We introduce a generic scheme to perform nonperturbative linked cluster expansions in long-range ordered quantum phases. Clusters are considered to be surrounded by an ordered reference state leading to effective edge fields in the exact diagonalization on clusters, which break the associated symmetry of the ordered phase. Two approaches, based either on a self-consistent solution of the order parameter or on minimal sensitivity with respect to the ground-state energy per site, are formulated to find the optimal edge field in each NLCE order. Furthermore, we investigate the scaling behavior of the NLCE data sequences towards the infinite-order limit. We apply our scheme to gapped and gapless ordered phases of XXZ Heisenberg models on various lattices and for spins 1/2 and 1 using several types of cluster expansions ranging from a full-graph decomposition, rectangular clusters, up to more symmetric square clusters. It is found that the inclusion of edge fields allows to regularize nonperturbative linked-cluster expansions in ordered phases yielding convergent data sequences. This includes the long-range spin-ordered ground state of the spin-1/2 and spin-1 Heisenberg model on the square and triangular lattice as well as the trimerized valence bond crystal of the spin-1 Heisenberg model on the kagome lattice.

Multiband touchings, such as three-band, six-band, and eight-band touchings, together with the emergence of high-pseudospin fermions were predicted recently at high-symmetry points in three-dimensional space. In this paper, we propose a simple cubic model whose unit cell contains three atoms. There are six bands in the system due to the spin degrees of freedom. The four-band and two-band touchings are realized at high-symmetry points, where we derive low-energy theories, demonstrating the emergence of pseudospin-3/2 fermions and Weyl fermions, respectively. Away from the high-symmetry points, we find critical Weyl fermions present exactly at the boundary between the type-I and type-II Weyl fermions. This critical Weyl fermion transforms into the type-I or type-II Weyl fermion once the magnetic field is applied.

Searching for two-dimensional (2D) materials with multifunctionality is one of the main goals of current research in 2D materials. Magnetism and semiconducting are certainly two desirable functional properties for a single 2D material. In line with this goal, here we report a density functional theory (DFT) study of bulk and single-layer magnetic semiconductor ${\mathrm{CrPS}}_4$. We find that the ground-state magnetic structure of bulk ${\mathrm{CrPS}}_4$ exhibits the A-type antiferromagnetic ordering, which transforms to ferromagnetic (FM) ordering in single-layer ${\mathrm{CrPS}}_4$. The calculated formation energy and phonon spectrum confirm the stability of single-layer ${\mathrm{CrPS}}_4$. The band gaps of FM single-layer ${\mathrm{CrPS}}_4$ calculated with a hybrid density functional are within the visible-light range. We also study the effects of FM ordering on the optical absorption spectra and band alignments for water splitting, indicating that single-layer ${\mathrm{CrPS}}_4$ could be a potential photocatalyst. Our work opens up ample opportunities of energy-related applications of single-layer ${\mathrm{CrPS}}_4$.

Dielectric screening is essential in determining semiconductor properties. Its assessment on the surface, however, is beyond the capability of conventional techniques due to their lack of surface sensitivity. Here we present the surface-sensitive measurement of the dielectric screening by using scanning tunneling microscopy and spectroscopy. Both single-atom and single-electron manipulations on the B $\delta$-doped Si(111) surface unravel that the dielectric screening on this surface is much in excess of what the classical image-charge model predicts, which we ascribe to the strained bonds and the ionic character of the surface layers. Also, as an exemplary application of the measured screening parameters, we demonstrate determining the ionization state of a surface defect from the defect-induced band bending.

