We investigate numerically and theoretically the effect of spatial disorder on two-dimensional split-step discrete-time quantum walks with two internal “coin” states. Spatial disorder can lead to Anderson localization, inhibiting the spread of quantum walks, putting them at a disadvantage against their diffusively spreading classical counterparts. We find that spatial disorder of the most general type, i.e., position-dependent Haar random coin operators, does not lead to Anderson localization but to a diffusive spread instead. This is a delocalization, which happens because disorder places the quantum walk to a critical point between different anomalous Floquet-Anderson insulating topological phases. We base this explanation on the relationship of this general quantum walk to a simpler case more studied in the literature and for which disorder-induced delocalization of a topological origin has been observed. We review topological delocalization for the simpler quantum walk, using time evolution of the wave functions and level spacing statistics. We apply scattering theory to two-dimensional quantum walks and thus calculate the topological invariants of disordered quantum walks, substantiating the topological interpretation of the delocalization and finding signatures of the delocalization in the finite-size scaling of transmission. We show criticality of the Haar random quantum walk by calculating the critical exponent $\eta$ in three different ways and find $\eta \approx 0.52$ as in the integer quantum Hall effect. Our results showcase how theoretical ideas and numerical tools from solid-state physics can help us understand spatially random quantum walks.

We investigate the electronic structure of an interesting two-dimensional (2D) diagonally striped lattice (DSL). It consists of arrays of N different types of “atoms” or “molecules” with a fixed sequence in both horizontal and vertical directions. Using a tight-binding model, we show that the DSL $\left(N>2\right)$ has the symmetry group Amm2 and Pmm2, and exhibits an oscillatory metallic and insulating phases for the odd- and even- N number, respectively. Some conventional 2D lattices, such as the Lieb lattice, can be related to the derivative DSL via vacancy formation by removing one type of atom in every other $(N-1)$ row of the original DSL. Interestingly, there are multiple $(N-1)$-fold degenerate flat bands in one group of the derivative DSLs, which affords a unique platform for studying many-body physics. In addition to atomic and molecular lattices, we suggest other artificial DSLs, such as photonic and phononic, to be also constructed with possibly interesting properties.

The spin-current density functional theory (SCDFT), when formulated in a basis of Pauli spinors, provides a proper theoretical framework for the study of materials in an arbitrarily oriented external magnetic field and/or upon inclusion of spin-dependent relativistic effects, such as spin-orbit coupling. The SCDFT is formulated in terms of the particle-number density $n$, the Cartesian components of the magnetization $m_x,$ $m_y,$ and $m_z$, the orbital-current density $\mathit{j}$, and the three spin-current densities ${\mathit{J}}^x,$ ${\mathit{J}}^y,$ and ${\mathit{J}}^z$, where each of these density variables depends on specific blocks of the density matrix. Exchange-correlation (xc) functionals within the SCDFT should therefore depend on all of these eight fundamental density variables: $F_{xc}[n,m_x,m_y,m_z,\mathit{j},{\mathit{J}}^x,{\mathit{J}}^y,{\mathit{J}}^z]$, which makes their parametrization a formidable task. Here, we formulate the adiabatic connection of the SCDFT for a treatment of exact Fock exchange in the theory. We show how the inclusion of a fraction of Fock exchange in standard functionals of the (spin) DFT (either in their collinear or noncollinear versions: $F_{xc}\left[n\right],$ $F_{xc}[n,m_z]$ and $F_{xc}[n,m_x,m_y,m_z]$) allows for the two-electron potential to depend on all those blocks of the density matrix that correspond to the eight density variables of the SCDFT, in a sensible and yet practical way. In particular, in the local-density and generalized-gradient approximations of the SCDFT, the treatment of the current densities solely from the Fock exchange term is formally justified by the short-range behavior of the exchange hole. We discuss that the adiabatic coupling strength parameter modulates the two-electron coupling of the orbital- and spin-current densities with the particle-number density and magnetization. Formal considerations are complemented by numerical tests on a periodic model system in the presence of spin-orbit coupling and in the absence of an external magnetic field.

