We investigate the valley-coupled transport of Dirac electrons in graphene with a uniform Y-shaped Kekulé lattice distortion, in which the original $K$ and $K^{\prime }$ valleys of the pristine graphene are folded together due to the $\sqrt{3}\times \sqrt{3}$ enlargement of the primitive cell. We show that the Klein tunneling effect of Dirac electrons tunneling through a rectangle potential barrier is significantly enhanced: The perfect transmission is not limited to normal incidence but occurs in a range of oblique incidence angle when the inversion symmetry of the system is broken to form a single Dirac-cone phase. It is also found that the C-C bond-length modulation of the Kekulé lattice that keeps the inversion symmetry of the system can be used to manipulate the valley degree of freedom in a similar way to the exchange field precessing spin, and such valley manipulation can be implemented conveniently by a gate voltage controlling the local potential of the device. The disorder and temperature effects are also discussed.

Recently, the crystal symmetry-protected topological semimetals have aroused extensive interest, especially the nonsymmorphic symmetry-protected one. We list the possible nonmagnetic topological semimetals and develop their $k·p$ Hamiltonian in all layer groups with multiple screw axes in the absence of spin-orbital coupling. We find a cat's-cradle-like topological semimetal phase which looks like multiple hourglasslike band structures staggered together. Furthermore, we propose monolayer borophene and borophane with the $pmmn$ layer group as the first material class to realize such a semimetal phase. A pair of tilted anisotropic Dirac cones at the Fermi level is revealed in two-dimensional boron-based materials, and the low-energy effective models are given. Moreover, akin to a three-dimensional Weyl semimetal, the topological property of these cat's-cradle-like Dirac semimetals can be verified by the calculation of a quantized Berry phase and the demonstration of a flat Fermi-arc edge state connecting two Dirac points as well. Our finding that borophene and borophane are cat's-cradle-like Dirac semimetals is of great interest for experiment and possible applications in the future.

Topological semimetals (TSMs) in which conduction and valence bands cross at zero-dimensional (0D) Dirac nodal points (DNPs) or 1D Dirac nodal lines (DNLs), in 3D momentum space, have recently drawn much attention due to their exotic electronic properties. Here, we generalize the TSM state further to a higher-dimensional Dirac nodal sphere (DNS) or pseudo DNS (PDNS) state, with the band crossings forming a 2D closed or approximate sphere at the Fermi level. This TSM state can exhibit unique electronic properties, making DNS/PDNS a type of fermion beyond the DNP/DNL paradigm. In realistic crystals, we demonstrate two possible types of PDNS states underlain by different crystalline symmetries, which are characterized with a spherical backbone consisting of multiple DNLs and approximate band degeneracy in between the DNLs. We identify all the possible band crossings with pairs of 1D irreducible representations to form the PDNS states in 32 point groups. Importantly, we discover that strained $M{\mathrm{H}}_3$ ($M=\text{Y}$, Ho, Tb, Nd) and ${\mathrm{Si}}_3{\mathrm{N}}_2$ are material candidates to realize these two types of PDNS states, respectively. As a high-symmetry-required state, the PDNS semimetal can be regarded as the “parent phase” for other topological gapped and gapless states.

Two-dimensional and three-dimensional massless Dirac fermions can form a sequence of quasibound states with an attractive charged impurity. These quasibound states exhibit a discrete scaling symmetry, i.e., the energy ratio between two successive states is a constant. Through the calculation of the energy spectrum directly, we find that in two dimensions an applied magnetic field can shift or even destroy the quasibound states around the Dirac point and their discrete scaling symmetry disappears. However, as the magnetic field increases, the remaining quasibound states are pushed up to the Dirac point. When one quasibound state is close to the Dirac point, the spectrum is modified significantly, due to the resonant scattering. The magnetic oscillation of the spectrum displays the same discrete scaling symmetry as the quasibound state does in zero magnetic field. This phenomenon also occurs in the quantum limit of three-dimensional Dirac semimetals, where the system becomes quasi-one-dimensional essentially. Our theoretical analysis is in good agreement with the recent experimental observations.

