This article demonstrates an elegant method for experimental retrieval of the buried phase information of optical phenomena at metallic-dielectric interfaces, especially surface plasmon polaritons (SPP), employing a model explicitly based on roughness-induced cross-polarization scattering. This inherent roughness of the interfaces within typical SPP Attenuated Total Reflection (ATR) setups leads to two interlinked phenomena: Angular broadening and cross-polarization scattering. The microscopic interface features generate altered polarization vectors which are comparably weak but, because of their orthogonal polarization direction, appreciable within the specularly reflected light. The information contained in this s-polarized light enables us to retrieve the phase information of SPPs through the interference model of cross-polarization scattering described here. On that basis, this article demonstrates the retrieval of phase shifts for multiple silver thicknesses of SPPs generated within an ATR geometry. Additionally, the method permits the evaluation of surface roughness parameters, characterization of the angular broadening of reflection, and determination of the thicknesses of the metallic layers.

The scattering process in tip-enhanced Raman spectroscopy (TERS) can occur in distinct ways, depending on the number of interaction events and their respective time sequences. These events are fundamentally described by the interaction of the radiation field with the plasmonic nano-structure that generates local enhancement or with the scattering medium itself. The interactions are historically denominated as T, in reference to field-tip interaction, and S, referencing field-sample interaction. The TERS intensity was analytically derived for the ST and TST terms in Phys. Rev. X 4, 031054 (2014). Here we provide further development on the TERS theory by presenting a comprehensive description of the physical picture and the mathematical steps for the obtention of analytical expressions that account for the TERS intensity related to the TS term for one- and two-dimensional samples. Finally, we performed a tip-approach TERS experiment in graphene with considerably higher accuracy than what has been reported in the literature and, with the inclusion of the TS term, the phonon coherence length of graphene, as measured by TERS, is revised to $\approx 40$ nm.

We study analytically and numerically electronic properties of a circular quantum dot made from AA-stacked bilayer graphene. We observe a discrete set of dot radii for which the low-energy electron states are degenerate with respect to the layer parity. By analogy with the “magic angles” in the twisted bilayer graphene we refer to these radii as “magic.” Such a feature is unique for the AA structures and is related to a specific layer symmetry of the AA graphene bilayer: the parity of the highest occupied level changes from layer-symmetric to layer antisymmetric when the radius of the AA dot is equal to its magic value. We explore an analogy in the electronic structure between twisted bilayer graphene at the magic twist angle and the AA quantum dot with magic radius. We argue that this analogy can be helpful for theoretical description of the electronic properties of the twisted bilayer graphene.

The topological phase transitions (TPTs) in three-dimensional compounds have attracted great attention in both condensed-matter physics and applied physics. Compared to the TPT in bulk structures, TPTs in noncentrosymmetric two-dimensional materials are less common and require further study. This work explores an inversion asymmetry structure, ${\mathrm{ReC}}_2\mathrm{H}$ monolayer by first-principle calculation. We show that it undergoes two TPTs at the critical biaxial strain of 2.3 and 7.8%, where the material transforms from normal insulator to $Z_2$ topological insulator and back to normal insulator, respectively. In the first TPT, the band inversion occurs at the generic momentum. The second one occurs at the high-symmetric $K$ point, identified by an exchange in the components (or irreducible representations) of the wave functions. These quantities are challenging to be detected using experimental techniques, such as angle-resolved photoemission spectroscopy. Since the nonlinear optical (NLO) response is very sensitive to the components and symmetries of the engaged bands, we study the shift current generation during the two aforementioned TPTs. We find that in both TPTs, the shift vectors change sign around momenta where the band gap closes and reopens. By considering the overall contribution of shift vectors weighted by the absorption rate in the whole Brillouin zone, the shift current may keep its direction under band inversion. This work offers the insight that a scrutinized examination is highly demanded in utilizing the shift current to detect TPT.