We report the synthesis and magnetic properties of ternary iron nitride compounds ${\mathrm{Sn}}_{1-x}\mathrm{N}{\mathrm{Fe}}_{3+x}$ $(0\le x\le 0.4)$. The magnetic frustration state is found in $\mathrm{SnN}{\mathrm{Fe}}_3$, and the antiferromagnetic (AFM) exchange is dominant in ${\mathrm{Sn}}_{0.95}\mathrm{N}{\mathrm{Fe}}_{3.05}$ and ${\mathrm{Sn}}_{0.9}\mathrm{N}{\mathrm{Fe}}_{3.1}$, and then the ferromagnetic (FM) interaction occurs in ${\mathrm{Sn}}_{1-x}\mathrm{N}{\mathrm{Fe}}_{3+x}$ $(0.2\le x\le 0.4)$. Interestingly, the Griffiths phase is observed in $x=0.1$, 0.2, caused by the FM coupling competing over the AFM one and forming the short-range FM cluster. At the same time, the competitions between the AFM and FM interactions lead to a spin-glass behavior, which is embodied most evidently in ${\mathrm{Sn}}_{0.7}\mathrm{N}{\mathrm{Fe}}_{3.3}$ and further confirmed by the corresponding characteristic fitting parameters $({\tau }_0=8.89\times {10}^{-12}\mathrm{s},$ $T_0=25\mathrm{K}, \mathrm{and} zv=6.56)$. In addition, density functional theory (DFT) calculations exhibit the magnetic ground states, magnetic moments contribution, and bonds nature of Sn-Fe and N-Fe. The results of DFT calculations disclose some detailed magnetic interactions, which are demonstrated to be an evidential response to the interesting magnetic behavior in ${\mathrm{Sn}}_{1-x}\mathrm{N}{\mathrm{Fe}}_{3+x}$ compounds.

We use time- and angle-resolved photoemission spectroscopy to reveal momentum-resolved characteristics of interband transitions in InSb. The transitions along the Γ-K line are correctly described in terms of the independent-quasiparticle band picture up to 1.9 eV. However, the transitions along the Γ-L line turn out to be strongly excitonic above 1.7 eV, associated with the saddle-point excitons at the $E_1$ critical point. The momentum- and energy-resolved spectra of photoionization of the saddle-point excitons show that the wave function is composed of the electron-hole pair states with the wave vector of $0.453\pm 0.055{\AA }^{-1}$ along the Γ-L direction of the Brillouin zone. Time-resolved characteristics of the exciton photoionization show that the coherently generated excitonic polarization decays with a time constant of 22 ± 1 fs due to the autoionization from the excitonic state to uncorrelated electron-hole pair states.

Paramagnetic point defects in solids may exhibit a rich set of interesting and not yet fully resolved physics. In particular, character of wave functions and electron-phonon coupling in these defects may highly influence their interaction with external magnetic fields. Complex interplay among the electronic orbitals, phonons, and electron spin determines the effective pseudospin of the system that we demonstrate on vanadium and molybdenum defects in hexagonal silicon carbide by means of ab initio calculations. In this Rapid Communication, we find a giant anisotropy in the $g$ tensor of these defects with Kramers doublet spin ground state, resulting in reduced and vanishing interaction with the magnetic field in parallel and transverse directions, respectively. The consequences of our finding in the application of these defects for quantum information processing are briefly discussed.

We systematically study the impact of various electron-acoustic-phonon coupling mechanisms on the valley physics in two-dimensional materials. In the static strain limit, we find that the Dirac cone tilt and deformation potential have an analogous valley Hall response since they fall into the same universality class of pseudospin structure. However, such an argument fails for the coupling mechanism with position-dependent Fermi velocity. For the isotropic case, a significant valley Hall effect occurs near charge neutrality similar to the bond-length change, whereas for the anisotropic case, the geometric valley transport is suppressed, akin to the deformation potential. The gap opening mechanism by nonuniform strain is found to totally inhibit the valley Hall transport, even if the dynamics of the strains are introduced. By varying the gate voltage, a tunable phonon-assisted valley Hall response can be realized, which paves a way toward rich phenomena and new functionalities of valley acoustoelectronics.

