The dynamical quantum phase transition is characterized by the emergence of nonanalytic behaviors in the rate function, corresponding to the occurrence of exact zero points of the Loschmidt echo in the thermodynamical limit. In general, exact zeros of the Loschmidt echo are not accessible in a finite-size quantum system except for some fine-tuned quench parameters. In this work, we study the realization of the dynamical singularity of the rate function for finite-size systems under the twist boundary condition, which can be introduced by applying a magnetic flux. By tuning the magnetic flux, we illustrate that exact zeros of the Loschmidt echo can be always achieved when the postquench parameter is across the underlying equilibrium phase transition point, and thus the rate function of a finite-size system is divergent at a series of critical times. We demonstrate our theoretical scheme by calculating the Su-Schrieffer-Heeger model and the Creutz model in detail and exhibit its applicability to more general cases. Our result unveils that the emergence of dynamical singularity in the rate function can be viewed as a signature for detecting dynamical quantum phase transition in finite-size systems. We also unveil that the critical times in our theoretical scheme are independent on the systems size, and thus it provides a convenient way to determine the critical times by tuning the magnetic flux to achieve the dynamical singularity of the rate function.

We show that phase transitions in the quantum $q$-state clock model for $q\le 4$ can be characterized by an enhanced decay behavior of the Loschmidt echo via a small quench. The quantum criticality of the quantum $q$-state clock model is numerically investigated by the finite-size scaling of the first minimum of the Loschmidt echo and the short-time average of the rate function. The equilibrium correlation-length critical exponents are obtained from the scaling laws which are consistent with previous results. Furthermore, we study dynamical quantum phase transitions by analyzing the Loschmidt echo and the order parameter for any $q$ upon a big quench. For $q\le 4$, we show that dynamical quantum phase transitions can be described by the Loschmidt echo and the zeros of the order parameter. In particular, we find the rate function increases logarithmically with $q$ at the first critical time. However, for $q>4$, we find that the correspondence between the singularities of the Loschmidt echo and the zeros of the order parameter no longer exists. Instead, we find that the Loschmidt echo near its first minimum converges, while the order parameter at its first zero increases linearly with $q$.

The local structure and orientational correlations (OCs) of liquid oxygen up to supercritical conditions have been determined using highly accurate ab initio pair potentials and a spin-average approximation. The predicted radial distribution functions are in excellent agreement with all the available experimental data covering a wide range of temperatures and pressures. The elusive shoulder characteristic of several diatomic fluids is accurately reproduced and, more importantly, its true origin elucidated by performing an exhaustive analysis of the OCs, indicating the relevance of specific configurations.

As topological spin textures, magnetic skyrmions in chiral magnets show a universal current-velocity relation when driven by spin transfer torques. In general, the skyrmions in chiral magnets do not exhibit Walker breakdown—a phenomenon that domain walls' motion modes will change from steady to precessional motion when the driving forces are sufficiently large. In this work, we studied the dynamics of magnetic skyrmions in cylindrical nanotubes numerically and analytically. The skyrmion performs a helical motion in the nanotube without external fields. However, we show that the skyrmion exhibits the Walker breakdown phenomenon when an external field is applied to the nanotube perpendicularly. A steady skyrmion motion is observed in the low current regime, while the skyrmion moves forward and back when the current is larger than a critical density. Our findings reveal a new way to tune the skyrmion dynamics beyond planar geometries.