The Rényi (Shannon) entropy, i.e., $R{e}_{\alpha }\left(Sh\right)$, of the ground state of quantum systems in local bases normally show a volume-law behavior. For a subsystem of quantum chains at a critical point there is an extra logarithmic subleading term with a coefficient which is universal. In this paper we study this coefficient for generic time-reversal translational invariant quadratic critical free fermions. These models can be parametrized by a complex function which has zeros on the unit circle. When the zeros on the unit circle do not have degeneracy and there is no zero outside of the unit circle we are able to classify the coefficient of the logarithm. In particular, we numerically calculate the Rényi (Shannon) entropy in a configuration basis for a wide variety of these models and show that there are two distinct classes. For systems with $U\left(1\right)$ symmetry the coefficient is proportional to the central charge, i.e., one half of the number of points that one can linearize the dispersion relation of the system; for all the values of $\alpha$ with transition point at $\alpha =4$. For systems without this symmetry, when $\alpha >1$, this coefficient is again proportional to the central charge. However, the coefficient for $\alpha \le 1$ is a new universal number. Finally, by using the discrete version of the Bisognano-Wichmann modular Hamiltonian of the Ising chain we show that these coefficients are universal and dependent on the underlying CFT.

${\mathrm{CePtSi}}_2$ was reported to exhibit an antiferromagnetic order below $T^{*}=1.8$ K at ambient pressure, a valence state change at $\sim 1.2$ GPa, and superconductivity in the range between 1.4 and 2.1 GPa with a maximum transition temperature of 0.14 K [T. Nakano et al., Phys. Rev. B 79, 172507 (2009)]. We have performed polycrystalline and single-crystal neutron diffraction experiments to determine the magnetic structure under ambient and high pressures. We found incommensurate magnetic peaks with a magnetic propagation vector of $(0.32,0,0.11)$ at ambient pressure below $T_{\mathrm{SDW}}\sim 1.25$ K. Those magnetic peaks originate from a spin-density-wave order with the easy axis along the $c$ axis and an averaged ordered moment of $0.45\left(5\right){\mu }_{\mathrm{B}}$, suggesting that there may be an intermediate phase between $T^{*}$ and $T_{\mathrm{SDW}}$. Applying pressures, the magnetic propagation vector shows no change and the magnetic order disappears around 1.0 GPa, which is much lower than the critical pressure for the superconducting phase. The results suggest that other than magnetic fluctuations may play a primary role in the superconducting pairing mechanism.

We investigate the electronic band structure of modulation-doped GaAs/AlGaAs core-shell nanowires for both $n$ and $p$ doping. We developed an 8-band Burt-Foreman $\mathbf{k}·\mathbf{p}$ Hamiltonian approach to describe coupled conduction and valence bands in heterostructured nanowires of arbitrary composition, growth directions, and doping. Coulomb interactions with the electron/hole gas are taken into account within a mean-field self-consistent approach. We map the ensuing multiband envelope function and Poisson equations to optimized, nonuniform real-space grids by the finite element method. Self-consistent charge-density, single-particle subbands, density of states, and absorption spectra are obtained at different doping regimes. For $n$-doped samples, the large restructuring of the electron gas for increasing doping results in the formation of quasi-one-dimensional electron channels at the core-shell interface. Strong heavy-hole (HH)/light-hole (LH) coupling of hole states leads to nonparabolic dispersions with mass inversion, similarly to planar structures, which persist at large dopings, giving rise to direct LH and indirect HH gaps. In $p$-doped samples the hole gas forms an almost isotropic, ringlike cloud for a large range of doping. Here as a result of the increasing localization, HH and LH states uncouple, and mass inversion takes place at a threshold density. A similar evolution is obtained at fixed doping as a function of temperature. We show that signatures of the evolution of the band structure can be singled out in the anisotropy of linearly polarized optical absorption.