We show that III-V bismuth-based two-dimensional (2D) materials grown on an anion-terminated SrTe (111) substrate are 2D topological insulators. The III-Bi layers exhibit large nontrivial band gaps, ranging from 0.15 to 0.72 eV, depending on the passivation on the top surface, i.e., using hydrogen or halogens. We find that $\mathrm{\Gamma }$-centered Dirac helical states, protected by time-reversal symmetry, appear at the edges of nanoribbon structures made of III-Bi layers on the SrTe substrate. The nontrivial character of the band gap is also determined by calculations of the ${\mathrm{Z}}_2$ invariant. We also find that the topological phase is maintained in the ultrathin quantum well heterostructures SrTe/III-Bi/SrTe, i.e., when the 2D materials are sandwiched between SrTe along the [111] direction, opening a new route for the fabrication of nanostructured devices based on 2D quantum spin Hall insulators.

The spin-orbit coupling (SOC) effect has been known to be profound in monolayer pristine transition metal dichalcogenides (TMDs). Here we show that point defects, which are omnipresent in the TMD membranes, exhibit even stronger SOC effects and change the physics of the host materials drastically. In this article we chose the representative monolayer ${\mathrm{WS}}_2$ slabs from the TMD family together with seven typical types of point defects including monovacancies, interstitials, and antisites. We calculated the formation energies of these defects, and studied the effect of spin-orbit coupling (SOC) on the corresponding defect states. We found that the S monovacancy (${\mathrm{V}}_{\mathrm{S}}$) and S interstitial (adatom) have the lowest formation energies. In the case of ${\mathrm{V}}_{\mathrm{S}}$ and both of the ${\mathrm{W}}_{\mathrm{S}}$ and ${\mathrm{W}}_{\mathrm{S}2}$ antisites, the defect states exhibit strong splitting up to 296 meV when SOC is considered. Depending on the relative position of the defect state with respect to the conduction band minimum (CBM), the hybrid functional HSE will either increase the splitting by up to 60 meV (far from CBM), or decrease the splitting by up to 57 meV (close to CBM). Furthermore, we found that both the ${\mathrm{W}}_{\mathrm{S}}$ and ${\mathrm{W}}_{\mathrm{S}2}$ antisites possess a magnetic moment of 2 ${\mu }_B$ localized at the antisite W atom and the neighboring W atoms. The dependence of SOC on the orientation of the magnetic moment for the ${\mathrm{W}}_{\mathrm{S}}$ and ${\mathrm{W}}_{\mathrm{S}2}$ antisites is discussed. All these findings provide insights in the defect behavior under SOC and point to possibilities for spintronics applications for TMDs.

We analyze the electronic structure in the three-dimensional (3D) crystal formed by the $s{p}^2$ hybridized orbitals ($K_4$ crystal), by the tight-binding approach based on the first-principles calculation. We discover that the bulk Dirac-cone dispersions are realized in the $K_4$ crystal. In contrast to the graphene, the energy dispersions of the Dirac cones are isotropic in 3D and the pseudospin $S=1$ Dirac cones emerge at the $\mathrm{\Gamma }$ and $H$ points of the bcc Brillouin zone, where three bands become degenerate and merge at a single point belonging to the $T_2$ irreducible representation. In addition, the usual $S=1/2$ Dirac cones emerge at the $P$ point. By focusing the hoppings between the nearest-neighbor sites, we show an analytic form of the tight-binding Hamiltonian with a $4\times 4$ matrix, and we give an explicit derivation of the $S=1$ and $S=1/2$ Dirac-cone dispersions. We also analyze the effect of the spin-orbit coupling to examine how the degeneracies at Dirac points are lifted. At the $S=1$ Dirac points, the spin-orbit coupling lifts the energy level with sixfold degeneracy into two energy levels with two-dimensional ${\overline{E}}_2$ and four-dimensional $\overline{F}$ representations. Remarkably, all the dispersions near the $\overline{F}$ point show the linear dependence in the momentum with different velocities. We derive the effective Hamiltonian near the $\overline{F}$ point and find that the band contact point is described by the $S=3/2$ Weyl point.