This paper shows that the WKB quantization rule is suitable for the Andreev bound states in nonuniform superconductors. We consider nonhomogeneous superconductivity gap functions $\mathrm{\Delta }\left(x\right)$ in superconductors with the Bogoliubov quasiparticle energy $E$, the Fermi level $E_F$, and the total momentum $\mathbf{p}$ at $E_F+E$. The Andreev bound states in the well of slowly varying $\left|\mathrm{\Delta }\right(x\left)\right|$ are studied, and the well may also be induced by the phase variation of $\mathrm{\Delta }\left(x\right)$ for massless Dirac fermions. By applying the WKB method to the Bogoliubov–de Gennes equation, we obtain two main results: (i) For $E_F\sim 0$, the bound states are determined by ${\int }_{L_E}^{R_E}\left|\mathbf{p}d\mathbf{x}\right|=(\frac{1}{2}+n)\pi \hslash$, where $n\in {\mathbb{N}}_0$ and $L_E$ and $R_E$ are the boundary points between the classically allowed region and forbidden regions, and (ii) for $E_F\gg E$ and $\left|\mathrm{\Delta }\right(x\left)\right|$, the bound states are given by ${\int }_{L_E}^{R_E}|\mathbf{p}\pm {\mathbf{p}}_F|dx=(\frac{1}{2}+n)\pi \hslash$ with small $p_{y\left(z\right)}$. Empirical quantization conditions are provided for broader parameter regions. In addition to applying the traditional WKB method, we also develop a generalized WKB method to tackle semimetals with parabolic dispersion relationships. The applications of our results are discussed, for example, Dirac $\pi$ junctions or nonchiral Majorana wires, SNS junctions, the excitation threshold, and the tunneling rate in NSN junctions. In the $\pi$ junction, the Majorana zero modes correspond to the zero-point energy in the WKB formalism. This observation may provide insights into the Majorana bound state in a vortex and the Majorana fermions in high-energy physics.

The combined role of the spin-orbit effect (SOC), electron correlation ($U$), and magnetism has had a significant impact on the electron transport behavior in disordered systems. Here, we report an experimental investigation of weak localization (WL) behavior in layered SOC-dominated iridate ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ where these impacting parameters are further tuned with substitution of Ru and Ti, which have different magnetic and electronic characters. Magnetic ${\mathrm{Ru}}^{4+} \left(4d^4\right)$ participates in magnetic interaction with existing ${\mathrm{Ir}}^{4+}$ as well as with itself, while nonmagnetic ${\mathrm{Ti}}^{4+} \left(3d^0\right)$ will lead to the dilution of a magnetic lattice. ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ shows a crossover from negative to positive magnetoconductivity (MC) with the onset of magnetic ordering where the WL behavior is observed in a magnetically ordered state. In ${\mathrm{Sr}}_2{\mathrm{Ir}}_{1-x}{\mathrm{Ru}}_x{\mathrm{O}}_4$ series, a complete suppression of the magnetic and insulating state is observed with $x\sim 0.6$. However, an opposite result is seen in ${\mathrm{Sr}}_2{\mathrm{Ir}}_{1-x}{\mathrm{Ti}}_x{\mathrm{O}}_4$ series, where the magnetic ordering temperature is minimally influenced, though the magnetic moment is weakened and the insulating state is significantly strengthened. This contrasting effect on magnetism has a different impact on the crossover in MC and allied WL behavior, which basically follows the evolution of the magnetic and conducting state in both series. The ${\mathrm{Ti}}^{4+}$ further reverses the negative MC in the nonmagnetic state to positive MC with a reduction in SOC. This work demonstrates the critical role of magnetism, SOC, and $U$ in manipulating the quantum transport properties in one of the iridate materials which we believe has significance in other similar materials.

