Scanning tunneling microscopy (STM) reveals unusual sharp features in otherwise defect-free Bi nanolines self-assembled on Si(001). They appear as subatomic thin lines perpendicular to the Bi nanoline at positive biases and as atomic size beads at negative biases. Density functional theory (DFT) simulations show that these features can be attributed to buckled Si dimers substituting for Bi dimers in the nanoline, where the sharp feature is the counterintuitive signature of these dimers flipping during scanning. The perfect correspondence between the STM data and the DFT simulation demonstrated in this paper highlights the detailed understanding we have of the complex Bi-Si(001) Haiku system. This discovery has applications in the patterning of Si dangling bonds for nanoscale electronics.

A small polarizable object (an atom, molecule, or nanoparticle), placed above a medium with flowing dc current in it, is considered. It is shown that the dc current can have a strong effect on the force exerted on the particle. The Casimir-Lifshitz force, well studied in the absence of current, gets modified due to drifting mobile carriers in the medium. Furthermore, a force in the lateral direction appears. This force is a nonmonotonic function of the drift velocity and its maximal value is comparable with the Casimir-Lifshitz force. If the temperatures of the medium and the particle are different, this lateral force can be directed along the current (drag) or in the opposite direction (antidrag).

Chiral planar metamaterials are known for their possibility to show strong nonlinear optical effects such as second harmonic generation (SHG) circular dichroism or asymmetric SHG. The underlying mechanisms are commonly discussed in terms of local field effects and formation of localized SHG sources (so called “hotspots”) that are sensitive to the shape and size of meta-atoms. Nevertheless, a full characterization of the polarization state of the nonlinear optical radiation from the hotspots has not been performed until now. Here we present the results of the polarization-resolved second harmonic generation microscopy studies of planar chiral G-shaped metamaterials. We demonstrate that the SHG radiation coming from the hotspots that are localized within a single meta-atom is partially polarized; moreover, the SHG polarization state reveals the chirality of the structure. The observed effects are attributed to the induced plasmonic current oscillations at the fundamental frequency along with the local field distribution.

We propose and theoretically explore states of graphene superlattices with relaxed $\mathcal{P}$ and $\mathcal{T}$ symmetries created by strong circularly polarized ultrashort pulses. The conduction-band electron distribution in the reciprocal space forms an interferogram with discontinuities related to topological (Berry) fluxes at the Dirac points. This can be studied using time- and angle-resolved photoemission spectroscopy (TR-ARPES). Our findings hold promise for control and observation of ultrafast electron dynamics in topological solids and may be applied to petahertz-scale information processing.

Screening due to the surrounding dielectric medium reshapes the electron-hole interaction potential and plays a pivotal role in deciding the binding energies of strongly bound exciton complexes in quantum confined monolayers of transition metal dichalcogenides (TMDs). However, owing to strong quasiparticle band-gap renormalization in such systems, a direct quantification of estimated shifts in binding energy in different dielectric media remains elusive using optical studies. In this work, by changing the dielectric environment, we show a conspicuous photoluminescence peak shift at low temperature for higher energy excitons $\left(2s,3s,4s,5s\right)$ in monolayer $\mathrm{MoS}{\mathrm{e}}_2$, while the $1s$ exciton peak position remains unaltered – a direct evidence of varying compensation between screening induced exciton binding energy modulation and quasiparticle band-gap renormalization. The estimated modulation of binding energy for the $1s$ exciton is found to be $58.6\%$ $(72.8\%$ for $2s,75.85\%$ for $3s$, and $85.6\%$ for $4s)$ by coating an $\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$ layer on top, while the corresponding reduction in quasiparticle band-gap is estimated to be 246 meV. Such direct evidence of large tunability of the binding energy of exciton complexes as well as the band-gap in monolayer TMDs holds promise of novel device applications.

We study the growth of entanglement entropy in density-matrix renormalization-group calculations of the real-time quench dynamics of the Anderson impurity model. We find that with an appropriate choice of basis, the entropy growth is logarithmic in both the interacting and noninteracting single-impurity models. The logarithmic entropy growth is understood from a noninteracting chain model as a critical behavior separating regimes of linear growth and saturation of entropy, which correspond respectively to overlapping and gapped energy spectra of the set of bath states. We find that a logarithmic entropy growth is the generic behavior of quenched impurity models when the bath orbitals in the matrix product state are ordered in energy. A noninteracting calculation of the double-impurity Anderson model supports the conclusion in the multi-impurity case. The logarithmic growth of entanglement entropy enables studies of quench dynamics to very long times.