Despite recent transport studies of ABC-stacked multilayer graphene systems revealed various unusual quantum phenomena which arise from the nearly flat electronic bands, their quantum tunneling properties have rarely been addressed. Here we investigate the local tunneling characteristics of a gapped ABC-stacked trilayer graphene (TLG) and report the experimental observation of the nearly flat band induced atomic-site-dependent negative differential conductivity (NDC, characterized by a current drop with increasing voltage) via scanning tunneling spectroscopy (STS) measurements. We show that strong NDC emerges in the gap region next to a sharp STS peak induced by the very flat low-energy dispersion of ABC TLG. The NDC is found to mainly reside on one atomic sublattice of the surface layer due to the strong sublattice and layer localization of the nearly flat bands. The observed NDC behavior is explained by the tunnel-diode mechanism, namely, the coexistence of a sharp flat-dispersion STS peak in which tunneling is strongly enhanced and a subsequent gap region in which tunneling is forbidden. Furthermore, we also find that a local defect could effectively switch off the NDC over a large spatial range. Our result highlights a quantum tunneling effect unique to the graphene-based nearly flat band system and expands the potential application scope of ABC TLG.

We compare the trends on the strength of electronic correlations across the different phases of elemental Pu focusing on its site and orbital dependence, using a combination of density functional theory (DFT) and dynamical mean-field theory (DMFT) calculations within the vertex corrected one crossing approximation. We find that $\mathrm{Pu}\text{−}5f$ states are more correlated in $\delta$-Pu, followed by some crystallographic sites in $\alpha$ and $\beta$ phases. In addition, we observe that $\mathrm{Pu}\text{−}5f_{5/2}$ and $\mathrm{Pu}\text{−}5f_{7/2}$ orbital differentiation is a general feature of this material, as is site differentiation in the low-symmetry phases. The $\mathrm{Pu}\text{−}5f_{5/2}$ states show Fermi liquid like behavior, whereas the $\mathrm{Pu}\text{−}5f_{7/2}$ states remaining incoherent down to very low temperatures. We correlate the correlation strength in the different phases to their structure and the $\mathrm{Pu}\text{−}5f$ occupancy of their crystallographic sites.

Being a wide band gap system GaMnN attracted considerable interest after the discovery of highest reported ferromagnetic transition temperature $T_C\sim 940$ K among all diluted magnetic semiconductors. Later, it became a debate due to the observation of either very low $T_C\sim 8$ K or sometimes the absence of ferromagnetism. We address these issues by calculating the ferromagnetic window $T_C$ vs $p$, within the $t\text{−}{t}^{\prime }$ Kondo lattice model using a spin-fermion Monte Carlo method on a simple cubic lattice. The next-nearest-neighbor hopping $t^{\prime }$ is exploited to tune the degree of delocalization of the free carriers to show that the carrier localization (delocalization) significantly widens (shrinks) the ferromagnetic window with a reduction (enhancement) of the optimum $T_C$ value. We correlate our results with the experimental findings and explain the ambiguities in ferromagnetism in GaMnN.

We present a detailed study of the time-resolved photoluminescence of narrow-line emission centers in $\mathrm{W}{\mathrm{Se}}_2$ monolayers and bilayers. Our experiments reveal noninstantaneous photoluminescence intensity rise after the laser pulse. This shows that the simplest excitation model in which the localized states are directly populated by free excitons is not sufficient to fully reproduce experimental results. We, therefore, analyze a more complex phenomenological model where the relaxation of the carriers is mediated by long-lived intermediate states. Strong suppression of the lifetime of those intermediate states at elevated temperatures reveals their unique character, not matching any relaxed excitonic state in $\mathrm{W}{\mathrm{Se}}_2$ monolayer.

High quality factor ($Q$) nanomechanical resonators have received a lot of attention for sensor applications with unprecedented sensitivity. Despite the large interest, few investigations into the frequency stability of high-$Q$ resonators have been reported. Such resonators are characterized by a linewidth significantly smaller than typically employed measurement bandwidths, which is the opposite regime to what is normally considered for sensors. Here, the frequency stability of high-$Q$ silicon nitride string resonators is investigated both in open-loop and closed-loop configurations. The stability is here characterized using the Allan deviation. For open-loop tracking, it is found that the Allan deviation gets separated into two regimes, one limited by the thermomechanical noise of the resonator and the other by the detection noise of the optical transduction system. The point of transition between the two regimes is the resonator response time, which can be shown to have a linear dependence on $Q$. Laser power fluctuations from the optical readout are found to present a fundamental limit to the frequency stability. Finally, for closed-loop measurements, the response time is shown to no longer be intrinsically limited but instead given by the bandwidth of the closed-loop tracking system. Computed Allan deviations based on theory are given as well and found to agree well with the measurements. These results are of importance for the understanding of fundamental limitations of high-$Q$ resonators and their application as high performance sensors.

