We discuss a method of numerically identifying exact energy eigenstates for a finite system, whose form can then be obtained analytically. We demonstrate our method by identifying and deriving exact analytic expressions for several excited states, including an infinite tower, of the one-dimensional spin-1 Affleck-Kennedy-Lieb-Tasaki (AKLT) model, a celebrated nonintegrable model. The states thus obtained for the AKLT model can be interpreted as from one to an extensive number of quasiparticles on the ground state or on the highest excited state when written in terms of dimers. Included in these exact states is a tower of states spanning energies from the ground state to the highest excited state. Some of the states of the tower appear to be in the bulk of the energy spectrum, allowing us to make conjectures on the strong eigenstate thermalization hypothesis. We also generalize these exact states including the tower of states to the generalized integer spin AKLT models. Furthermore, we establish a correspondence between some of our states and those of the Majumdar-Ghosh model, yet another nonintegrable model, and extend our construction to the generalized integer spin AKLT models.

We investigate the effects of periodic fields and disorder on topological properties of a Weyl-semimetal thin film. The two periodic fields, i.e., a periodic magnetic field and elliptically polarized light, are discussed, respectively. By use of the Floquet theory, we find that both the two periodic drives can resonantly induce the topological transitions from normal insulator (NI) phases to Floquet topological insulator (FTI) phases. The Floquet topological transitions are characterized by a variation of the Chern number. Moreover, we show that the Floquet topological transitions can be explained by a combination of the quantum well approximation and the rotating wave approximation. In the disordered Weyl-semimetal thin film model under periodic fields, we calculate the Bott index to characterize the topological phase. It is found that the FTI phase is robust against weak disorder, and collapses for strong disorder strength. Interestingly, we find that disorder can also induce a topological transition from a topological trivial phase to an FTI phase, establishing the Floquet topological Anderson insulator (FTAI) phase. Finally, an effective-medium theory based on the Born approximation further confirms the numerical conclusions.

We study the effects of limited entanglement in the one-dimensional Hubbard model by representing the ground states in the form of matrix product states. Finite-entanglement scaling behavior over a wide range is observed at half-filling. The critical exponents characterizing the length scale in terms of the size of the matrices used are obtained, confirming the theoretical prediction that the values of the exponents are solely determined by the central charge. The entanglement spectrum shows that a global double degeneracy occurs in the ground states with a charge gap. We also find that the Mott transition, tuned by changing the chemical potential, always occurs through a first-order transition, and the metallic phase has a few conducting states, including the states with a mean-field nature close to the critical point, as expected in variational matrix product states with a finite amount of entanglement.

The emergence of the Pomeranchuk instability (PI) in a helical Fermi liquid (HFL) residing on the surface of a three-dimensional topological insulator (3D TI) is addressed at the mean-field level. An expression for the PI condition is derived in terms of a few microscopic parameters in each angular momentum channel corresponding to a central interaction between the helical electrons. It is found that because of the presence of strong spin-orbit coupling (SOC), the Landau parameter ${\overline{F}}_l$ corresponding to a particular angular momentum channel $l$ depends not only on the electron-electron interaction in the same channel, but also interactions in $(l+1)$ and $(l-1)$ channels. The formalism automatically excludes the $l=1$ PI in the HFL where the Galilean invariance is broken because of the presence of strong SOC. It is also found that the competing PIs can only be avoided until the appearance of $l=2$ PI. In this case, the corresponding nematic instability can even be achieved in the $l=1$ angular momentum channel of interaction between the electrons. The range of interaction between the electrons plays a pivotal role in bringing out the PIs. This is established by analyzing a few realistic profiles of the interaction. Another class of instability, involving a change in the topology of the Fermi surface without breaking the rotational symmetry, is found which competes with the PIs. Quantum phase transition originating from this instability is quite similar to the Lifshitz transition but is driven by electron-electron interaction. Possible connections of this instability with experiments are also described briefly.

We investigate the collective plasmon modes in the double layer of two-dimensional materials where either one or both of the layers have tilted Dirac cone. Consistent with quite generic hydrodynamic treatment, similar to double-layer graphene systems, we find two branches of plasmons. The in-phase oscillations of the two layers disperse as $\sqrt{q}$, while the out-of-phase mode disperses as $q$. When even one of the layers hosts tilted Dirac cone spectrum, the plasmonic kink which is a salient feature of a monolayer of tilted Dirac cone is inherited by both of these branches. In double layers composed of graphene (nontilted) and borophene (tilted), where the two layers have two different Fermi velocities, the velocity scale of plasmonic modes is set by the greater of the two. The kink always takes place when each plasmon mode crosses an energy scale ${\omega }_{\mathrm{kink}}$. When the two layers have different chemical potentials, there will be two such scales, and both in-phase and out-of-phase mode develop two kinks. Moreover, we find that an additional linearly dispersing overdamped mode of monolayer tilted Dirac cone system survives in the double-layer system.