We derive general expressions for resonant inelastic x-ray scattering (RIXS) operators for $t_{2g}$ orbital systems, which exhibit a rich array of unconventional magnetism arising from unquenched orbital moments. Within the fast collision approximation, which is valid especially for $4d$ and $5d$ transition metal compounds with short core-hole lifetimes, the RIXS operators are expressed in terms of total spin and orbital angular momenta of the constituent ions. We then map these operators onto pseudospins that represent spin-orbit entangled magnetic moments in systems with strong spin-orbit coupling. Applications of our theory to such systems as iridates and ruthenates are discussed, with a particular focus on compounds based on $d^4$ ions with Van Vleck-type nonmagnetic ground state.

While much is known about the entanglement characteristics of ground states, the properties of reduced thermal density matrices have received significantly less attention. Here we investigate the total correlations in reduced thermal density matrices for momentum-space bipartitioning in Luttinger liquids using analytical and numerical methods. The low-lying part of its spectrum contains an “entanglement gap”, which persists up to temperatures comparable to the level spacing. With increasing temperature, the low-energy modes acquire dispersion and resemble those in the physical Hamiltonian with an enhanced effective temperature. The momentum-space entanglement is carried by high-energy modes (compared to temperature), featuring a completely flat spectrum. The von Neumann entropy increases with temperature with a universal Sommerfeld coefficient. The effective Hamiltonian of the right-moving excitations turns out to be as universal as the physical Hamiltonian.

We adopted the time-dependent density functional theory (TDDFT) within the linear augmented Slater-type orbitals basis and the cluster averaging method to compute the excitation spectra of III-V ternary alloys with arbitrary concentration $x$. The TDDFT was carried out with the use of adiabatic meta-generalized gradient approximation (mGGA), which contains the $1/q^2$ singularity in the dynamical exchange-correlation kernel $\left[f_{\text{XC,}00}\left(\mathbf{q}\right)\right]$ as $q\to 0$. We found that, by using wave functions obtained in local density approximation while using mGGA to compute self-energy correction to the band structures, we can get good overall agreement between theoretical results and experimental data for the excitation spectra. Thus, our paper provides some insight into the theoretical calculation of optical spectra of semiconductor alloys.

Photoinduced absorption in rutile ${\mathrm{TiO}}_2$ has been studied by means of Fourier transform infrared spectroscopy. It is shown that near-band-gap illumination results in a charge-state transition of a hydrogen defect with an O–H stretch mode at 3500 ${\mathrm{cm}}^{-1}$, as evidenced by the appearance of an anticorrelated vibrational mode with a blueshift of $\sim 1.3{\mathrm{cm}}^{-1}$. The charge-state transition is accompanied by a broad near-infrared absorption band with maximum intensity at $\sim 7000{\mathrm{cm}}^{-1}$. Our data on both the photoinduced vibrational mode and the near-infrared absorption can be conclusively explained in the framework of a model of small electron polarons bound to a Ti atom adjacent to the O–H group of the hydrogen defect.

Charged excitons, or $X^{\pm }$ trions, in monolayer transition-metal dichalcogenides have binding energies of several tens of meV. Together with the neutral exciton $X^0$ they dominate the emission spectrum at low and elevated temperatures. We use charge-tunable devices based on ${\mathrm{WSe}}_2$ monolayers encapsulated in hexagonal boron nitride to investigate the difference in binding energy between $X^{+}$ and $X^{-}$ and the $X^{-}$ fine structure. We find in the charge-neutral regime, the $X^0$ emission accompanied at lower energy by a strong peak close to the longitudinal optical (LO) phonon energy. This peak is absent in reflectivity measurements, where only the $X^0$ and an excited state of the $X^0$ are visible. In the $n$-doped regime, we find a closer correspondence between emission and reflectivity as the trion transition with a well-resolved fine-structure splitting of 6 meV for $X^{-}$ is observed. We present a symmetry analysis of the different $X^{+}$ and $X^{-}$ trion states and results of the binding energy calculations. We compare the trion binding energy for the $n$- and $p$-doped regimes with our model calculations for low carrier concentrations. We demonstrate that the splitting between the $X^{+}$ and $X^{-}$ trions as well as the fine structure of the $X^{-}$ state can be related to the short-range Coulomb-exchange interaction between the charge carriers.

