Recently the evidence of the helical magnetic structure modulated along the $c$ axis with the period of four lattice parameters was obtained in easy $ab$ plane ferromagnetic superconductor ${\mathrm{EuRbFe}}_4{\mathrm{As}}_4$ [K. Iida et al., Phys. Rev. B 100, 014506 (2019)]. We argue that such structure may appear due to the presence of superconductivity. In spite of the very small value of the exchange field acting on the superconducting electrons in ${\mathrm{EuRbFe}}_4{\mathrm{As}}_4$, the exchange mechanism of interaction between superconductivity and ferromagnetism could dominate over the electromagnetic one and this circumstance could favor the emergence of the short-period magnetic structure (with the period less than the superconducting coherence length). Such a situation differs from one in the similar compound P-doped ${\mathrm{EuFe}}_2{\mathrm{As}}_2$, where the electromagnetic mechanism dominates and results in the magnetic structure with significantly larger period (of the order of London penetration depth). We also analyze the effect of the external magnetic field on the onset temperature of the modulated magnetic structure.

We present a computationally efficient approach to solve the time-dependent Kohn-Sham equations in real time using higher order finite-element spatial discretization, applicable to both pseudopotential and all-electron calculations. To this end, we develop an a priori mesh adaption technique, based on the semidiscrete (discrete in space but continuous in time) error estimate on the time-dependent Kohn-Sham orbitals, to construct an efficient finite-element discretization. Subsequently, we obtain the full-discrete error estimate to guide our choice of the time step. We employ spectral finite elements along with special reduced order quadrature to render the overlap matrix diagonal, thereby simplifying the inversion of the overlap matrix that features in the evaluation of the discrete time-evolution operator. We use the second-order Magnus operator as the time-evolution operator, wherein the action of the discrete Magnus operator, expressed as exponential of a matrix, on the Kohn-Sham orbitals is obtained efficiently through an adaptive Lanczos iteration. We observe close to optimal rates of convergence of the dipole moment with respect to spatial and temporal discretization, for both pseudopotential and all-electron calculations. We demonstrate a staggering 100-fold reduction in the computational time afforded by higher order finite elements over linear finite elements, for both pseudopotential and all-electron calculations. Further, for similar level of accuracy, we obtain significant computational savings by our approach as compared to state-of-the-art finite-difference methods. We also demonstrate the competence of higher order finite elements for all-electron benchmark systems. Lastly, we observe good parallel scalability of the proposed method on many hundreds of processors.

We perform systematic density functional theory (DFT) calculations to assess the performance of various exchange-correlation potentials $V_{xc}$ in describing the chalcogenide $\mathrm{Ga}{M}_4{Q}_8$ lacunar spinels ($M=\text{Mo}$, V, Nb, Ta; $Q=\text{S}$, Se). We examine the dependency of crystal structure (in cubic and rhombohedral symmetries), electronic structure, magnetism, optical conductivity, and lattice dynamics in lacunar spinels at four different levels of $V_{xc}$: The local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA, and hybrid with fractional Fock exchange. We find that LDA underperforms the Perdew-Burke-Ernzerhof (PBE) and PBE revised for solids (PBEsol) GGA functionals in predicting lattice constants as well as reasonable electronic structures. The performance of LDA and GGAs can be improved both quantitatively and qualitatively by including an on-site Coulomb interaction (LDA/$\mathrm{GGA}+U$) with a Hubbard $U$ value ranging from 2 to 3 eV. We find that the PBE functional is able to produce a semiconducting state in the distorted polar $R3m$ phase without on-site Coulomb interactions. The meta-GGA functional SCAN (strongly constrained and appropriately normed) predicts reasonable lattice constants and electronic structures; it exhibits behavior similar to the $\mathrm{GGA}+U$ functionals for small $U$ values of 1 to 2 eV. The hybrid functional HSE06 is accurate in predicting the lattice constants but leads to a band gap greater than the experimental estimation of 0.2 eV in this family. All of the lacunar spinels in the cubic phase are metallic at these levels of band theory; however, the predicted valence bandwidths are extremely narrow ($\approx 0.5\mathrm{eV}$). The DFT ground states of cubic vanadium chalcogenides are found to be highly spin polarized, which contrast with previous experimental results. With spin-orbit coupling (SOC) interactions and a Hubbard $U$ value of 2 to 3 eV, we predict a semiconducting cubic phase in all compounds studied. SOC does not strongly impact the electronic structures of the symmetry-broken $R3m$ phase. We also find that these $V_{xc}$ potentials do not quantitatively agree with the available experimental optical conductivity on ${\mathrm{GaV}}_4{\mathrm{S}}_8$; nonetheless, the LDA and GGA functionals correctly reproduce its lattice dynamical modes. Our findings suggest that accurate qualitative and quantitative simulations of the lacunar spinel family with DFT requires careful attention to the nuances of the exchange-correlation functional and considered spin structures.

