An alternative method of writing down the path integral for spin-1 Heisenberg antiferromagnetic chain is introduced. In place of the conventional coherent-state basis that leads to the nonlinear $\sigma$ model, we use a basis called the fluctuating matrix product states which embodies intersite entanglement from the outset. It forms an overcomplete set spanning the entire Hilbert space of the spin-1 chain. Saddle-point analysis performed for the bilinear-biquadratic spin model predicts the Affleck-Kennedy-Lieb-Tasaki (AKLT) state as the ground state in the vicinity of the AKLT Hamiltonian. Quadratic effective action derived by gradient expansion around the saddle point is free from constraints that plagued the nonlinear $\sigma$ model and exactly solvable. The obtained excitation modes agree precisely with the single-mode approximation result for the AKLT Hamiltonian. Excitation spectra for other bilinear-biquadratic Hamiltonians are obtained as well by diagonalizing the quadratic action.

The Hubbard model and its extensions are important microscopic models for understanding high-$T_c$ superconductivity in cuprates. In the model with next-nearest-neighbor hopping $t^{\prime }$ (the $t^{\prime }$-Hubbard model), pairing is strongly influenced by $t^{\prime }$. In particular, a recent study on a width-4 cylinder observed quasi-long-range superconducting order, associated with a negative $t^{\prime }$, which was taken to imply superconductivity in the two-dimensional (2D) limit. In this work we study more carefully pairing in the width-$4t^{\prime }$-Hubbard model. We show that in this specific system, the pairing symmetry with $t^{\prime }<0$ is not the ordinary $d$-wave one would expect in the 2D limit. Instead we observe a so-called plaquette $d$-wave pairing. We show that the plaquette $d$-wave or its extension is difficult to generalize in other geometries, for example a 4-leg ladder with open boundaries or a width-6 cylinder. We find that a negative $t^{\prime }$ suppresses the conventional $d$-wave, leading to plaquette pairing. In contrast, a different $t^{\prime \prime }$ coupling acting diagonally on the plaquettes suppresses plaquette pairing, leading to conventional $d$-wave pairing.

We investigate a disorderly mesoscopic device that supports spin-orbit interaction. The system is connected to four semi-infinite leads embedded in the Landauer-Buttiker setup for quantum transport and, according to our analysis, exhibits spin Hall angle fluctuations. We show analytically and numerically the fingerprint of the universal fluctuation of the polarization mediated by the conversion of charge current into spin current. Our investigation shows the complete compatibility of our analytical and numerical results with the most recent experiments. Furthermore, we show nonzero and universal features of spin Hall effect in Rashba two-dimensional electron gas with disorder. All the results show the relevance of microscopic parameters for electronic transport with charge-spin conversion and, in many cases, inevitably lead to universal numbers.

We study ribbons of the dice two-dimensional lattice (that we call “dice ladders”) known to have nontrivial topological properties, such as Chern numbers 2 [Wang and Ran, Phys. Rev. B 84, 241103(R) (2011)]. Our main results are two fold. (1) Analyzing the tight-binding model in the presence of Rashba spin-orbit coupling and an external magnetic field, we observed that dice ladders qualitatively display properties similar to their two-dimensional counterpart all the way to the limit of only two legs in the short direction. This includes flat bands near the Fermi level, edge currents and edge charge localization near zero energy when open boundary conditions are used, two chiral edge modes, and a nonzero Hall conductance. (2) We studied the effect of Hubbard correlation $U$ in the two-leg dice ladder using Lanczos and density matrix renormalization group techniques. We show that by increasing $U$ the flat bands split without the need of introducing external fields. Moreover, robust ferrimagnetic order develops. Overall, our work establishes dice ladders as a promising playground to study the combined effect of topology and correlation effects, one of the frontiers in quantum materials.