We investigate the unitary evolution following a quantum quench in quantum spin models possessing a (nearly) flat band in the linear excitation spectrum. Inspired by the perspective offered by ensembles of individually trapped Rydberg atoms, we focus on the paradigmatic trasverse-field Ising model on two-dimensional lattices featuring a flat band as a result of destructive interference effects (Lieb and kagomé lattice), or a nearly flat band due to a strong energy mismatch among sublattices (triangular lattice). Making use of linear spin-wave theory, we show that quantum quenches, equipped with single-spin imaging, can directly reveal the spatially localized nature of the dispersionless excitations, and their slow propagation or lack of propagation altogether. Moreover, we show that Fourier analysis applied to the postquench time evolution of wave-vector-dependent quantities allows for the spectroscopic reconstruction of the flat bands. Our results pave the way for future experiments with Rydberg quantum simulators, which can extend our linear spin-wave study to the fully nonlinear regime, characterized by the appearance of dense, strongly interacting gases of dispersionless excitations.

We study the quantum phases of spinless fermions at one-third filling on a kagome lattice featuring a quadratic band touching Fermi point. In the presence of weak first and second nearest-neighbor repulsive interactions ($V_1$ and $V_2$), we demonstrate an interaction driven quantum anomalous Hall effect by employing exact diagonalization and density-matrix renormalization group methods. The time-reversal symmetry is broken spontaneously by forming loop currents that exhibit long-range correlation. Quantized Hall conductance corresponding to a Chern number of $\pm 1$ is obtained by measuring the pumped charge through inserting flux in a cylinder geometry. We find that the energy gap, which topologically protects the emerging ground states, can be enhanced remarkably by a moderate $V_2<V_1$ via calculating the spectrum and charge excitation gaps, which highlights the experimentally feasible scheme of realizing the interaction driven topological phase by spatially decaying interactions on topologically trivial lattice models.

Higher-order topological insulators (HOTIs) which go beyond the description of conventional bulk-boundary correspondence, broaden the understanding of topological insulating phases. Being mainly focused on electronic materials, HOTIs have not yet been found in photonic crystals. Here, we propose a type of two-dimensional second-order photonic crystals with zero-dimensional corner states and one-dimensional boundary states for optical frequencies. All of these states are topologically nontrivial and can be understood based on the theory of topological polarization. Moreover, by tuning the easily fabricated structure of the photonic crystals, different topological phases can be realized straightforwardly. Our study can be generalized to higher dimensions and provides a platform for higher-order photonic topological insulators and semimetals.

We use the greatly improved optical linewidths provided by highly enriched ${}^{28}\mathrm{Si}$ to study a photoluminescence line near $1017\mathrm{meV}$ previously observed in the luminescence spectrum of natural Si diffused with Mg and suggested to result from the recombination of an isoelectronic bound exciton localized at a Mg-pair center. In ${}^{28}\mathrm{Si}$, this no-phonon line is found to consist of five components whose relative intensities closely match the relative abundances of Mg pairs formed by random combinations of the three stable isotopes of Mg, thus confirming the Mg-pair hypothesis. We further present the results of temperature-dependence studies of this center that reveal unusual and as-yet unexplained behavior.

We propose a tunable topological Josephson junction in silicene where electrostatic gates could switch between a trivial and a topological junction. These aspects are a consequence of a tunable phase transition of the topologically confined valley-chiral states from a spin-degenerate to a spin-helical regime. We calculate the Andreev bound states in such a junction analytically using a low-energy approximation to the tight-binding model of silicene in proximity to $s$-wave superconductors as well as numerically in the short- and long-junction regime and in the presence of intervalley scattering. Combining topologically trivial and nontrivial regions, we show how intervalley scattering can be effectively switched on and off within the Josephson junction. This constitutes a topological Josephson junction with an electrically tunable quasiparticle poisoning source.

We investigate the electron and hole spin relaxation in an ensemble of self-assembled InAs/${\mathrm{In}}_{0.53}{\mathrm{Al}}_{0.24}{\mathrm{Ga}}_{0.23}\mathrm{As}$/InP quantum dots with emission wavelengths around 1.5 $\mu \mathrm{m}$ by using pump-probe Faraday rotation spectroscopy. Electron-spin dephasing due to the randomly oriented nuclear Overhauser fields is observed. At low temperatures we find a submicrosecond longitudinal electron-spin relaxation time $T_1$ which depends unexpectedly strongly on temperature. At high temperatures the electron-spin relaxation time is limited by optical phonon scattering through spin-orbit interaction decreasing down to 0.1 ns at 260 K. We show that the hole spin relaxation is activated much more effectively by a temperature increase compared with the electrons.