Incommensurate spiral order is a common occurrence in frustrated magnetic insulators. Typically, all magnetic moments rotate uniformly, through the same wavevector. However the honeycomb iridates family ${\mathrm{Li}}_2{\mathrm{IrO}}_3$ shows an incommensurate order where spirals on neighboring sublattices are counterrotating, giving each moment a different local environment. Theoretically describing its spin dynamics has remained a challenge: The Kitaev interactions proposed to stabilize this state, which arise from strong spin-orbit effects, induce magnon umklapp scattering processes in spin-wave theory. Here we propose an approach via a (Klein) duality transformation into a conventional spiral of a frustrated Heisenberg model, allowing a direct derivation of the dynamical structure factor. We analyze both Kitaev and Dzyaloshinskii-Moriya based models, both of which can stabilize counterrotating spirals, but with different spin dynamics, and we propose experimental tests to identify the origin of counterrotation.

In $1T-\mathrm{TaS}{\mathrm{e}}_2$, annular dark-field scanning transmission electron microscopy (ADF-STEM) of the commensurate charge density wave (CCDW) phase shows the periodic image contrast superimposed on the atomic columns. The periodicity of the image contrast is consistent with the superlattice formed by the periodic displacement of Ta atoms by the CCDW. Comparing the ADF-STEM with simulated images shows that the image contrast is formed by the displacement of Ta atoms. This result means that the displacement of Ta atoms by the CCDW is directly observed in real space and suggests that a coherent CDW forms on every layer of $1T-\mathrm{TaS}{\mathrm{e}}_2$.

We present a new method for describing the electronic structure of graphene, by treating the honeycomb lattice as an arrangement of crisscrossing one-dimensional quantum wires. The electrons travel as free particles along the wires and interfere at the three-way junctions formed by the carbon atoms. The approach produces the linearly dispersive Dirac band structure as well as the chiral pseudo-spin-wave functions. When vacancies are incorporated, the model reproduces the well known zero mode states.

Recent experiments have revealed an intriguing pressure-induced isostructural transition of the low temperature monoclinic $\mathrm{V}{\mathrm{O}}_2$ and hinted to the existence of a new metallization mechanism in this system. The physics behind this isostructural phase transition and the metallization remains unresolved. In this work, we show that the isostructural transition is a result of pressure-induced instability of a phonon mode that relates to a $\mathrm{CaC}{\mathrm{l}}_2$-type of rotation of the oxygen octahedra, which alleviates, but does not completely remove, the dimerization and zigzagging arrangement of V atoms in the M1 phase. This phonon mode shows an increasing softening with pressure, ultimately leading to an isostructural phase transition characterized by the degree of the rotation of the oxygen octahedra. We also find that this phase transition is accompanied by an anisotropic compression, in excellent agreement with experiments. More interestingly, in addition to the experimentally identified M1′ phase, we find a closely related ${\mathrm{M}1}^{\prime \prime }$ phase, which is nearly degenerate with the ${\mathrm{M}1}^{\prime }$ phase. Unlike the ${\mathrm{M}1}^{\prime }$ phase, which has a nearly pressure-independent electronic band gap, the gap of the ${\mathrm{M}1}^{\prime \prime }$ drops quickly at high pressures and vanishes at a theoretical pressure of about 40 GPa.

We introduce a continuum model of deposition and surface diffusion tackling semiconductor heteroepitaxy also in the presence of misfit dislocations. During the evolution defects are inserted on the fly whenever their presence lowers the energy of the system, and the corresponding stress field is added to the one produced by lattice mismatch. An application to Ge/Si is provided. The wealth of qualitatively different behaviors experimentally reported in the literature is reproduced.