There has been an upsurge in the discovery of topological quantum materials, where various topological insulators and semimetals have been theoretically predicted and experimentally observed. However, very few of them contain silicon, the most widely used element in the electronics industry. Recently, ternary compound $\mathrm{CaA}{\mathrm{l}}_2\mathrm{S}{\mathrm{i}}_2$ has been predicted to be a topological Dirac semimetal, hosting Lorentz-symmetry-violating quasiparticles with a strongly tilted conical band dispersion. In this work, by using high-resolution angle-resolved photoemission spectroscopy, we investigated the comprehensive electronic structure of $\mathrm{CaA}{\mathrm{l}}_2\mathrm{S}{\mathrm{i}}_2$. A pair of topological Dirac crossings is observed along the $k_z$ direction, in good agreement with the ab initio calculations, confirming the topological Dirac semimetal nature of the compound. Our study expands the topological material family on Si-containing compounds, which have great application potential in realizing low-cost, nontoxic electronic devices with topological quantum states.

We analyze the phase diagram of twisted graphene bilayers near a magic angle. We consider the effect of the long-range Coulomb interaction, treated within the self-consistent Hartree-Fock approximation, and we study arbitrary band fillings. We find a rich phase diagram, with different broken symmetry phases, although they do not show necessarily a gap at the Fermi energy. There are nontrivial effects of the electrostatic potential on the shape and the gaps of the bands in the broken symmetry phases. The results suggest that the nonsuperconducting broken symmetry phases observed experimentally are induced by the long-range exchange interaction.

We study the ground-state phase diagram of an interacting staggered Su-Schrieffer-Heeger (SSH) ladder in the vicinity of the Gaussian quantum critical point. The corresponding effective field theory, which nonperturbatively treats correlation effects in the ladder, is a double-frequency sine-Gordon (DSG) model. It involves two perturbations at the Gaussian fixed point: the deviation from criticality, and umklapp scattering processes. While massive phases with broken symmetries are identified by means of local order parameters, a topological distinction between thermodynamically equivalent phases becomes feasible only when nonlocal fermionic fields, parity, and the string order parameter are included in consideration. We prove that a noninteracting fermionic staggered SSH ladder is exactly equivalent to an O(2)-symmetric model of two decoupled Kitaev-Majorana chains, or two one-dimensional $p$-wave superconductors. Close to the Gaussian fixed point, the SSH ladder maps to an Ashkin-Teller-like system when interactions are included. Thus, the topological order in the SSH ladder is related to broken-symmetry phases of the associated quantum spin-chain degrees of freedom. The obtained phase diagram includes a Tomonaga-Luttinger liquid state that, due to umklapp processes, can become unstable against either spontaneous dimerization or the onset of a charge-density wave (CDW). In these gapped phases, elementary bulk excitations are quantum kinks carrying the charge $Q_F=1/2$. For sufficiently strong, long-range interactions, the phase diagram of the model exhibits a bifurcation of the Gaussian critical point into two outgoing Ising criticalities. The latter sandwich a mixed phase in which dimerization coexists with a site-diagonal CDW. In this phase, elementary bulk excitations are represented by two types of topological solitons carrying different fermionic charges, which continuously interpolate between 0 and 1. This phase has also mixed topological properties with coexisting parity and string order parameters.

Spin-orbit coupling (SOC) provides a lot of interesting phenomena in condensed-matter physics, and the strength of the SOC is one of the key factors to control such physical properties. In this paper, we present a systematic first-principles study of the strength of SOC in crystals by using the on-site SOC, namely, the atomic SOC defined by Wannier functions of the corresponding atomic orbitals. By calculating the on-site SOC in isolated atoms, monatomic crystals, and binary compounds, we find that the valence dependence of the atomic SOC in isolated atoms cannot explain the strength of the on-site SOC in crystals. Instead, it is shown that the spread of the Wannier function well describes the material dependence and pressure dependence of the on-site SOC in crystals. The material dependence is found to be substantially larger than the valence dependence for isolated atoms. Particularly, for Bi, the strength of the on-site SOC for the Bi $6p$ orbitals changes from 1.0 eV (${\mathrm{Cs}}_3\mathrm{Bi}$) to 2.5 eV (${\mathrm{BiF}}_3$).

