Nonuniform strain applied to graphene's honeycomb lattice can induce pseudo-Landau levels in the single-particle spectrum. Various generalizations have been put forward, including a particular family of hopping models in $d$ space dimensions. Here we show that the key ingredient for sharp pseudo-Landau levels in higher dimensions is dimensional reduction. We consider particles moving on a $d$-dimensional hyperdiamond lattice which displays a semimetallic band structure, with a $(d-2)$-dimensional nodal manifold. By applying a suitable strain pattern, the single-particle spectrum evolves into a sequence of relativistic Landau levels. We develop and solve the corresponding field theory: Each nodal point effectively generates a Landau-level problem which is strictly two dimensional to leading order in the applied strain. While the effective pseudovector potential varies across the nodal manifold, the Landau-level spacing does not. Our theory paves the way for strain engineering of single-particle states via dimensional reduction and beyond global minimal coupling.

We adapt a machine-learning approach to study the many-body localization transition in interacting fermionic systems on disordered one-dimensional (1D) and two-dimensional (2D) lattices. We perform supervised training of convolutional neural networks (CNNs) using labeled many-body wave functions at weak and strong disorder. In these limits, the average validation accuracy of the trained CNNs exceeds 99.95%. We use the disorder-averaged predictions of the CNNs to generate energy-resolved phase diagrams, which exhibit many-body mobility edges. We provide finite-size estimates of the critical disorder strengths at $W_c\sim 2.8$ and 9.8 for 1D and 2D systems of 16 sites, respectively. Our results agree with the analysis of energy-level statistics and inverse participation ratio. By examining the convolutional layer, we unveil its feature extraction mechanism which highlights the pronounced peaks in localized many-body wave functions while rendering delocalized wave functions nearly featureless.

Quantum anomalous Hall (QAH) state in six quintuple layer ${\mathrm{Cr}}_{0.1}{\left({\mathrm{Bi}}_{0.2}{\mathrm{Sb}}_{0.8}\right)}_{1.9}{\mathrm{Te}}_3$ thin films were studied through scanning tunneling spectroscopy (STS) and electrical transport measurements. While the surface state is gapless above the Curie temperature ($T_{\mathrm{C}}\approx 30$ K), scanning tunneling spectroscopy (STS) of the sample reveals a topologically nontrivial gap with an average value of $\approx 13.5$ meV at 4.2 K below the ferromagnetic transition. Nonetheless, areal STS scans of the magnetic topological insulator exhibit energy modulations on the order of several meV's in the surface bands, which result in the valence band maximum in some regions becoming higher than the energy of the conduction band minimum of some other regions that are spatially separated by no more than 3 nm. First-principles calculations demonstrate that the origin of the observed inhomogeneous energy band alignment is an outcome of many-body interactions, namely electron-defect interactions and electron-phonon interactions. Defects play the role of locally modifying the energy landscape of surface bands while electron-phonon interactions renormalize the surface bands such that the surface gap becomes reduced by more than 1 meV as temperature is raised from 0 to 4.2 K. These many-body interactions at a finite temperature result in substantial increase of electron tunneling across the spatially separated conduction band pockets even for finite temperatures well below $T_{\mathrm{C}}$, thus driving the magnetic topological insulator out of its QAH insulating phase into a metallic phase at a relatively low temperature.

We theoretically propose a quantum simulation scheme for the toric-code Hamiltonian, the paradigmatic model of a quantum spin liquid, based on time-periodic driving. We develop a hybrid continuous-digital strategy that exploits the commutativity of different terms in the target Hamiltonian. It allows one to realize the required four-body interactions in a nonperturbative way, attaining strong coupling and the suppression of undesired processes. In addition, we design an optimal protocol for preparing the topologically ordered ground states with high fidelity. A proof-of-principle implementation of a topological device and its use to simulate the topological phase transition are also discussed. The proposed scheme finds natural implementation in architectures of superconducting qubits with tunable couplings.