In this paper we use a close connection between the coupled-wire construction (CWC) of Abelian quantum Hall states and the theory of composite bosons to extract the Laughlin wave function and the hydrodynamic effective theory in the bulk, including the Wen-Zee topological action, directly from the CWC. We show how rotational invariance can be recovered by fine tuning the interactions. A simple recipe is also given to construct general Abelian quantum Hall states described by the multicomponent Wen-Zee action.

The anisotropic changes in the electronic structure of a metal-to-insulator transition (MIT) material, RuAs, with a two-step phase transition are reported by using polarized optical conductivity $\sigma \left(\omega \right)$ spectra, angle-integrated photoelectron (PE) spectra, and band calculations based on the local-density approximation (LDA). Both the PE and $\sigma \left(\omega \right)$ spectra, not only in the high-temperature (HT) phase but also in the low-temperature (LT) phase as well as the energy gap formation owing to the MIT, were almost consistent with those derived from the LDA band calculations, so the fundamental electronic structure in the HT and LT phases can be explained without electron correlations. However, the electronic structure in the middle phase between the HT and LT phases has not been clarified. The polarized $\sigma \left(\omega \right)$ spectra revealed not only the anisotropic energy gap formation but also the anisotropic gap-opening temperature; that is, the energy gap along the $c$ axis in the HT phase starts to open near the higher transition temperature, but that along the $b$ axis opens below the lower transition temperature. The finding suggests that the two-step MIT originates from the anisotropic energy gap formation.

Two-dimensional graphene is fascinating because of its unique electronic properties. From a fundamental perspective, one among them is the geometric phase structure near the Dirac points in the Brillouin zone, owing to the SU(2) nature of the Dirac cone wave functions. We ask if there are geometric phase structures in two dimensions which go beyond that of a Dirac cone. Here we write down a family of three-band continuum models of noninteracting fermions which have more intricate geometric phase structures. This is connected to the SU(3) nature of the wave functions near threefold degeneracies. We also give a tight-binding free fermion model on a two-dimensional graphene-like lattice where the threefold degeneracies are realized at fine-tuned points. Away from them, we obtain new “three-band” Dirac cone structures with associated nonstandard Landau level quantization, whose organization is strongly affected by the non-SU(2) or beyond-Dirac geometric phase structure of the fine-tuned points.

In the frame of Huang-Rhys's model, we study multiple orders of Raman scattering in monolayer transition metal chalcogenides (TMDC) based on the intrinsic excitons coupled with three types of phonon modes, including longitudinal optical (LO) phonon, surface optical (SO) phonon, and longitudinal acoustic (LA) phonon. We find that multiphonon structures display multiple order overtones at equal interval energies of $\hslash {\omega }_{\text{LO}}$ and $\hslash {\omega }_{\text{SO}}$, respectively, and intensities of overtones depend on the obtained values of Huang-Rhys factor, which can be modulated by the strength of exciton-optical phonons coupling, cutoff wave vector of optical phonon modes, and large exciton Bohr radius. Moreover, we propose the combined multiphonon processes of $p\hslash {\omega }_{\text{LO}}+m\hslash {\omega }_{\text{SO}}$ and $p\hslash {\omega }_{\text{LO}}\left(m\hslash {\omega }_{\text{SO}}\right)+\hslash {\omega }_{\text{LA}}$. These combined processes with weaker intensity could be used to analyze the fine structure of multiphonon Raman spectra in experiments. Our theoretical results indicate that the strong exciton effect in monolayer TMDC provides an excellent platform for exploring multiphonon Raman scattering.

