quench from a bipartitioned state asymptotically close to the $T=\infty$ equilibrium state of the system, and another where the system is coupled to two Markovian reservoirs at the two edges of the chain.

At low lattice temperatures the nuclear spins in a solid form a closed thermodynamic system that is well isolated from the lattice. Thermodynamic properties of the nuclear spin system are characterized by the local field of spin-spin interactions, which determines its heat capacity and the minimal achievable nuclear spin temperature in demagnetization experiments. We report the results of measurement of the local field for the nuclear spin system in GaAs, which is a model material for semiconductor spintronics. The choice of the structure, a weakly doped GaAs epitaxial layer with weak residual deformations, and of the measurement method, the adiabatic demagnetization of optically cooled nuclear spins, allowed us to refine the value of the nuclear spin-spin local field, which turned out to be two times less than one previously obtained. Our experimental results are supported by calculations, which take into account dipole-dipole and indirect (pseudodipolar and “exchange”) nuclear spin interactions as well as quadrupole splitting of nuclear spins in the vicinity of charged impurity centers.

Electron interactions in quantum devices can exhibit intriguing phenomena. One example is assembling an electronic device in series with an on-chip resistor. The quantum laws of electricity of the device are modified at low energies and temperatures by dissipative interactions induced by the resistor, a phenomenon known as the dynamical Coulomb blockade (DCB). The DCB strength is usually nonadjustable in a fixed environment defined by the resistor. Here, we design an on-chip circuit for InAs-Al hybrid nanowires where the DCB strength can be gate-tuned in situ. InAs-Al nanowires could host Andreev or Majorana zero-energy states. This technique enables tracking the evolution of the same state while tuning the DCB strength from weak to strong. We observe the transition from a zero-bias conductance peak to split peaks for Andreev zero-energy states. Our technique opens the door to in situ tuning interaction strength on zero-energy states.

Combining non-Hermiticity and interactions yields unique effects in open quantum many-body systems. Here, we develop the generalized Schrieffer-Wolff transformation, discuss its symmetry properties, and derive the effective Hamiltonian suitable for various quasidegenerate non-Hermitian systems. We apply our results to an exemplary $\mathcal{P}\mathcal{T}$-symmetric circuit QED composed of two non-Hermitian qubits embedded in a lossless resonator. We consider a resonant quantum circuit as $|{\omega }_r-\mathrm{\Omega }|\ll {\omega }_r$, where $\mathrm{\Omega }$ and ${\omega }_r$ are qubits and resonator frequencies, respectively, providing well-defined groups of quasidegenerate resonant states. For such a system, using direct numerical diagonalization we obtain the dependence of the low-lying eigenspectrum on the interaction strength between a single qubit and the resonator $g$ and the gain (loss) parameter $\gamma$, and compare that with the eigenvalues obtained analytically using the effective Hamiltonian of resonant states. We identify $\mathcal{P}\mathcal{T}$-symmetry broken and unbroken phases, trace the formation of exceptional points of the second and the third order, and provide a complete phase diagram $g-\gamma$ of low-lying resonant states. We relate the formation of exceptional points to the additional $\mathcal{P}$-pseudo-Hermitian symmetry of the system and show that non-Hermiticity mixes the “dark” and the “bright” states, which has a direct experimental consequence.

We employ the Lindblad master equation method to study the nonequilibrium dynamics following a parametric quench in the Hamiltonian of an open, two-dimensional superconducting system coupled to an external bath. Within our approach we show how, in the open system, the dissipation works as an effective stabilization mechanism in the time evolution of the system after the quench. Eventually, we evidence how the mismatch between the phases corresponding to the initial and to the final state of the system determines a dynamical phase transition between the two distinct phases. Our method allows for fully characterizing the dynamical phase transition in an open system in several cases of physical relevance, by means of a combined study of the time-dependent superconducting gap and of the fidelity between density matrices.