We report room-temperature measurements of the spin-relaxation times $T_1$ and $T_2$ of electron-hole charge-carrier spins in an organic light-emitting diode based on the $\pi$-conjugated polymer SY-PPV at low ($1\mathrm{m}\mathrm{T}\lesssim B_0\lesssim 10\mathrm{m}\mathrm{T}$) static magnetic fields, using electrically detected—through spin-Rabi oscillation-controlled recombination currents—magnetic resonant Hahn-echo and inversion-recovery pulse sequences. When random local hyperfine fields and external magnetic fields compete in magnitude, charge carrier spin-quantization axes are no longer well defined, and striking magnetic-field dependencies of spin-lattice relaxation times are found, while spin coherence times remain mostly field-independent. These results corroborate the magnetic-field sensitivities of observables governed by radical-pair physics.

The Josephson diode effect (JDE) is a nonreciprocal transport phenomenon in which, the oppositely flowing critical currents are asymmetric and has great potential for applications in superconducting electronic devices. In this study, we present a theoretical investigation of the JDE on the two helical edge states of a two-dimensional topological insulator with asymmetric magnetization on each edge. It is shown that for a single-edge Josephson junction, the optimal JDE efficiency is approximately $35\%$, but for a double-edged Josephson junction with appropriate asymmetric magnetization on two edges, the JDE efficiency can be enhanced to around $68\%$. The origin of this enhancement lies in the fact that the two individual magnetizations not only can independently affect the asymmetric critical currents of the single-edge Josephson junction but also can shift the current-phase relation of the junction.

In this work we use a phenomenological theory of ferroelectric switching in ${\text{BiFeO}}_3$ thin films to uncover the mechanism of the two-step process that leads to the reversal of the weak magnetization of these materials. First, we introduce a realistic model of a ${\text{BiFeO}}_3$ film, including the Landau energy of isolated domains as well as the constraints that account for the presence of the substrate and the multidomain configuration found experimentally. We use this model to obtain statistical information about the switching behavior—by running dynamical simulations based on the Landau-Khalatnikov time-evolution equation, including thermal fluctuations—and we thus identify the factors that drive the two-step polarization reversal observed in the experiments. Additionally, we apply our model to test potential strategies for optimizing the switching characteristics.

Second-order nonlinear optical responses, including photogalvanic effect (PGE) and second harmonic generation (SHG), are fundamental and important physical phenomena in nonlinear optics and optoelectronics. The PGE and SHG associated with linearly and circularly polarized light are called the linear photogalvanic effect (LPGE), circular photogalvanic effect (CPGE), linear second harmonic generation, and circular second harmonic generation, respectively. In this paper, we use the quantum kinetics under the relaxation time approximation to investigate the dependence of second-order nonlinear optical responses on the Fermi level and frequency under different out-of-plane electric fields in $T_d\text{−}{\mathrm{WTe}}_2$ monolayer from radio to infrared region. We find that the maximum frequency at which the Berry curvature dipole mechanism for the nonlinear Hall effect plays a major role is about 1 THz. From the aspect of the Fermi level, in the radio and microwave regions, the two large peaks of nonlinear conductivities occur when the Fermi level is equal to the energy corresponding to the vicinity of the gap-opening points in the band dispersion. From the aspect of frequency, in the radio region, the LPGE and SHG conductivities maintain a large constant while the CPGE conductivity almost disappears. In the microwave region, the LPGE and SHG conductivities start to decrease gradually with increasing frequency while the CPGE conductivity is large. In the infrared region, the frequency and Fermi-level dependence of second-order nonlinear optical responses is complicated. In the 125 THz–300 THz region and in the $y$ direction, the presence of dc current without the disturbance of second harmonic current under circularly polarized light may be useful for the fabrication of unique optoelectronic devices. Moreover, we illustrate that when calculating the nonlinear Hall effect or second-order nonlinear optical responses of practical materials, the theories in the clean limit fail and it is necessary to use a theory that takes into account scattering effects (e.g., relaxation time approximation). Our study is promising to promote the more accurate calculation of second-order nonlinear optical responses in practical materials.