We introduce a variational wave function for many-body ground states that involves imaginary-time evolution with two different Hamiltonians in an alternating fashion with variable time intervals. We successfully apply the ansatz on the one- and two-dimensional transverse-field Ising model and systematically study its scaling for the one-dimensional model at criticality. We find the total imaginary time required scales logarithmically with system size, in contrast to the linear scaling in conventional quantum Monte Carlo. We suggest this is due to unique dynamics permitted by alternating imaginary-time evolution, including exponential growth of bipartite entanglement. For generic models, the superior scaling of our ansatz potentially mitigates the negative sign problem at the expense of having to optimize variational parameters.

We argue that the magnetic circular dichroism (MCD) of the hard x-ray Raman scattering (XRS) could be used as an element selective probe of local spin polarization. The magnitude of the XRS-MCD signal is directly proportional to the local spin polarization when the angle between the incident wave vector and the magnetization vector is ${135}^{\circ }$ or $-{45}^{\circ }$. By comparing the experimental observation and the configuration interaction calculation at the $L_{2,3}$ and $M_{2,3}$ edges of ferromagnetic iron, we suggest that the integrated MCD signal in terms of the transferred energy could be used to estimate the local spin moment even in the case where the application of the spin sum rule in x-ray absorption is questionable. We also point out that the XRS-MCD signal could be observed at the $M_1$ edge with a magnitude comparable to that at the $M_{2,3}$ edge, although the spin-orbit coupling is absent in the core orbital. By combining the XRS-MCD at various edges, spin polarization distribution depending on the orbital magnetic quantum number would be determined.

We report results of the neutron scattering investigations of frustrated quantum magnet ${\mathrm{Ba}}_3{\mathrm{CoSb}}_2{\mathrm{O}}_9$ in magnetic fields up to 25.9 T. Contrary to other materials, ${\mathrm{Ba}}_3{\mathrm{CoSb}}_2{\mathrm{O}}_9$ exhibits properties typical of an ideal $S=\frac{1}{2}$ triangular lattice Heisenberg antiferromagnet, making it a perfect model system for testing theoretical predictions. In this work, we looked into the magnetization process in ${\mathrm{Ba}}_3{\mathrm{CoSb}}_2{\mathrm{O}}_9$ on a microscopic scale with a magnetic field applied in plane. A sequence of magnetic phase transitions, including the new high-field phase at 22.5 T reported recently has been followed at low temperatures as a function of field and modeled using the large-size cluster mean-field plus scaling method. Showing good agreement with the model, our results bridge the theory and the experiment providing microscopic information about the high-field spin ordering in $S=\frac{1}{2}$ triangular lattice Heisenberg-like antiferromagnet ${\mathrm{Ba}}_3{\mathrm{CoSb}}_2{\mathrm{O}}_9$.

We determine the optimal conditions to achieve topological superconducting phases having spin-singlet pairing for a planar nanowire with a finite lateral width in the presence of an in-plane external magnetic field. We employ a microscopic description that is based on a three-band electronic model including both the atomic spin-orbit coupling and the inversion asymmetric potential at the interface between oxide band-gap insulators. We consider amplitudes of the pairing gap, spin-orbit interactions, and electronic parameters that are directly applicable to nanowires of ${\mathrm{LaAlO}}_3\text{−}{\mathrm{SrTiO}}_3$. The lateral confinement introduces a splitting of the $d$ orbitals that alters the orbital energy hierarchy and significantly affects the electron filling dependence of the topological phase diagram. Due to the orbital directionality of the $t_{2g}$ states, we find that in the regime of strong confinement the onset of topological phases is pinned at electron filling where the quasiflat heavy bands start to get populated. The increase of the nanowire thickness leads to a changeover from a sparse-to-dense distribution of topologically nontrivial domains which occurs at the crossover associated with the orbital population inversion. These findings are corroborated by a detailed analysis of the most favorable topological superconducting phases in the electron doping–magnetic field plane highlighting the role of orbital-selective confinement.