Using density-functional and many-body perturbation theory, we study the electronic, optical, and excitonic properties of indium nitride as single monolayer and bilayer in comparison with the bulk phase. We investigate the stable geometry for the monolayer, the graphenelike unbuckled honeycomb structure, and for the bilayer the AA' stacking geometry. We demonstrate that the quasiparticle and optical gaps, going from bulk to two-dimensional systems, open dramatically due to strong quantum confinement and reduced screening. Large excitonic effects, which survive at room temperature, are predicted. Our results suggest that low-dimensional InN is a promising material for optoelectronic devices in the visible to near-infrared spectral ranges varying with the number of atomic layers and light propagation.

Phase transitions and symmetry are intimately linked. Melting of ice, for example, restores translation invariance. The mysterious hidden order (HO) phase of ${\mathrm{URu}}_2{\mathrm{Si}}_2$ has, despite relentless research efforts, kept its symmetry breaking element intangible. Here, we present a high-resolution x-ray diffraction study of the ${\mathrm{URu}}_2{\mathrm{Si}}_2$ crystal structure as a function of hydrostatic pressure. Below a critical pressure threshold $p_c\approx 3$ kbar, no tetragonal lattice symmetry breaking is observed even below the HO transition $T_{\text{HO}}=17.5$ K. For $p>p_c$, however, a pressure-induced rotational symmetry breaking is identified with an onset temperatures $T_{\text{OR}}\sim 100$ K. The emergence of an orthorhombic phase is found and discussed in terms of an electronic nematic order that appears unrelated to the HO, but with possible relevance for the pressure-induced antiferromagnetic (AF) phase. Existing theories describe the HO and AF phases through an adiabatic continuity of a complex order parameter. Since none of these theories predicts a pressure-induced nematic order, our finding adds an additional symmetry breaking element to this long-standing problem.

We investigate topological charge pumping in a system of interacting bosons in the tight-binding limit, described by the Rice-Mele model. An appropriate topological invariant for the many-body case is the change of polarization per pump cycle, which we compute for various interaction strengths from infinite-size matrix-product-state simulations. We verify that the charge pumping remains quantized as long as the pump cycle avoids the superfluid phase. In the limit of hardcore bosons, the quantized pumped charge can be understood from single-particle properties such as the integrated Berry curvature constructed from Bloch states, while this picture breaks down at finite interaction strengths. These two properties—robust quantized charge transport in an interacting system of bosons and the breakdown of a single-particle invariant—could both be measured with ultracold quantum gases extending a previous experiment [Lohse et al., Nat. Phys. 12, 350 (2016)]. Furthermore, we investigate the entanglement spectrum of the Rice-Mele model and argue that the quantized charge pumping is encoded in a winding of the spectral flow in the entanglement spectrum over a pump cycle.

We study the stability of the electronic states in circular two-dimensional topological-insulator quantum dots against electric perturbations, as quantified by the susceptibility $\chi$ of the Stark shift $\mathrm{\Delta }E=\chi F^2/2$ of each energy level due to a small electric field $F$. We find the typical susceptibility ${\chi }_{\mathrm{edge}}\sim 1$ meV/(mV/${\mathrm{nm})}^2$ for edge states is 4 orders of magnitude smaller than ${\chi }_{\mathrm{bulk}}\sim {10}^4$ meV/(mV/${\mathrm{nm})}^2$ for normal bulk states. We show that the origin of this strong stability of the edge states is the equidistance nature of the edge states, which follows from the linear dispersion of the one-dimensional edge channel. Therefore, we expect this strong stability to be a general feature for edge states in relatively large topological-insulator quantum dots. This finding identifies a new physical mechanism for protecting the edge states against electrical perturbations, which may be relevant to the applications of these edge states in quantum technologies.