For applications in energy harvesting and environmentally friendly cooling, and for power sources in remote or portable applications, it is desired to enhance the efficiency of thermoelectric materials. One strategy consists of reducing the thermal conductivity while increasing or retaining the thermoelectric power factor. An approach to achieve this is doping to enhance the Seebeck coefficient and electrical conductivity, while simultaneously introducing defects in the materials to increase phonon scattering. Here, we use Mg ion implantation to induce defects in epitaxial ScN (111) films. The films were implanted with $\mathrm{M}{\mathrm{g}}^{+}$ ions with different concentration profiles along the thickness of the film, incorporating 0.35 to 2.2 at. % of Mg in ScN. Implantation at high temperature (600 °C), with few defects due to the temperature, does not substantially affect the thermal conductivity compared to a reference ScN. Samples implanted at room temperature, in contrast, exhibited a reduction of the thermal conductivity by a factor of 3. The sample doped with 2.2 at. % of Mg also showed an increased power factor after implantation. This paper thus shows the effect of ion-induced defects on thermal conductivity of ScN films. High-temperature implantation allows the defects to be annealed out during implantation, while the defects are retained for room-temperature implanted samples, allowing for a drastic reduction in thermal conductivity.

We report on quantum Hall stripes (QHSs) formed in higher Landau levels of GaAs/AlGaAs quantum wells with high carrier density ($n_e>4\times {10}^{11}{\mathrm{cm}}^{-2}$) which is expected to favor QHS orientation along the unconventional $〈1\overline{1}0〉$ crystal axis and along the in-plane magnetic field $B_{\parallel }$. Surprisingly, we find that at $B_{\parallel }=0$ QHSs in our samples are aligned along the $〈110〉$ direction and can be reoriented only perpendicular to $B_{\parallel }$. These findings suggest that high density alone is not a decisive factor for either abnormal native QHS orientation or alignment with respect to $B_{\parallel }$, while quantum confinement of the 2DEG likely plays an important role.

We have investigated the atomic and electronic structure of the $\left(\sqrt{3}\times \sqrt{3}\right)R{30}^{\circ }\mathrm{SnA}{\mathrm{u}}_2\text{/}\mathrm{Au}\left(111\right)$ surface alloy. Low-energy electron diffraction and scanning tunneling microscopy measurements show that the native herringbone reconstruction of bare Au(111) surface remains intact after formation of a long-range ordered $\left(\sqrt{3}\times \sqrt{3}\right)R{30}^{\circ }\mathrm{SnA}{\mathrm{u}}_2\text{/}\mathrm{Au}\left(111\right)$ surface alloy. Angle-resolved photoemission and two-photon photoemission spectroscopy techniques reveal Rashba-type spin-split bands in the occupied valence band with comparable momentum space splitting as observed for the Au(111) surface state, but with a hole-like parabolic dispersion. Our experimental findings are compared with density functional theory (DFT) calculation that fully support our experimental findings. Taking advantage of the good agreement between our DFT calculations and the experimental results, we are able to extract that the occupied Sn-Au hybrid band is of $\left(s,d\right)$-orbital character, while the unoccupied Sn-Au hybrid bands are of $\left(p,d\right)$-orbital character. Hence we can conclude that the Rashba-type spin splitting of the hole-like Sn-Au hybrid surface state is caused by the significant mixing of Au $d$ with Sn $s$ states in conjunction with the strong atomic spin-orbit coupling of Au, i.e., of the substrate.

We compute the nonlinear optical response of doped monolayer and bilayer graphene using the full dispersion based on tight-binding models. The response is derived with the density matrix formalism using the length gauge and is valid for any periodic system, with arbitrary doping. By collecting terms that define effective nonlinear response tensors, we identify all nonlinear Drude-like terms (up to third order) and show that all additional spurious divergences present in the induced current vanish. The nonlinear response of graphene comprises a large Drude-like divergence and three resonances that are tightly connected with transitions occurring in the vicinity of the Fermi level. The analytic solution derived using the Dirac approximation captures accurately the first- and third-order responses in graphene, even at very high doping levels. The quadratic response of gapped graphene is also strongly enhanced by doping, even for systems with small gaps such as commensurate structures of graphene on SiC. The nonlinear response of bilayer graphene is significantly richer, combining the resonances that stem from doping with its intrinsic strong low-energy resonances.