The dynamical equation of a single magnetic moment constituted by a rigid circular current loop is derived from the mechanical Lagrange equations of motion, introducing the Lorentz force and the damping process, described by a well-defined dissipative mechanism. It is demonstrated that magnetic inertial effects arise naturally by simple mechanical considerations and superimpose onto the Gilbert original dynamical equation. The comparison with models proposed in the recent literature is drawn and discussed.

Skyrmions can be driven by spin-orbit torques as a result of the spin Hall effect. Here we model an additional contribution in ultrathin multilayers, arising from the spin accumulation at heavy metal/ferromagnetic interfaces and observe the effects on a large range of skyrmion diameters. The combination of the interfacial spin-transfer torque and the spin-orbit torque results in skyrmion motion which helps to explain the observation of small skyrmion Hall angles for skyrmion diameters less than 100 nm. We show that this additional term has a significant effect on the skyrmion dynamics and leads to rapidly decreasing skyrmion Hall angles for small skyrmion diameters, as well as a skyrmion Hall angle versus skyrmion velocity dependence nearly independent of the surface roughness characteristics. Also, the effect of various disordered energy landscapes, in the form of surface roughness, on the skyrmion Hall angle and velocity is shown to be largely drive dependent. Our results show good agreement with those found in experiments thus concluding that the interfacial spin-transfer torque should be included in micromagnetics simulations for the reproduction of experimental results.

We study the quantum ground state of ultracold bosons in a two-dimensional square lattice. The bosons interact via the repulsive dipolar interactions and $s$-wave scattering. The dynamics is described by the extended Bose-Hubbard model including correlated hopping due to the dipolar interactions, and the coefficients are found from the second quantized Hamiltonian using the Wannier expansion with realistic parameters. We determine the phase diagram using the Gutzwiller ansatz in the regime where the coefficients of the correlated hopping terms are negative and can interfere with the tunneling due to single-particle effects. We show that this interference gives rise to staggered superfluid and supersolid phases at vanishing kinetic energy, while we identify parameter regions at finite kinetic energy where the phases are incompressible. We compare the results with the phase diagram obtained with the cluster Gutzwiller approach and with the results found in one dimension using the density-matrix renormalization group.

We have investigated the sample dependence of the half-integer thermal Hall effect in $\alpha \text{−}{\mathrm{RuCl}}_3$ under a magnetic field tilted ${45}^{\circ }$ from the $c$ axis to the $a$ axis. We find that the sample with the largest longitudinal thermal conductivity ${\kappa }_{xx}$ shows the half-integer quantized thermal Hall effect expected in the Kitaev model. On the other hand, the quantized thermal Hall effect was not observed in the samples with smaller ${\kappa }_{xx}$. We suggest that suppressing the magnetic scattering effects on the phonon thermal conduction, which broaden the field-induced gap protecting the chiral edge current of the Majorana fermions, is important to observe the quantized thermal Hall effect.

We report theoretical predictions on the pairing symmetry of the newly discovered superconducting nickelate ${\mathrm{Nd}}_{1-x}{\mathrm{Sr}}_x{\mathrm{NiO}}_2$ based on the renormalized mean-field theory for a generalized model Hamiltonian. For practical values of the key parameters, we find a transition between a gapped ($d+is$)-wave pairing state in the small doping region to a nodal $d$-wave pairing state in the large doping region, accompanying with an abrupt Fermi surface change at the critical doping. Our overall phase diagram also shows the possibility of a ($d+is$)- to $s$-wave transition if the electron hybridization is relatively small. In either case, the low-doping ($d+is$)-wave state is a gapped superconducting state with broken time-reversal symmetry. Our results are in qualitative agreement with recent experimental observations and predict several key features to be examined in future measurements.