The quadrupole insulator, a higher-order topological insulator, with on-site Hubbard interaction is numerically studied by large-scale projector quantum Monte Carlo simulations. The Green's function formalism is successfully used to characterize topological properties in interacting quadrupole insulators. We find that the topological quadrupole insulator is stable against weak interactions and turns into a trivial antiferromagnetic insulator by a continuous topological phase transition (TPT) for strong interactions. The critical exponents related to the TPT are estimated to be $\nu =0.67\left(4\right)$, $\beta =0.40\left(2\right)$, which are consistent with the three-dimensional Heisenberg universality class.

${\mathrm{TaIrTe}}_4$ is an example of a candidate Weyl type-II semimetal with a minimal possible number of Weyl nodes. Four nodes are reported to exist in a single plane in $k$ space. The existence of a conical dispersion linked to Weyl nodes has yet to be shown experimentally. Here, we use optical spectroscopy as a probe of the band structure on a low-energy scale. Studying optical conductivity allows us to probe intraband and interband transitions with zero momentum. In ${\mathrm{TaIrTe}}_4$, we observe a narrow Drude contribution and an interband conductivity that may be consistent with a tilted linear band dispersion up to 40 meV. The interband conductivity allows us to establish the effective parameters of the conical dispersion; effective velocity $v=1.1\times {10}^4$ m/s and tilt $\gamma =0.37$. The transport data, Seebeck and Hall coefficients, are qualitatively consistent with conical features in the band structure. Quantitative disagreement may be linked to the multiband nature of ${\mathrm{TaIrTe}}_4$.

We study electron transport in two-dimensional materials with parabolic and linear (graphene) dispersions of the carriers in the presence of surface acoustic waves and an external magnetic field using semiclassical Boltzmann equations approach. We observe an oscillatory behavior of both the longitudinal and Hall electric currents as functions of the surface acoustic wave frequency at a fixed magnetic field and as functions of the inverse magnetic field at a fixed frequency of the acoustic wave. We explain the former by the phenomenon of geometric resonances, while we relate the latter to the Weiss-like oscillations in the presence of the dynamic superlattice created by the acoustic wave. Thus we demonstrate the dual nature of the acoustomagnetoelectric effect in two-dimensional electron gas.

The dynamics of electrons, spins, and phonons induced by optical femtosecond pulses has been simulated for the polaronic crystal ${\mathrm{Pr}}_{1/2}{\mathrm{Ca}}_{1/2}{\mathrm{MnO}}_3$. The model used for the simulation has been derived from first-principles calculations. The simulations reproduce the experimentally observed melting of charge and orbital order with increasing fluence. The loss of charge order in the high-fluence regime induces a transition to a ferromagnetic metal. At low fluence, the dynamics is deterministic and coherent phonons are created by the repopulation of electronic orbitals, which are strongly coupled to the phonon degrees of freedom. In contrast to the low-fluence regime, the magnetic transitions occurring at higher fluence can be attributed to a quasithermal transition of a cold-plasma-like state with hot electrons and cold phonons and spins. The findings can be rationalized in a more complete picture of the electronic structure that goes beyond the simple ionic picture of charge order.

Investigating magnetic materials at realistic conditions with first-principles methods is a challenging task due to the interplay of vibrational and magnetic degrees of freedom. The most difficult contribution to include in simulations is represented by the longitudinal magnetic degrees of freedom [longitudinal spin fluctuation (LSF)] due to their inherent many-body nature; nonetheless, schemes that enable to take into account this effect on a semiclassical level have been proposed and employed in the investigation of magnetic systems. However, assessment of the effect of vibrations on LSF is lacking in the literature. For this reason, in this work we develop a supercell approach within the framework of constrained density functional theory to calculate self-consistently the size of local-environment-dependent magnetic moments in the paramagnetic, high-temperature state in the presence of lattice vibrations and for liquid Fe in different conditions. First, we consider the case of bcc Fe at the Curie temperature and ambient pressure. Then, we perform a similar analysis on bcc Fe at Earth's inner-core conditions, and we find that LSFs stabilize nonzero moments which affect atomic forces and the electronic density of states of the system. Finally, we employ the present scheme on liquid Fe at the melting point at ambient pressure and at Earth's outer-core conditions ($p\approx 200$ GPa, $T\approx 6000$ K). In both cases, we obtain local magnetic moments of sizes comparable to the solid-state counterparts.