We investigate the quasiparticle spin relaxation with superconducting-velocity–tunable state in GaAs (100) quantum wells in proximity to an $s$-wave superconductor. We first present the influence of the supercurrent on the quasiparticle state in GaAs (100) quantum wells, which can be tuned by the superconducting velocity. Rich features such as the suppressed Cooper pairings, large quasiparticle density and nonmonotonically tunable momentum current can be realized by varying the superconducting velocity. In the degenerate regime, the quasiparticle Fermi surface is composed by two arcs, referred to as Fermi arcs, which are contributed by the electron- and holelike branches. The D'yakonov-Perel' spin relaxation is then explored, and intriguing physics is revealed when the Fermi arc emerges. Specifically, when the order parameter tends to zero, it is found that the branch-mixing scattering is forbidden in the quasielectron band. When the condensation process associated with the annihilation of the quasielectron and quasihole is slow, this indicates that the electron- and holelike Fermi arcs in the quasielectron band are independent. The open structure of the Fermi arc leads to the nonzero angular average of the effective magnetic field due to the spin-orbit coupling, which acts as an effective Zeeman field. This Zeeman field leads to spin oscillations even in the strong-scattering regime. Moreover, in the strong-scattering regime, we show that the open structure of the Fermi arc also leads to the insensitiveness of the spin relaxation to the momentum scattering, in contrast to the conventional motional narrowing situation. Nevertheless, with a finite order parameter, the branch-mixing scattering can be triggered, opening the interbranch spin relaxation channel, which is dominant in the strong-scattering regime. In contrast to the situation with an extremely small order parameter, due to the interbranch channel, the spin oscillations vanish and the spin relaxation exhibits a motional narrowing feature in the strong-scattering regime.

We investigate a hybrid quantum system consisting of spatially separated resonant exchange qubits, defined in three-electron semiconductor triple quantum dots, that are coupled via a superconducting transmission line resonator. Drawing on methods from circuit quantum electrodynamics and Hartmann-Hahn double resonance techniques, we analyze three specific approaches for implementing resonator-mediated two-qubit entangling gates in both dispersive and resonant regimes of interaction. We calculate entangling gate fidelities as well as the rate of relaxation via phonons for resonant exchange qubits in silicon triple dots and show that such an implementation is particularly well suited to achieving the strong coupling regime. Our approach combines the favorable coherence properties of encoded spin qubits in silicon with the rapid and robust long-range entanglement provided by circuit QED systems.

Results are presented for the entanglement entropy and spectrum of half-filled graphene following the switch on of a circularly polarized laser. The laser parameters are chosen to correspond to several different Floquet-Chern insulator phases. The entanglement properties of the unitarily evolved wave functions are compared with the state where one of the Floquet bands is completely occupied. The true states show a volume law for the entanglement, whereas the Floquet states show an area law. Qualitative differences are found in the entanglement properties of the off-resonant and on-resonant laser. Edge states are found in the entanglement spectrum corresponding to certain physical edge states expected in a Chern insulator. However, some edge states that would be expected from the Floquet band structure are missing from the entanglement spectrum. An analytic theory is developed for the long-time structure of the entanglement spectrum. It is argued that only edge states corresponding to off-resonant processes appear in the entanglement spectrum.

We report a study of the strain state of epitaxial MnSi films on Si(111) substrates in the thick film limit (100–500 Å) as a function of film thickness using polarization-dependent extended x-ray absorption fine structure (EXAFS). All films investigated are phase-pure and of high quality with a sharp interface between MnSi and Si. The investigated MnSi films are in a thickness regime where the magnetic transition temperature $T_{\mathrm{c}}$ assumes a thickness-independent enhanced value of $\ge 43$ K as compared with that of bulk MnSi, where $T_{\mathrm{c}}\approx 29\mathrm{K}$. A detailed refinement of the EXAFS data reveals that the Mn positions are unchanged, whereas the Si positions vary along the out-of-plane [111] direction, alternating in orientation from unit cell to unit cell. Thus, for thick MnSi films, the unit cell volume is essentially that of bulk MnSi—except in the vicinity of the interface with the Si substrate (thin film limit). In view of the enhanced magnetic transition temperature we conclude that the mere presence of the interface, and its specific characteristics, strongly affects the magnetic properties of the entire MnSi film, even far from the interface. Our analysis provides invaluable information about the local strain at the MnSi/Si(111) interface. The presented methodology of polarization dependent EXAFS can also be employed to investigate the local structure of other interesting interfaces.