In recent years, reduced-basis methods (RBMs) have been adapted to the many-body eigenvalue problem and they have been used, largely in nuclear physics, as fast emulators able to bypass expensive direct computations while still providing highly accurate results. This work is meant to show that the RBM is an efficient and accurate emulator for the strong correlations induced by the pairing interaction in a variety of finite systems like ultrasmall superconducting grains, interacting topological superfluids, and mesoscopic hybrid superconductor-semiconductor devices, all of which require an expensive, beyond-mean-field, particle-number conserving description. These systems are modeled by the number-conserving Richardson pairing Hamiltonian and its appropriate generalizations. Their ground state is solved for exactly using the density matrix renormalization group. The reduced basis is assembled iteratively from a small number of exact ground-state vectors, well-chosen from across the relevant parameter space using a fast estimate of the emulation error and a greedy local optimization algorithm. The RBM emulation is found to accurately describe the weak-to-strong pairing crossover in small grains, the third-order topological phase transition of the interacting Richardson-Kitaev chain, and the complex charge stability diagram of a hybrid quantum dot–superconductor device. For all considered systems the emulation error decreases exponentially with the reduced-basis dimensionality. The number of basis vectors necessary to reach a fixed emulation accuracy only shows a modest linear growth with increasing system size. RBMs are confirmed to be cheap and accurate emulators for the widely encountered superconducting phenomena. Capable of providing orders of magnitude computational speedup with respect to approaches based only on traditional many-body solvers, they open new possibilities in building and solving models of interacting many-body systems and in better interfacing them with experimental design and data analysis.

Spin pumping from a ferromagnetic insulator into a high-$T_c$ superconductor with a $d$-wave superconducting order parameter has recently been experimentally observed. Such unconventional superconducting order is known to produce interfacial bound states for certain crystallographic orientations. Here, we present a methodology which can be used to study spin pumping into unconventional superconductors, including the role of interfacial bound states. As an example, we determine how the crystallographic orientation of the $d$-wave order parameter relative to the interface changes the spin-pumping effect. We find that the spin-pumping effect is slightly enhanced at low temperatures for orientations hosting interfacial bound states compared to other superconducting states. However, the spin-pumping effect does not show a coherence peak close to $T_c$ for such orientations, and instead remains smaller than the normal-state value for all $T$. For orientations not hosting interfacial bound states, we find that the pumped spin current can be increased to several times the normal-state spin current at frequencies that are small compared to the superconducting gap. Our results show that the spin-pumping dependency on frequency and temperature changes qualitatively depending on the crystallographic orientation of unconventional superconducting order parameters relative to the interface.

The low-frequency dynamical magnetic properties in paramagnetic diluted magnetic semiconductors are addressed in the framework of the dynamical mean-field theory applied for the Kondo lattice model. In the infinite-dimensional limit, a set of self-consistent equations is derived so the single-particle Green's function and its self-energy can be evaluated numerically. In terms of the Green's function and self-energies, the local dynamical spin susceptibility function and then the spin-relaxation rate are explicitly expressed based on the Baym-Kadanoff approach. It is found that the spin fluctuations become dominated, indicated by the sharp peak appearing at the low frequency of the spin dynamical susceptibility function in the case of large magnetic coupling and temperature close to the paramagnetic-ferromagnetic transition point. The low-frequency spin dynamic in the systems is also addressed in the signatures of the spin-relaxation process. In the case of large temperature and small magnetic coupling, the spin-relaxation rate releases the scenario of the Korringa process specifying the weak correlation systems likely normal metals. Otherwise, i.e., at small temperature and large magnetic coupling, we find exponential behavior of the spin-relaxation rate versus temperature. Moreover, at a temperature approaching the paramagnetic-ferromagnetic transition point, one finds sharp suppression of the spin-relaxation rate or speeding up of the spin-relaxation time. These scenarios are attributed to the appearance of the magnetic coherence bound state or the spin clusters in diluted magnetic semiconductors due to the strongly magnetic correlations.

Quantum anomalous Hall (QAH) insulators host topologically protected dissipationless chiral edge states, the number of which is determined by the Chern number. Up to now, the QAH state has been realized in a few magnetic topological insulators, but usually with a low Chern number. Here, we develop a Dirac-fermion approach which is valuable to understand and design high Chern numbers in various multilayers of layered magnetic topological insulators. Based on the Dirac-fermion approach, we demonstrate how to understand and tune high Chern numbers in ferromagentic ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ films through the van der Waals (vdW) gap modulation. Further, we also employ the Dirac-fermion approach to understand the experimentally observed high Chern numbers and topological phase transition from the Chern number $C=2$ to $C=1$ in the $\left[\mathrm{3QL}\text{−}\right(\mathrm{Bi}\text{,}{\mathrm{Sb})}_{1.76}{\mathrm{Cr}}_{0.24}{\mathrm{Te}}_3]$/$\left[\mathrm{4QL}\text{−}\right(\mathrm{Bi}\text{,}{\mathrm{Sb})}_2{\mathrm{Te}}_3]$ multilayers. Our work provides a powerful tool to design the QAH states with a high Chern number in layered magnetic topological insulator multilayers.