We describe a method for exactly diagonalizing clean $D$-dimensional lattice systems of independent fermions subject to arbitrary boundary conditions in one direction, as well as systems composed of two bulks meeting at a planar interface. The specification of boundary conditions and interfaces can be easily adjusted to describe relaxation, reconstruction, or disorder away from the clean bulk regions of the system. Our diagonalization method builds on the generalized Bloch theorem [A. Alase et al., Phys. Rev. B 96, 195133 (2017)] and the fact that the bulk-boundary separation of the Schrödinger equation is compatible with a partial Fourier transform. Bulk equations admit a rich symmetry analysis that can considerably simplify the structure of energy eigenstates, often allowing a solution in fully analytical form. We illustrate our approach to multicomponent systems by determining the exact Andreev bound states for a simple SNS junction. We then analyze the Creutz ladder model, by way of a conceptual bridge from one to higher dimensions. Upon introducing a new Gaussian duality transformation that maps the Creutz ladder to a system of two Majorana chains, we show how the model provides a first example of a short-range chiral topological insulator that hosts topological zero modes with a power-law profile. Additional applications include the complete analytical diagonalization of graphene ribbons with both zigzag-bearded and armchair boundary conditions, and the analytical determination of the edge modes in a chiral $p+ip$ two-dimensional topological superconductor. Lastly, we revisit the phenomenon of Majorana flat bands and anomalous bulk-boundary correspondence in a two-band gapless $s$-wave topological superconductor. Beside obtaining sharp indicators for the presence of Majorana modes through the use of the boundary matrix, we analyze the equilibrium Josephson response of the system, showing how the presence of Majorana flat bands implies a substantial enhancement in the $4\pi$-periodic supercurrent.

We theoretically model the spin-orbit interaction in silicon quantum dot devices, relevant for quantum computation and spintronics. Our model is based on a modified effective mass approach which properly accounts for spin-valley boundary conditions, derived from the interface symmetry, and should have applicability for other heterostructures. We show how the valley-dependent interface-induced spin-orbit 2D (3D) interaction, under the presence of an electric field that is perpendicular to the interface, leads to a $g$-factor renormalization in the two lowest valley states of a silicon quantum dot. These $g$-factors can change with electric field in opposite direction when intervalley spin-flip tunneling is favored over intravalley processes, explaining recent experimental results. We show that the quantum dot level structure makes only negligible higher order effects to the $g$-factor. We calculate the $g$-factor as a function of the magnetic field direction, which is sensitive to the interface symmetry. We identify spin-qubit dephasing sweet spots at certain directions of the magnetic field, where the $g$-factor renormalization is zeroed: these include perpendicular to the interface magnetic field, and also in-plane directions, the latter being defined by the interface-induced spin-orbit constants. The $g$-factor dependence on electric field opens the possibility for fast all-electric manipulation of an encoded, few electron spin qubit, without the need of a nanomagnet or a nuclear spin-background. Our approach of an almost fully analytic theory allows for a deeper physical understanding of the importance of spin-orbit coupling to silicon spin qubits.

We show that electron paramagnetic resonance (EPR) tagged high resolution photoexcitation spectroscopy is a powerful method for the correlation of zero phonon photoluminescence spectra with atomic point defects. Applied to the case of NV centers in $4H$-SiC it allows to associate the photoluminescence zero phonon lines (ZPL) at 1243, 1223, 1180, and 1176 nm with the (hk, kk, hh, kh) configurations of the ${\mathrm{NV}}^{-}$centers in this material. These results lead to a revision of a previous tentative assignment. Contrary to theoretical predictions, we find that the NV centers in $4H$-SiC show a negligible Franck-Condon shift as their ZPL absorption lines are resonant with the ZPL emission lines. The high subnanometer energy resolution of this technique allows us further to resolve additional fine-structure of the ZPL lines of the axial NV centers which show a doublet structure with a splitting of 0.8 nm. Our results confirm that NV centers in $4H$-SiC provide strong competitors for sensing and qubit application due to the shift of their optical transitions into the technology compatible near-infrared region and the superior material properties of SiC. Given that single center spin readout will be realized, they are suitable for scalable nanophotonic devices compatible with optical communication network.

This paper provides a theoretical investigation of negative refraction and focusing of elastic guided waves in a freestanding plate with a steplike thickness change. Under certain conditions, a positive phase velocity (forward) Lamb mode can be converted into a negative phase velocity (backward) mode at such interface, giving rise to negative refraction. A semianalytical model is developed to study the influence of various parameters such as the material Poisson's coefficient, the steplike thickness, the frequency, and the incidence angle. To this end, all the Lamb and shear horizontal propagating modes and also a large number of their inhomogeneous and evanescent counterparts are taken into account. The boundary conditions applied to the stress-displacement fields at the thickness step yields an equation system. Its inversion provides the transmission and reflection coefficients between each mode at the interface. The steplike thickness and Poisson's ratio are shown to be key parameters to optimize the negative refraction process. In terms of material, Duralumin is found to be optimal as it leads to a nearly perfect conversion between forward and backward modes over broad frequency and angular ranges. An excellent focusing ability is thus predicted for a flat lens made of two symmetric thickness steps. A laser ultrasonic experiment quantitatively confirms those theoretical predictions. This study paves the way toward the optimization of elastic devices based on negative refraction, in particular for cloaking or superfocusing purposes.