By first-principles methods combined with Boltzmann transport theory, we perform a systematic investigation of the thermoelectric properties of $\mathrm{RbGe}{\mathrm{I}}_3/\mathrm{CsSn}{\mathrm{I}}_3$ superlattices. $\mathrm{RbGe}{\mathrm{I}}_3/\mathrm{CsSn}{\mathrm{I}}_3$ superlattices construct a quantum well with valence and conduction states near the Fermi level located in $\mathrm{CsSn}{\mathrm{I}}_3$ layers, which yields a periodic repetition of two-dimensional transport channels. The quantum-confinement effects and the ultralow lattice thermal conductivity of the superlattices greatly enhance the in-plane thermoelectric power factor and figure of merit ($\mathit{ZT}$), which further increase when decreasing the thickness of $\mathrm{CsSn}{\mathrm{I}}_3$ layers in the superlattices. In ${\left(\mathrm{RbGe}{\mathrm{I}}_3\right)}_5/{\left(\mathrm{CsSn}{\mathrm{I}}_3\right)}_1$ superlattice, the power factor increases by two times, and $\mathit{ZT}$ is enhanced by nine times, compared to the parent $\mathrm{CsSn}{\mathrm{I}}_3$. The $\mathit{ZT}$ of this superlattice is 1.34 at 300 K and 3.78 at 550 K, providing a potential candidate for room-temperature thermoelectric applications. These results also confirm a way to improve the thermoelectric performance of $\mathrm{CsSn}{\mathrm{I}}_3$.

Vertical integration of dissimilar layered materials in a so-called van der Waals (vdW) heterostructure (HS) has emerged as a useful tool to engineer band alignments and interfaces. In this paper, we investigate thermoelectric currents in a phosphorene/graphene vdW nanoribbon consisting of an armchair graphene nanoribbon (AGNR) stacked on an armchair phosphorene nanoribbon (APNR). We focus on the currents driven by a temperature difference between the leads in a two-probe junction. In contrast to pristine AGNRs and APNRs, such an armchair-edged HS can provide several nanoamperes of the current at room temperature, without any external field. External electric fields modify the electronic band structure and can induce a type I-to-II band alignment transition and a direct-to-indirect band gap transition. Biasing the APNR/AGNR by an external electric field is found to strongly increase the thermally induced current and control the direction of current flow at moderate temperatures. These results are important for potential applications of the APNR/AGNR vdW HS in flexible electronics and thermoelectric devices.

We investigate the effective Landé factor in semiconductor nanowires with strong Rashba spin-orbit coupling. Using the $\mathbf{k}·\mathbf{p}$ theory and the envelope function approach we derive a conduction band Hamiltonian where $g^{*}$ is explicitly related to the spin-orbit coupling constants ${\mathit{\alpha }}_R$. Our model includes orbital effects from the Rashba spin-orbit term, leading to a significant enhancement of the effective Landé factor which is naturally anisotropic. For nanowires based on the low-gap, high spin-orbit coupled material InSb, we investigate the anisotropy of the effective Landé factor with respect to the magnetic field direction, exposing a twofold symmetry for the bottom gate architecture. The anisotropy results from the competition between the localization of the envelope function and the spin polarization of the electronic state, both determined by the magnetic field direction.

Uniaxial magnetocrystalline anisotropy (UMA) is vital for fundamental research, such as maintaining two-dimensional ferromagnetic order and realizing topological phases. However, in most cases, UMA rapidly decreases with increasing temperature and finally vanishes approaching the Curie temperature ($T_{\mathrm{C}}$). The increasing UMA with increasing temperature is very rare in almost all traditional ferromagnetic materials and in emerging van der Waals (vdW) ferromagnets, which generally have relatively low $T_{\mathrm{C}}$. Here, we experimentally unveil the anomalous temperature dependence of the UMA constant $K_{\mathrm{u}1}$($T$) in the vdW ferromagnet ${\mathrm{Fe}}_3\mathrm{Ge}{\mathrm{Te}}_2$. Surprisingly, the $K_{\mathrm{u}1}$($T$) first anomalously increases and then slowly decreases. We found that the anomalous $K_{\mathrm{u}1}$($T$) can be perfectly fitted by Carr's model. Further analysis and temperature-dependent x-ray diffraction measurements suggest that the partial localization of $3d$ electrons and considerable lattice expansion are crucial for anomalous $K_{\mathrm{u}1}$($T$). We propose that the complex competition between the two-ion mechanism and the itinerant-electron mechanism leads to the anomalous behavior of $K_{\mathrm{u}1}$($T$) in ${\mathrm{Fe}}_3\mathrm{Ge}{\mathrm{Te}}_2$. Our findings from this unusual case help deepen the understanding of the temperature dependence of UMA.