Two-dimensional compounds made of one monolayer of Tl and one-third monolayer of Pb, Bi, Te, or Se (but not of Sn or Sb) on Si(111) have been found to have a similar atomic arrangement which can be visualized as a $\sqrt{3}\times \sqrt{3}$-periodic honeycomb network of chained Tl trimers with atoms of the second adsorbate occupying the centers of the honeycomb units. Structural and electronic properties of the compounds have been examined in detail theoretically using density functional theory (DFT) calculations and experimentally using low-energy electron diffraction (LEED), scanning tunneling microscopy (STM), and angle-resolved photoelectron spectroscopy (ARPES) observations. It has been found that though structural parameters of the compounds are very similar for all species, the only common feature of their band structure is a considerable spin-splitting of the surface-state bands, while other basic electronic properties vary greatly with a change of species. The Tl-Pb compound is strongly metallic with two metallic surface-state bands; the Tl-Bi compound is also metallic but with a single metallic band; the Tl-Te and Tl-Se compounds appear to be insulators.

We study the anomalous Hall effect in monolayers of transition-metal dichalcogenides 2H-$M{X}_2$ ($M$ = Mo, W, and $X$ = S, Se, Te) under a proximity effect of ferromagnetic substrate. If a proximity-induced exchange field is introduced, the spin-polarized energy bands in $K$ and $K^{\prime }$ valleys are shifted in the opposite directions, and it causes the Hall effect by breaking time-reversal symmetry. The induced Hall effect is the most prominent in the valence band, which has a large intrinsic spin splitting. Moreover, we find that tilting the magnetization from the perpendicular direction gives rise to a sensitive change in the Hall conductivity only in the electron side, and it is attributed to the mixing of the Berry phase by the in-plane field in the nearly degenerate conduction bands.

We have investigated the electronic structure of charged bilayer and trilayer phoshporene using first-principles density functional theory calculations. We find that the effective dielectric constant for an external electric field applied perpendicular to phosphorene layers increases with the charge density and is twice as large as in an undoped system if the electron density is around $5\times {10}^{13}$ ${\mathrm{cm}}^{-2}$. It is known that if few-layer phosphorene is placed under such an electric field, the electron band gap decreases, and if the strength of the electric field is further increased, the band gap closes. We show that the electronic screening due to added charge carriers reduces the amount of this reduction in the band gap and increases the critical strength of the electric field for gap closure. If the electron density is around $4\times {10}^{13}$ ${\mathrm{cm}}^{-2}$, for example, this critical field for trilayer phosphorene is 40% higher than that for a charge-neutral system. The results are directly relevant to experiments on few-layer phosphorene with top and bottom electrical gates and/or with chemical dopants.

Coherent diffraction imaging (CDI) is a rapidly developing form of imaging that offers the potential of wavelength-limited resolution without image-forming lenses. In CDI, the intensity of the diffraction pattern is measured directly by the detector, and various iterative phase retrieval algorithms are used to “invert” the diffraction pattern and reconstruct a high-resolution image of the sample. However, there are certain requirements in CDI that must be met to reconstruct the object. Although most experiments are conducted in the “far-field”—or Fraunhofer—regime where the requirements are not as stringent, some experiments must be conducted in the “near field” where Fresnel diffraction must be considered. According to the derivation of Fresnel diffraction, successful reconstructions can only be obtained when the small-angle number, a derived quantity, is much less than one. We show, however, that it is not actually necessary to fulfill the small-angle condition. The Fresnel kernel well approximates the exact kernel in regions where the phase oscillates slowly, and in regions of fast oscillations, indicated by large $An$, the error between kernels should be negligible due to stationary-phase arguments. We experimentally verify this conclusion with a helium neon laser setup and show that it should hold at x-ray wavelengths as well.

Using large-scale quantum Monte Carlo simulations we show that a spin-$\frac{1}{2}XXZ$ model on a two-dimensional anisotropic kagome lattice exhibits a tripartite entangled plaquette state that preserves all of the Hamiltonian symmetries. It is connected via phase boundaries to a ferromagnet and a valence-bond solid that break $U\left(1\right)$ and lattice translation symmetries, respectively. We study the phase diagram of the model in detail, in particular the transitions to the tripartite entangled plaquette state, which are consistent with conventional order-disorder transitions. Our results can be interpreted as a description of the charge sector dynamics of a Hubbard model applied to the spin liquid candidate ${\mathrm{LiZn}}_2{\mathrm{Mo}}_3{\mathrm{O}}_8$, as well as a model of strongly correlated bosonic atoms loaded onto highly tunable trimerized optical kagome lattices.