Asymmetric Veselago lenses (AVLs) can be created from ballistic $p\text{−}n$ and $n\text{−}p\text{−}n$ homojunctions of uniaxially strained graphene. This atypical converging electron flow emerges by applying uniaxial tension out of the device's symmetry axes. Part of the electron flow needs to be positively refracted to focus on an asymmetric spot, whose location is tunable with the strain. In AVLs, Klein tunneling is angularly shifted with regard to the normal incidence. This perfect transmission occurs in the straight line that connects the point source and focus, which is unaffected by variation of the Fermi level and voltage gate. Moreover, the mirror symmetry breaking by the strain also causes the asymmetry in Fabry-Pérot interference. The novel electron optical laws allow us to evidence that reflected and refracted electrons in AVLs lie on the same straight line with opposite group velocities and pseudospins. Unlike isotropic graphene, electrons under normal incidence present backscattering, angles of reflection, and refraction different from zero. The average particle transmission is higher (lower) than the isotropic case when the tensile strain is increased near (far away from) the normal direction. These results may be useful for designing strain-bendable probing tips in scanning tunneling microscopes.

Higher-order topological phases feature topologically protected boundary states in lower dimensions. Specifically, the zero-dimensional corner states are protected by the $d\mathrm{th}$-order topology of a $d$-dimension system. In this work, we propose to predict different configurations of corner states from winding numbers defined for one-dimensional edges of the system. We first demonstrate the winding number characterization with a generalized two-dimensional square lattice belonging to the BDI symmetry class. In addition to the second-order topological insulating phase, the system may also be a nodal point semimetal or a weak topological insulator with topologically protected one-dimensional edge states coexisting with the corner states at zero energy. A three-dimensional cubic lattice with richer configurations of corner states is also studied. We further discuss several experimental implementations of our models with photonic lattices or electric circuits.

We present a systematic analysis and classification of several models of quantum batteries involving different combinations of two-level systems and quantum harmonic oscillators. In particular, we study energy-transfer processes from a given quantum system, termed a “charger,” to another one, i.e., the proper “battery.” In this setting, we analyze different figures of merit, including the charging time, the maximum energy transfer, and the average charging power. The role of coupling Hamiltonians which do not preserve the number of local excitations in the charger-battery system is clarified by properly accounting for them in the global energy balance of the model.

We search for stable compounds of boron and oxygen at pressures from 0 to 500 GPa using the ab initio evolutionary algorithm uspex. Only two stable stoichiometries of boron oxides, namely, ${\mathrm{B}}_6\mathrm{O}$ and ${\mathrm{B}}_2{\mathrm{O}}_3$, are found to be stable, in good agreement with experiment. A hitherto unknown phase of ${\mathrm{B}}_6\mathrm{O}$ at ambient pressure, $Cmcm\text{−}{\mathrm{B}}_6\mathrm{O}$, has recently been predicted by us and observed experimentally. For ${\mathrm{B}}_2{\mathrm{O}}_3$, we predict three previously unknown stable high-pressure phases—two of these ($Cmc{2}_1$ and $P{2}_1{2}_1{2}_1$) are dynamically and mechanically stable at ambient pressure, and should be quenchable to ambient conditions. Their predicted hardnesses, reaching 33–35 GPa, make them harder than $\mathrm{Si}{\mathrm{O}}_2$-stishovite. These are the hardest known oxides (if one disregards ${\mathrm{B}}_6\mathrm{O}$, which is essentially a boron-based insertion compound). Under pressure, the coordination number of boron atoms changes from 3 to 4 to 6, skipping fivefold coordination.

The entangling power and operator entanglement entropy are state-independent measures of entanglement. Their growth and saturation is examined in the time-evolution operator of quantum many-body systems that can range from the integrable to the fully chaotic. An analytically solvable integrable model of the kicked transverse-field Ising chain is shown to have ballistic growth of operator von Neumann entanglement entropy and exponentially fast saturation of the linear entropy with time. Surprisingly, a fully chaotic model with longitudinal fields turned on shares the same growth phase, and is consistent with a random matrix model that is also exactly solvable for the linear entropy entanglements. However, an examination of the entangling power shows that its largest value is significantly less than the nearly maximal value attained by the nonintegrable one. The importance of long-range spectral correlations, and not just the nearest-neighbor spacing, is pointed out in determining the growth of entanglement in nonintegrable systems. Finally, an interesting case that displays some features peculiar to both integrable and nonintegrable systems is briefly discussed.