The generation of out-of-plane polarized spin current is crucial for efficiently manipulating perpendicularly magnetized systems used in high-density magnetic recording. Here, we demonstrate the generation of out-of-plane polarized spin current at room temperature using an insulator, EuS. By employing angle-resolved spin-torque ferromagnetic resonance, we find a large unconventional out-of-plane torque conductivity, ${\sigma }_{\mathrm{DL}}^z=-0.13\times {10}^5(\hslash /2e){\left(\mathrm{\Omega }\mathrm{m}\right)}^{-1}$ in the $\mathrm{Py}(={\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19})/\mathrm{EuS}$ bilayer, which is comparable to the conventional in-plane dampinglike torque conductivity, ${\sigma }_{\mathrm{DL}}^y$. Additionally, a giant in-plane fieldlike torque (${\sigma }_{\mathrm{FL}}^z$) with a magnitude of 27 times larger than that of the conventional out-of-plane fieldlike torque (${\sigma }_{\mathrm{FL}}^y$) is also observed in the Py/EuS bilayer. The unconventional torques due to the out-of-plane polarized spin current (${\sigma }_{\mathrm{DL}}^z$ and ${\sigma }_{\mathrm{FL}}^z$) persist even by inserting a 10-nm-thick Cu layer between Py and EuS. Our findings demonstrate that the unconventional torques in these systems originate from the interfaces through spin swapping and/or spin-orbit precession mechanisms.

Quadratic band touching (QBT) points are widely observed in two- and three-dimensional (2D and 3D) materials, including bilayer graphene and Luttinger semimetals, and attract significant attention from theory to experiment. However, even in its simplest form, the 2D checkerboard lattice QBT model, the phase diagram characterized by temperature and interaction strength, still remains unknown beyond the weak-coupling regime. Intense debates persist regarding the existence of various interaction-driven insulating states in this system. To address these uncertainties, we employ thermal tensor network simulations, specifically exponential tensor renormalization group and tangent space tensor renormalization group, along with density matrix renormalization group calculations to provide a comprehensive finite-temperature phase diagram for this model and shed light on previous ambiguities. Notably, our findings reveal the emergence of a robust bond-nematic Dirac semimetal phase with distinct thermodynamic properties that set it part from the nematic insulating state and other symmetry-broken states. This previously overlooked feature is found to be ubiquitous in interacting QBT systems. We also discuss the implications of these results for experimental systems such as bilayer graphene and iridate compounds.

We study the parton construction of chiral spin liquids (CSLs) using projected Gaussian fermionic entangled pair states (GfPEPSs). First, we show that GfPEPSs can represent generic spinless Chern insulators faithfully with finite bond dimensions. Then by applying the Gutzwiller projection to a bilayer GfPEPSs, spin-$\frac{1}{2}$ Abelian and non-Abelian CSLs are obtained for Chern number $C=1$ and 2, respectively. As a consequence of the topological obstruction for GfPEPSs, very weak Gossamer tails are observed in the correlation functions of the fermionic projected entangled pair state (PEPS) Ansätze, suggesting that the no-go theorem for chiral PEPS is universal but does not bring any practical limitation. Remarkably, without finetuning, all topological sectors can be constructed showing the expected number of chiral branches in the respective entanglement spectra, providing a sharp improvement with respect to the known bosonic PEPS approach.