Combining ab initio and model Hamiltonian approaches, we investigate the electronic, magnetic, and topological properties of potassium manganese chalcogenides that host square nets of Mn and chalcogen atoms. Our analysis establishes these compounds to be robust half-metallic ferromagnets. The origin of ferromagnetism in these compounds is found to be based on a kinetic energy-driven double-exchange mechanism, first proposed for ${\mathrm{Sr}}_2{\mathrm{FeMoO}}_6$, a double-perovskite compound. The presence of finite spin-orbit coupling at chalcogen sites triggers nontrivial topology of the chalcogen-derived bands at the conducting channel, dominating the electronic structure close to the Fermi level. This puts the studied compounds in the class of topological half-metals with appreciable values of anomalous Hall conductivity, opening up the application possibility in topological quantum spintronics. Cleavability of these layered compounds makes the situation further promising.

Long coherence time and compatibility with semiconductor fabrication make spin qubits in silicon an attractive platform for quantum computing. In recent years, hole spin qubits are being developed as they have the advantages of weak coupling to nuclear spin noise and strong spin-orbit coupling (SOC), in constructing high-fidelity quantum gates. However, there are relatively few studies on the hole spin qubits in a single acceptor, which requires only low density of the metallic gates. In particular, the investigation of flexible tunability using controllable strain for fault-tolerant quantum gates of acceptor-based qubits is still lacking. Here, we study the tunability of electric dipole spin resonance (EDSR) of acceptor-based hole spin qubits with controllable strain. The flexible tunability of heavy hole-light hole splitting and spin-hole coupling (SHC) with the two kinds of strain can avoid a high electric field at the “sweet spot”, and the operation performance of the acceptor qubits could be optimized. Longer relaxation time or stronger EDSR coupling at a low electric field can be obtained. Moreover, with asymmetric strain, two sweet spots are induced and may merge together, and form a second-order sweet spot. As a result, the quality factor $Q$ can reach ${10}^4$ for a single-qubit operation, with a high tolerance for the electric field variation. Furthermore, the two-qubit operation of acceptor qubits based on dipole-dipole interaction is discussed for high-fidelity two-qubit gates. The quality factors of single-qubit gates and two-qubit gates can be enhanced by 100 and 7 times respectively with tunable strain. The tunability of spin qubit properties in an acceptor via strain could provide promising routes for spin-based quantum computing.

Electron-spin resonance carried out with scanning tunneling microscopes (ESR-STM) is a recently developed experimental technique that is attracting enormous interest on account of its potential to carry out single-spin on-surface resonance with subatomic resolution. Here we carry out a theoretical study of the role of tip-adatom interactions and provide guidelines for choosing the experimental parameters in order to optimize spin resonance measurements. We consider the case of the Fe adatom on a MgO surface and its interaction with the spin-polarized STM tip. We address three problems: first, how to optimize the tip-sample distance to cancel the effective magnetic field created by the tip on the surface spin, in order to carry out proper magnetic field sensing. Second, how to reduce the voltage dependence of the surface-spin resonance frequency, in order to minimize tip-induced decoherence due to voltage noise. Third, we propose an experimental protocol to infer the detuning angle between the applied field and the tip magnetization, which plays a crucial role in the modeling of the experimental results.