Global optimization with first-principles energy expressions (GOFEE) is an efficient method for identifying low-energy structures in computationally expensive energy landscapes such as the ones described by density functional theory (DFT), van der Waals enabled DFT, or even methods beyond DFT. GOFEE is an evolutionary algorithm, that in order to explore configuration space creates several candidates in parallel. These are treated approximately using a machine learned surrogate model of energies and forces, trained on the fly, eliminating the need for expensive relaxations using first-principles methods. Eventually, using Bayesian statistics, GOFEE chooses one candidate and treats that at the full first-principles level. In this paper we elaborate on the importance of the use of a Gaussian kernel with two length scales in the Gaussian process regression surrogate model. We further explore the role of the use in GOFEE of the lower confidence bound for relaxation and selection of candidate structures. In addition, we present details of a sampling scheme for obtaining parent structures in the evolution. Using machine learning clustering of the entire pool of low-energy structures ever calculated, and choosing the most stable member from each cluster, the scheme ensures a highly diverse sample of structures that plays the role of a population. The versatility of the GOFEE method is demonstrated by applying it to identify the low-energy structures of gas-phase fullerene-type 24-atom carbon clusters and of dome-shaped 18-atom carbon clusters supported on Ir(111).

We construct an explicit matrix product ansatz for the steady state of a boundary driven XYZ spin-$\frac{1}{2}$ chain for arbitrary local polarizing channels at the ends of the chain. The ansatz, where the Lax operators are written explicitly in terms of infinite-dimensional bidiagonal (triangular) site-dependent matrices, becomes exact either in the (Zeno) limit of infinite dissipation strength or the thermodynamic limit of infinite chain length. The solution is based on an extension of the recently discovered family of separable eigenstates of the model.

Graphene band renormalization near the van Hove singularity (VHS) has been investigated by angle-resolved photoemission spectroscopy (ARPES) on Li-doped quasifreestanding graphene on a cobalt (0001) surface. The absence of graphene band hybridization with the substrate, the doping contribution well represented by a rigid energy shift, and the excellent electron-electron interaction screening ensured by the metallic substrate offer a privileged point of view for such an investigation. A clear ARPES signal is detected along the $KMK$ direction of the graphene Brillouin zone, giving rise to an apparent flattened band. By simulating the graphene spectral function from the density functional theory calculated bands, we demonstrate that the photoemission signal around the $M$ point originates from the “tail” of the spectral function of the unoccupied band above the Fermi level. Such an interpretation puts forward the absence of any additional strong correlation effects near the VHS, reconciling the mean-field description of the graphene band structure even in a highly doped scenario.

In this Letter we present a detailed theoretical analysis for the spectral properties of Andreev bound states in the multiterminal Josephson junctions by employing a symmetry-constrained scattering matrix approach. We find that in the synthetic multidimensional space of superconducting phases, crossings of Andreev bands may support non-Abelian $\text{SU}\left(2\right)$ monopoles with a topological charge characterized by the second class Chern number. We propose that these topological defects can be detected via a nonlinear response measurement of the current autocorrelations. In addition, multiterminal Josephson junction devices can be tested as a hardware platform for realizing holonomic quantum computation.

We develop a description of spin waves in a $3D$ quantum $XY$ antiferromagnet (AFM) in terms of macroscopic variables, magnetization and Néel vector densities. We consider a layered AFM with spins located on the honeycomb lattice. In the discussed system, the spectrum of spin waves consists of four modes, all well captured by our macroscopic description. The gapless mode of the spin waves, i.e., magnons, is described by a system of equations, which has a structure general for the Goldstone mode in AFMs. We demonstrate that the parameters in the spin Hamiltonian can be evaluated by fitting the experimental data with the results obtained for the four modes using the macroscopic variable approach. The description of AFM in terms of macroscopic variables can be easily extended to the case when the lattice of the magnetic substance is deformed by an external strain or acoustic wave.