We perform a systematic DMRG investigation of the two natural spin-1 generalizations of the spin-1/2 Majumdar-Ghosh chain, the spin-1 $J_1\text{−}{J}_2$ Heisenberg chain, where $J_2$ is a next-nearest-neighbor Heisenberg coupling, and the spin-1 $J_1\text{−}{J}_3$ model, where $J_3$ refers to a three-site interaction defined by $J_3\left[({\mathbf{S}}_{i-1}·{\mathbf{S}}_i)({\mathbf{S}}_i·{\mathbf{S}}_{i+1})+\mathrm{H}.\mathrm{c}.\right]$. Although both models are rigorously equivalent to the Majumdar-Ghosh chain for spin 1/2, their physics appears to be quite different for spin 1. Indeed, when all couplings are antiferromagnetic, the spin-1 $J_1\text{−}{J}_2$ model undergoes an effective decoupling into two next-nearest-neighbor (NNN) Haldane chains upon increasing $J_2$, while the $J_1\text{−}{J}_3$ chain undergoes a spontaneous dimerization similar to the spin-1/2 Majumdar-Ghosh chain upon increasing $J_3$. By extending the phase diagram to all signs of the couplings, we show that both the dimerized and the NNN-Haldane phase are actually present in the $J_1\text{−}{J}_3$ model, the former one adjacent to the Haldane one, the latter to the ferromagneric one, with an Ising transition between them. By contrast, the $J_1\text{−}{J}_2$ chain only has a NNN-Haldane phase between the Haldane phase and the ferromagnetic phase for positive $J_2$. In both cases, our DMRG data are consistent with a continuous Kosterlitz-Thouless transition between the NNN-Haldane and the ferromagnetic phases.

The photoexcited state associated with superconducting fluctuations above the superconducting critical temperature $T_c$ is studied based on the time-dependent Ginzburg-Landau approach. The excited state is created by an electric-field pulse and is probed by a weak secondary external field, which is treated by the linear response theory mimicking pump-probe spectroscopy experiments. The behavior is basically controlled by two relaxation rates: one is ${\gamma }_1$ proportional to the temperature measured from the critical point $T-T_c$, and the other is ${\gamma }_2$ proportional to the excitation intensity of the pump pulse. The excited state approaches the equilibrium state exponentially in a long time $t\gg {\gamma }_1^{-1}$, while in the intermediate-time domain we find a power-law or logarithmic decay with different exponents for $t\ll {\gamma }_2^{-1}$ and ${\gamma }_2^{-1}\ll t\ll {\gamma }_1^{-1}$, even though the system is located away from the critical point. This is interpreted as the critical point in equilibrium being extended to a finite region in the excited situation. The parameter dependences on both the pump and probe currents are also systematically studied in all dimensions.

We study the interplay of interactions and topology in a pseudospin Weyl system, obtained from a minimally modified Hubbard model, using the numerically exact auxiliary-field quantum Monte Carlo method complemented by mean-field theory. We find that the pseudospin plays a key role in the structure of the pairing amplitude. An attractive on-site interaction leads to pairing between quasiparticles carrying opposite spin and opposite topological charge, resulting in the formation of real-spin singlet pairs that are a mixture of pseudospin singlet and pseudospin triplet. Our results provide a detailed characterization of the exotic pairing behavior in this system, and they represent an important step toward a more complete understanding of superconductivity in the context of topological band structures, which will help guide searches for topological superconductivity in real materials and ultracold atoms.

For gapped graphene, we predict that an intense ultrashort (single-oscillation) circularly polarized optical pulse can induce a large population of the conduction band and a large valley polarization. With an increase in the band gap, the magnitude of the valley polarization gradually increases from zero (for the native gapless graphene) to a value on the order of unity. The energy bandwidth of the electrons excited into the conduction band can be very large ($\gtrsim 10$ eV for a reasonable pulse amplitude of $\sim 0.5$ V/Å). These phenomena are due to the effect of topological resonance: The matching of the topological (geometric) phase and the dynamic phase. Gapped graphene with a tunable band gap can be used as a convenient generic model of two-dimensional semiconductors with honeycomb generic lattice structures and broken inversion symmetry, such as transition-metal dichalcogenides.