The rich electron correlations and highly coherent transport in reconfigurable devices sketched by a conductive atomic force microscope tip at the $\mathrm{LaAl}{\mathrm{O}}_3/\mathrm{SrTi}{\mathrm{O}}_3$ interface have enabled the oxide platform an ideal playground for studying correlated electrons and quantum technological applications. Why these one-dimensional devices possess enhanced properties over the two-dimensional interface, however, has remained elusive. Here, we provide evidence that one-dimensional $\mathrm{LaAl}{\mathrm{O}}_3/\mathrm{SrTi}{\mathrm{O}}_3$ nanowires are intrinsically ferroelastic domain walls by nature through thermodynamic study. We have observed spreading resistance anomalies under thermostimulus and temperature cycles with characteristic temperatures matching domain-wall polarity. This information is crucial in understanding the novel phenomena including superconductivity and high mobility quantum transport.

We propose an efficient method of heat rectification in a simple system consisting of a quantum dot asymmetrically coupled to four mutually perpendicular electrodes. In such a device, the perpendicular charge and heat currents appear in response to the voltage bias or temperature difference between one pair of electrodes. Even though both longitudinal (along the bias) and perpendicular (to the bias) currents are rectified under appropriate conditions, the rectification factor is typically much bigger for the latter currents. This is true for heat and charge flow. The perpendicular currents are predicted to exist in linear as well as nonlinear transport regimes and require broken mirror symmetry but not time reversal symmetry. The linear effect exists only in geometry which breaks two inversion symmetries along two pairs of electrically coupled terminals. The proposed system is attainable within current technology and provides a novel platform of simultaneous heat and charge management at the nanoscale.

It is widely comprehended that temperature may cause phonon-exciton scattering, enhancing the energy level's linewidth and leading to some spectrum shifts. However, in the present paper, we suggest a different mechanism that allows the thermal motion of the exciton's center of mass (c.m.) to affect the magnetoexciton energies in monolayer dichalcogenides (TMDCs). By the nontrivial but precise separation of the c.m. motion from an exciton in a monolayer TMDC with a magnetic field, we obtain an equation for the relative motion containing a motional Stark term proportional to the c.m. pseudomomentum, related to the temperature of the exciton gas but neglected in the previous studies. Solving the Schrödinger equation without omitting the motional Stark potential at room temperature shows approximately a few meV thermal-magnetic shifts in the exciton energies, significant enough for experimental detection. Moreover, this thermal effect causes a change in exciton radius and diamagnetic coefficient and enhances the exciton lifetime as a consequence. Surprisingly, the thermoinduced motional Stark potential breaks the system's SO(2) symmetry, conducting new peaks in the exciton absorption spectra at room temperature besides those of the $s$ states. This mechanism could be extended for other magnetoquasiparticles such as trions and biexcitons.

We present a semilocal exchange-correlation energy functional for noncollinear spin density functional theory based on short-range expansions of the spin-resolved exchange hole and the two-body density matrix. Our functional is explicitly derived for noncollinear magnetism, is U(1) and SU(2) gauge invariant, and gives rise to nonvanishing exchange-correlation torques. Testing the functional for frustrated antiferromagnetic chromium clusters, the exchange part is shown to perform favorably compared with the far more expensive Slater and optimized effective potentials, and a delicate interplay between exchange and correlation torques is uncovered.

We adapt and optimize the projected-pair-entangled-state (PEPS) algorithm on finite lattices (fPEPS) for two-dimensional Hubbard models and apply the algorithm to the Hubbard model with nearest-neighbor hopping on a square lattice. In particular, we formulate the PEPS algorithm using projected entangled pair operators, incorporate SU(2) symmetry in all tensor indices, and optimize the PEPS using both iterative-diagonalization-based local bond optimization and gradient-based optimization of the PEPS. We discuss the performance and convergence of the algorithm for the Hubbard model on lattice sizes of up to $8\times 8$ for PEPS states with U(1) symmetric bond dimensions of up to $D=8$ and SU(2) symmetric bond dimensions of up to $D=6$. Finally, we comment on the relative and overall efficiency of schemes for optimizing fPEPS.