Substantial understanding of spin-orbit interactions in heavy-metal (HM)/ferromagnet (FM) heterostructures is crucial in developing spin-orbit torque (SOT) spintronics devices utilizing spin Hall and Rashba effects. Though the study of SOT effective field dependence on the out-of-plane magnetization angle has been relatively extensive, the understanding of in-plane magnetization angle dependence remains unknown. Here, we analytically propose a method to compute the SOT effective fields as a function of the in-plane magnetization angle using the harmonic Hall technique in perpendicular magnetic anisotropy (PMA) structures. Two different samples with PMA, a $\mathrm{Pt}\text{/}\mathrm{Co}\text{/}\mathrm{Pt}\text{/}\mathrm{Co}\text{/}\mathrm{Ta}\text{/}\mathrm{BaTi}{\mathrm{O}}_3$ (BTO) test sample and a Pt/Co/Pt/Co/Ta reference sample, are studied using the derived formula. Our measurements reveal that only the dampinglike field of the test sample with a BTO capping layer exhibits an in-plane magnetization angle dependence, while no angular dependence is found in the reference sample. The presence of the BTO layer in the test sample, which gives rise to a Rashba effect at the interface, is ascribed as the source of the angular dependence of the dampinglike field.

In the presence of an applied magnetic field introducing Zeeman spin splitting, a superconducting (SC) proximitized one-dimensional (1D) nanowire with spin-orbit coupling can pass through a topological quantum phase transition developing zero-energy topological Majorana bound states (MBSs) on the wire ends. One of the promising experimental platforms in this context is a Coulomb-blockaded island, where by measuring the two-terminal conductance one can in principle investigate the MBS properties. Here, we theoretically study the tunneling transport of a single electron across the superconducting Coulomb-blockaded nanowire at finite temperature in order to obtain the generic conductance equation. By considering all possible scenarios where only MBSs are present at the ends of the nanowire, we compute the nanowire conductance as a function of the magnetic field, the temperature, and the gate voltage. In the simplest 1D topological SC model, the oscillations of the conductance peak spacings (OCPSs) arising from the Majorana overlap from the two wire ends manifest an increasing oscillation amplitude with increasing magnetic field (in disagreement with a recent experimental observation). We develop a generalized finite-temperature master-equation theory including not only multiple subbands in the nanowire, but also the possibility of ordinary Andreev bound states in the nontopological regime. Inclusion of all four effects (temperature, multiple subbands, Andreev bound states, and MBSs) provides a complete picture of the tunneling transport properties of the Coulomb-blockaded nanowire. Based on this complete theory, we indeed obtain OCPSs whose amplitudes decrease with increasing magnetic field in qualitative agreement with recent experimental results, but this happens only for rather high temperatures with multisubband occupancy and the simultaneous presence of both Andreev bound states and MBSs in the system. Thus, the experimentally observed OCPSs manifesting decreasing amplitude with increasing magnetic field can be explained in our theory only if the experimental magnetic field range encompasses both the nontopological and the topological regimes so that both Andreev bound states and Majorana bound states are contributing to these oscillations as well as the applicable electron temperature in the nanowire is rather high. A particularly significant aspect of our theory is that in such a high-temperature Coulomb-blockaded nanowire, the OCPSs no longer have a one-to-one correspondence with the nanowire quasiparticle energy spectrum as is generic in the low-temperature unblockaded situation. This implies that the OCPSs cannot be used to conclude about the low-energy spectrum so that no statement can be made about the so-called “topological protection” based on such OCPSs. In particular, the length dependence of the oscillation peak in such a situation is nongeneric and does not directly contain useful information about the Majorana splitting energy, reflecting only the physics of Andreev bound states in the finite-size nanowires used in the experiment.

We report a polarized Raman scattering study of nonsymmorphic topological insulator KHgSb with hourglasslike electronic dispersion. Supported by theoretical calculations, we show that the lattice of the previously assigned space group $P{6}_3/mmc$ (No. 194) is unstable in KHgSb. While we observe one of two calculated Raman active ${\mathrm{E}}_{2g}$ phonons of space group $P{6}_3/mmc$ at room temperature, an additional ${\mathrm{A}}_{1g}$ peak appears at 99.5 ${\mathrm{cm}}^{-1}$ upon cooling below $T^{*}=150$ K, which suggests a lattice distortion. Several weak peaks associated with two-phonon excitations emerge with this lattice instability. We also show that the sample is very sensitive to high temperature and high laser power, conditions under which it quickly decomposes, leading to the formation of Sb. Our first-principles calculations indicate that space group $P{6}_{3}mc$ (No. 186), corresponding to a vertical displacement of the Sb atoms with respect to the Hg atoms that breaks the inversion symmetry, is lower in energy than the presumed $P{6}_3/mmc$ structure and preserves the glide-plane symmetry necessary to the formation of hourglass fermions.