Understanding the dynamics of open quantum systems is intrinsically important to control and utilize quantum hardware in various applications. The generic behavior of purely dissipative open quantum many-body systems with $k$-local, normal dissipation processes can be investigated using random matrix theory, revealing different decay timescales of observables determined by their complexity, as shown by Wang et al. [K. Wang et al., Phys. Rev. Lett. 124, 100604 (2020)]. The time evolution of an open quantum system is entirely described by the eigenvalue spectrum of the Lindbladian, in which the hierarchy of decay timescales is reflected in the formation of well-separated eigenvalue clusters. Here, we extend the analysis of this spectrum to the presence of unitary dynamics using a random matrix model. In the case of strong dissipation, the unitary dynamics can be treated perturbatively and the $k$ locality of the Hamiltonian determines how susceptible the spectrum is to such a perturbation. For the physically most relevant case of (dissipative) two-body interactions, the correction in the first order of the perturbation vanishes, leading to the relative robustness of the spectral features, which in turn implies the same robustness of the corresponding separation of decay timescales. We find the perturbative approach for the spectrum to yield an excellent agreement with exact-diagonalization results. For weak dissipation, the spectrum flows into clusters except for outlier eigenmodes, which we identify to be the local symmetries of the Hamiltonian. We support our analytic findings by numerical simulations and show that our generic model applies to a nonrandom Heisenberg chain.

We performed ${}^{23}\mathrm{Na}$ NMR measurements on a single-domain crystal of the Kitaev material ${\mathrm{Na}}_3{\mathrm{Co}}_2{\mathrm{SbO}}_6$ with magnetic field applied along the crystalline $a$ axis. A positive Curie-Weiss constant is obtained from the NMR Knight shift, which suggests the existence of ferromagnetic exchange couplings. The antiferromagnetic ordering is found to be suppressed at a field of 1.9 T. Inside the ordered phase, our data reveal two additional phase transitions. At 1.9 T the spin-lattice relaxation rate $1{/}^{23}{T}_1$ establishes a quantum critical behavior at high temperatures. However, at low temperatures a gapped behavior is observed at the “critical” field, which suggests a weak first-order transition instead and a possible field-induced quantum spin liquid. Our results reveal complex microscopic interactions in the system that may help to search for possible quantum spin liquids.

We theoretically study the topological properties of magnons and the relevant magnon thermal Hall effect in trimerized Lieb lattice ferromagnets in the presence of next-nearest-neighbor Dzyaloshinskii-Moriya interactions. By calculating the magnon band structures and their Chern numbers with the linear spin-wave theory, we show that the system can undergo a phase transition between a magnonic topological insulator phase and a magnonic trivial insulator phase. The main results are presented in the form of topological phase diagrams, where the Chern numbers or magnon thermal Hall conductivity are shown as a function of the two lattice trimerization parameters. We find a sharp change of the thermal Hall conductivity across the critical point of phase transformations associated with topological nontrivial edge states. The behaviors reflect that the existence of trimerizations breaks the ${\mathbf{C}}_4$ rotational symmetry of the Lieb lattice. Finally, we show that our theoretical predictions could be experimentally realized in high-temperature cuprate superconductors or organic magnetic materials.

High-quality monoclinic ${\mathrm{Cr}}_3{\mathrm{Te}}_4$ crystals are synthesized by the chemical vapor transport method and confirmed by synchrotron powder x-ray diffraction. Critical behaviors of ${\mathrm{Cr}}_3{\mathrm{Te}}_4$ are studied by bulk isothermal magnetization measurements around its paramagnetic to ferromagnetic phase transition. From these data, we evaluate the modified Arrott plot, the Kouvel-Fisher plot, and critical isotherms, and estimate critical exponent values of $\beta \sim 0.3827, \gamma \sim 1.2119$, and $\delta \sim 4.16$, and the Curie temperature $T_C\approx 321$ K. After the scaling, the isothermal magnetization curves below and above the critical temperatures collapse into two independent universal branches which signifies the reliability of our critical exponent estimation. The estimated critical exponent values of ${\mathrm{Cr}}_3{\mathrm{Te}}_4$ do not match well with theoretically calculated values of any three-dimensional models.