Motivated by recent experiments on the frustrated quantum magnetic compound ${\mathrm{YbMgGaO}}_4$, we study an effective spin model on triangular lattice taking into account the effects of the spin-orbit coupling. We determine the classical ground-state phase diagram of this model, which includes a ${120}^{\circ }$ Néel and two collinear antiferromagnetic phases. In the vicinity of the phase boundary between the Néel and collinear phases, we identify three intermediate noncollinear antiferromagnetic phases. In each of them the magnetic moments are ordered at multiple incommensurate wave vector $\mathbf{Q}$ values. We further study the effects of quantum fluctuations in this model via a linear spin-wave theory. We find that the spin excitation gap of the noncollinear multi-$\mathbf{Q}$ antiferromagnetic states is vanishingly small. We also find that multi-$\mathbf{Q}$ states are most fragile against quantum fluctuations, and hence most unstable toward spin liquid phases.

We have systematically investigated the Gilbert damping constant $\alpha$ for $L{1}_0$-FePd films using the time-resolved magneto-optical Kerr effect (TRMOKE). The field angle dependence of TRMOKE signals was measured and analyzed. The field angle dependence of the lifetime of magnetization precession was explained by evaluating extrinsic contributions such as the anisotropy distribution and two-magnon scattering. The crystalline uniaxial perpendicular magnetic anisotropy constant $K_u$ and $\alpha$ values were evaluated for FePd films for various $L{1}_0$ order parameters $S$. $K_u$ values of approximately 15 Merg/${\mathrm{cm}}^3$ were obtained for films with large-$S$ values (i.e., over 0.8). In addition, $\alpha$ for the low-$S$ film was found to be approximately 0.007 and decreased with increasing $S$. Smaller values of $\alpha$ (of 0.002–0.004) were obtained for films with $S$ values of approximately 0.6–0.8. Results revealed that FePd films have both large-$K_u$ and small-$\alpha$ values, which is a useful property for low-power magnetization switching while maintaining high thermal stability in spin-transfer-torque magnetoresistive random access memory applications.

We introduce the cut-averaged entanglement entropy in disordered periodic spin chains and prove it to be a concave function of subsystem size for individual eigenstates. This allows us to identify the entanglement scaling as a function of subsystem size for individual states in inhomogeneous systems. Using this quantity, we probe the critical region between the many-body localized (MBL) and ergodic phases in finite systems. In the middle of the spectrum, we show evidence for bimodality of the entanglement distribution in the MBL critical region, finding both volume law and area law eigenstates over disorder realizations as well as within single disorder realizations. The disorder-averaged entanglement entropy in this region then scales as a volume law with a coefficient below its thermal value. We discover in the critical region, as we approach the thermodynamic limit, that the cut-averaged entanglement entropy density falls on a one-parameter family of curves. Finally, we also show that without averaging over cuts the slope of the entanglement entropy vs subsystem size can be negative at intermediate and strong disorder, caused by rare localized regions in the system.

Dielectric spectroscopy measurements are carried out in the temperature range from about 100 to 145 K on nominally pure ice V as well as on crystals doped with KOH and with HCl in order to investigate their reorientation dynamics at ambient pressure. The orientational glass transition temperature of pure ice V is detected at 123 K, in agreement with previous indications from calorimetry. KOH doped ice V displays an about 60-fold enhanced hydrogen dynamics and the dipolar relaxation induced by HCl doping is even by a factor of about 40 000 faster than that of the undoped material. The phase transition of HCl doped ice V to ice XIII is accompanied by a significant reorientational slowdown and a pronounced freeze-out of the electrical susceptibility. The results obtained near this transition are discussed in relation to other order/disorder ice pairs such as ice I/XI and ice XII/XIV.