Recent outbreaks in bottom-up chemical techniques have demonstrated the synthesis of atomically perfect zigzag graphene nanoribbons (ZGNRs) and of their corresponding analogs with phenyl-edge functionalization [P. Ruffieux et al., Nature 531, 489 (2016)]. Since spin-polarized currents can be generated at the edges of the ZGNRs, the control of phenyl decoration at the zigzag edges could accurately tune the electronic properties of these carbon-based nanoribbons. In the present paper, using first-principles calculations and a Landauer-Büttiker approach, the electronic and magnetic properties as well as the spin-resolved transmissions are investigated in various phenyl-edge-modified ZGNRs. The understanding of the spin-dependent transport properties in relation to the atomic structure opens the way to design devices such as spin valves for future spintronics applications.

Ever since its discovery in 1996, ultrafast demagnetization has ignited immense research interest due to its scientific rigor and technological potential. A flurry of recent theoretical and experimental investigations has proposed direct and indirect excitation processes in separate systems. However, it still lacks a unified mechanism and remains highly debatable. Here, we demonstrate that instead of either direct or indirect interaction, simultaneous and controlled excitation of both direct and indirect mechanisms of demagnetization is possible in multilayers composed of repeated Co/Pd bilayers. Moreover, we are able to modulate demagnetization time (from ∼350 to ∼750 fs) by fluence and thickness-dependent indirect excitation due to heat current flowing vertically downward from top layers, which is combined with an altogether different scenario of direct irradiation. Finally, by regulating the pump wavelength, we can effectively control the contribution of indirect process, which gives a confirmation to our understanding of the ultrafast demagnetization process.

We microscopically derive the spin diffusion equation in an $s$-wave superconductor in the vicinity of the superconducting transition temperature $T_c$. Applying the general relation between the relaxation function and the response function to the present spin diffusion problem, we examine how the spin relaxation time and the spin diffusion coefficient are renormalized in the superconducting state. The analysis reveals that, below $T_c$, both the spin relaxation time and the spin diffusion coefficient are increased, resulting in an enhancement of the spin diffusion length. The present result may provide an explanation for the recent observation of an enhanced spin pumping signal below $T_c$ in a Py/Nb/Pt system that is free from the coherence peak effect.

Time-resolved scanning Kerr microscopy (TRSKM) was used to study precessional magnetization dynamics induced by a radio frequency (RF) current within a ${\mathrm{Al}}_2{\mathrm{O}}_3$/Py(5 nm)/Pt(6 nm)/Au(150 nm) spin Hall nano-oscillator structure. The Au layer was formed into two needle-shaped electrical contacts that concentrated the current in the center of a Py/Pt mesa of 4 $\mu \mathrm{m}$ diameter. Due to the spin Hall effect, current within the Pt layer drives a spin current into the Py layer, exerting a spin transfer torque (STT). By injecting RF current and exploiting the phase sensitivity of TRSKM and the symmetry of the device structure, the STT and Oersted field torques have been separated and spatially mapped. The STT and torque due to the in-plane Oersted field are observed to exhibit minima at the device center that is ascribed to spreading of RF current that is not observed for DC current. Torques associated with the RF current may destabilize the position of the self-localized bullet mode excited by the DC current and inhibit injection locking. The present study demonstrates the need to characterize both DC and RF current distributions carefully.

We present angle-dependent measurements of the damping properties of epitaxial Fe layers with MgO, Al, and Pt capping layers. Based on the preferential distribution of lattice defects following the crystal symmetry, we make use of a model of the defect density to separate the contribution of two-magnon scattering to the damping from the isotropic contribution originating in the spin pumping effect, viscous Gilbert damping, and the magnetic proximity effect. The separation of the two-magnon contribution, which depends strongly on the defect density, allows for the measurement of a value of the effective spin mixing conductance that is closer to the value exclusively due to spin pumping. The influence of the defect density for bilayer systems due to the different capping layers and to the unavoidable spread in defect density from sample to sample is thus removed. This shows the potential of studying spin pumping phenomena in fully ordered systems in which this separation is possible, contrary to polycrystalline or amorphous metallic thin films.