We locally probe the magnetic fields generated by a spin-torque oscillator (STO) in a microbar of ferrimagnetic insulator yttrium-iron-garnet using the spin of a single nitrogen-vacancy (NV) center in diamond. The combined spectral resolution and sensitivity of the NV sensor allows us to resolve multiple spin-wave modes and characterize their damping. When damping is decreased sufficiently via spin injection, the modes auto-oscillate, as indicated by a strongly reduced linewidth, a diverging magnetic power spectral density, and synchronization of the STO frequency to an external microwave source. These results open the way for quantitative, nanoscale mapping of the microwave signals generated by STOs, as well as harnessing STOs as local probes of mesoscopic spin systems.

We provide a detailed account for a method to measure superconducting stiffness ${\rho }_s$, critical current density $j_c$, and coherence length $\xi$, in one apparatus, without subjecting the sample to magnetic field or attaching leads. The method is based on the London equation $\mathbf{j}=-{\rho }_s\mathbf{A}$, where $\mathbf{j}$ is the current density and $\mathbf{A}$ is the vector potential. Using a rotor free $\mathbf{A}$ and a measurement of $\mathbf{j}$ via the magnetic moment of a superconducting ring, we determine ${\rho }_s$. By increasing $\mathbf{A}$ until the London equation fails we determine $j_c$ and $\xi$. The method is sensitive to very small stiffness, which translates to penetration depth $\lambda \lesssim 1$ mm. It is also sensitive to low critical current density $j_c\sim {10}^3{\mathrm{A}\mathrm{mm}}^{-2}$ or long coherence length $\xi \sim 1\mu \mathrm{m}$. Naturally the method does not suffer from demagnetization factor complications, the presence of vortices, or out-of-equilibrium conditions. Therefore, the absolute values of the different parameters can be determined. We demonstrate the application of this method to ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ with $x=0.17$.

The discovery of quadrupole topology opens a new horizon in the study of topological phenomena. However, the existing experimental realizations of quadrupole topological insulators in symmorphic lattices with $\pi$ fluxes often break the protective mirror symmetry. Here, we present a theory for anomalous quadrupole topological insulators in nonsymmorphic crystals without flux using two-dimensional sonic crystals with $p4gm$ and $p2gg$ symmetry groups as concrete examples. We reveal that the anomalous quadrupole topology is protected by two orthogonal glide symmetries in square or rectangular lattices. The distinctive features of the anomalous quadrupole topological insulators include: (i) minimal four bands below the topological band gap, (ii) nondegenerate gapped Wannier bands and special Wannier sectors with gapped composite Wannier bands, and (iii) quantized Wannier band polarizations in these Wannier sectors. With no need for flux insertion, the protective glide symmetries are well preserved in the sonic-crystal realizations where higher-order topological transitions can be triggered by symmetry or geometry engineering.

Topological semimetals with band crossings (BCs) near the Fermi level have attracted intense research activity in the past several years. Among various BCs, those enforced by an hourglasslike connectivity pattern, which are located just at the vertex in the neck of an hourglass and thus called hourglass BCs (HBCs), show interesting topological properties and are intimately related with the space group symmetry. Through checking compatibility relations in the Brillouin zone, we list all possible HBCs for all 230 space groups by identifying positions of HBCs as well as the compatibility relations related with the HBCs. The HBCs can be compatible with conventional topological BCs such as Dirac and Weyl fermions and, based on our exhaustive list, the dimensionality and degeneracy of the HBCs can be quickly identified. It is also found that the HBCs can be classified into two categories: one contains essential HBCs which are guaranteed to exist, while the HBCs in the other category may be tuned to disappear. Our results can help in efficiently predicting hourglass semimetals combined with first-principles calculations as well as studying transitions among various topological crystalline phases.