Placing the layers of the $3d$ magnetic elements in the van der Waals gap pulls the Nb/Ta-based transition metal dichalcogenides family from a nonmagnetic to a magnetic zone. However, the magnetic spectrum is strongly sensitive to the specific combination of host lattice and type of intercalated magnetic element and thus each combination needs a proper explicit study. In this context, we systematically investigate the magnetization of the Mn-intercalated layered ferromagnet ${\mathrm{Mn}}_{1/4}{\mathrm{NbS}}_2$ single crystal. Magnetization measurement revealed paramagnetic to ferromagnetic phase transition at around 105 K and an easy in-plane ($H\perp c$) significantly high magnetic anisotropy. The in-plane magnetic anisotropic energy (MAE) evaluated via the noncollinear first-principle approach is $\sim -600 \mu \mathrm{eV}$ per unit cell. The position of the Fermi level in between the spin-up and spin-down Mn states suppresses the positive contribution in the overall MAE, which lifts the overall MAE negative (in plane) with a larger size in ${\mathrm{Mn}}_{1/4}{\mathrm{NbS}}_2$. The comprehensive analysis of magnetization isotherms measured in the vicinity of $T_c$ with magnetic field $H$ applied parallel to the $ab$ plane ($H\perp c$) yields the asymptotic critical exponents $\beta =0.3251\left(2\right)$ and $\gamma =1.2\left(1\right)$, and $\delta =4.691\left(1\right)$. These critical exponents fulfill the scaling relation and scaling equation of the magnetic state predicted by the scaling theory. The determined critical exponents agree well with those obtained from the results of the renormalization group theory approach for a three-dimensional Ising system coupled with a long-range interaction between spins decaying as $J\left(r\right)\approx r^{-(d+\sigma )}$ with $\sigma$ = 1.84. The Ising-type spin state in ${\mathrm{Mn}}_{1/4}{\mathrm{NbS}}_2$ is attributed to the higher size of MAE. Our theoretical analysis shows that indirect exchange interaction between Mn-Mn along the $c$ axis, mediated via spins' polarized conduction electrons of Nb atoms, a Ruderman-Kittel-Kasuya-Yoshida (RKKY) type ferromagnetic interaction, dominates over the direct in-plane Mn-Mn exchange interaction (less favorable due to large $d_{\text{Mn-Mn}}\sim 6.67\mathring{\mathrm{A}}$) and is thus responsible for the macroscopic magnetization in ${\mathrm{Mn}}_{1/4}{\mathrm{NbS}}_2$. The RKKY-type ferromagnetic interaction in ${\mathrm{Mn}}_{1/4}{\mathrm{NbS}}_2$ arises due to the large spin polarization of the conduction electrons associated with the Nb atoms at the Fermi energy and existence of unoccupied Mn $3d$ states well above the Fermi level.

We present an analytical study of the exchange interactions between pseudospin one-half $d^5$ ions in honeycomb lattices with edge-shared octahedra. Various exchange channels involving Hubbard $U$, charge-transfer excitations, and cyclic exchange are considered. Hoppings within $t_{2g}$ orbitals as well as between $t_{2g}$ and $e_g$ orbitals are included. Special attention is paid to the trigonal crystal field $\mathrm{\Delta }$ effects on the exchange parameters. The obtained exchange Hamiltonian is dominated by ferromagnetic Kitaev interaction $K$ within a wide range of $\mathrm{\Delta }$. It is found that a parameter region close to the charge-transfer insulator regime and with a small $\mathrm{\Delta }$ is most promising to realize the Kitaev spin liquid phase. Two representative honeycomb materials ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ and $\alpha \text{−}{\mathrm{RuCl}}_3$ are discussed based on our theory. We have found that both materials share dominant ferromagnetic $K$ and positive nondiagonal $\mathrm{\Gamma }$ values. However, their Heisenberg $J$ terms have opposite signs: AFM $J>0$ in ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ and FM $J<0$ in $\alpha \text{−}{\mathrm{RuCl}}_3$. This brings different magnetic fluctuations and results in their different magnetization behaviors and spin excitation spectra. Proximity to FM state due to the large FM $J$ is emphasized in $\alpha \text{−}{\mathrm{RuCl}}_3$. The differences between the exchange couplings of these two materials originate from the opposite $\mathrm{\Delta }$ values, indicating that the crystal field can serve as an efficient control parameter to tune the magnetic properties of $d^5$ spin-orbit Mott insulators.

The magnetization process of a superconductor is determined by the potential barrier for vortex nucleation and escape. In multicomponent superconductors, fractional vortices with a winding in the phase of only one of the components can be stable topological solitons that carry a fraction of the flux quantum. While the formation of such objects in the bulk costs logarithmically or linearly divergent energy, these objects were shown to be stable near the samples' boundaries in the two-component London model. Therefore the conventional Bean-Livingston picture of magnetic flux entry does not apply to these superconductors, since the entry process can involve fractionalization of a vortex. In this paper, we address the nonlinear problem of determining the potential barrier for fluxoid penetration in a multicomponent superconductor, including the effects of various intercomponent couplings, by using the recently developed gauged string method. The method allows numerically exact (i.e., convergent) calculation of a sphaleron configuration in a gauge theory and thus the height of the nucleation barrier. We show how the fractionalized nucleation processes result in multiple sphalerons and intermediate states due to the complex shape of the energy landscape of multicomponent superconductors.

Magnetotransport and magneto-optics experiments offer a very powerful probe for studying the physical properties of materials. Here, we investigate the second-order nonlinear magnetoconductivity of the tilted type-I Weyl and multi-Weyl semimetals. In contrast to the existence of chiral charge pumping in the linear response regime, we reproduce the absence of chiral charge pumping in the nonlinear transport regime, using the Boltzmann transport framework with the Landau levels. We predict that an inversion symmetry broken and tilted Weyl semimetal can support finite longitudinal nonlinear magnetoconductivity, which is otherwise absent in untilted Weyl semimetals. The nonlinear magnetoconductivity vanishes in the ultraquantum limit, oscillates in the intermediate magnetic field regime, and saturates in the semiclassical limit. The nonlinear magnetoconductivity depends intricately on the tilt orientation, and it can be used to determine the tilt orientation in Weyl and multi-Weyl semimetals, via nonlinear magnetoresistivity or second harmonic generation experiments.

We study the vanishing of the topological properties of a quantum spin Hall insulator induced by a deformation of the band structure that interpolates between the Dirac and the semi-Dirac limits of a tight-binding model on a honeycomb lattice. The above scenario is mimicked in a simple model, where there exists a differential hopping along one of the three neighbors (say, $t_1$) compared with the other two (say, $t$). For $t_1=t$, the properties of the quantum spin Hall phase is described by the familiar Kane-Mele model, while $t<t_1<2t$ denotes a situation in which the spin-resolved bands are continuously deformed. $t_1=2t$ represents a special case which is called as the semi-Dirac limit. Here, the spectral gaps between the conduction and the valence bands vanish. A closer inspection of the properties of such a deformed system yields insights on a topological phase transition occurring at the semi-Dirac limit, which continues to behave as a band insulator for $t_1>2t$. We demonstrate the evolution of the topological phase in presence of the Rashba and intrinsic spin-orbit couplings via computing the electronic band structure, edge modes in a nanoribbon and the ${\mathbb{Z}}_2$ invariant. The latter aids in arriving at the phase diagram which conclusively shows vanishing of the topological phase in the semi-Dirac limit. Furthermore, we demonstrate in gradual narrowing down of the plateau in the spin Hall conductivity, which along with a phase diagram provide robust support on the vanishing of the ${\mathbb{Z}}_2$ invariant and hence the quantum spin Hall phase.

The 8-$Pmmn$ borophene, a boron analog of graphene, hosts tilted and anisotropic massless Dirac fermion quasiparticles owing to the presence of a distorted graphenelike sublattice. First-principles calculations show that stacked 8-$Pmmn$ borophene is transformed into fused three-dimensional borophene under pressure, being accompanied by partial bond breaking and bond reformation. Strikingly, fused 8-$Pmmn$ borophene inherits the Dirac band dispersion resulting in an unusual semimetal-semimetal transition. A simple tight-binding model derived from graphene qualitatively reveals the underlying physics due to the maximum preservation of the graphenelike substructure after the phase transition, which contrasts greatly to the transformation of graphite into diamond associated with the semimetal-insulator transition.