The bilinear-biquadratic model is a promising candidate to study spin-1 systems and to design quantum simulators based on its underlying Hamiltonian. The variety of different phases contains among other valuable and exotic phases the Haldane phase. We study the Kibble-Zurek physics of linear quenches into the Haldane phase. We outline ideal quench protocols to minimize defects in the final state while exploiting different linear quench protocols via the uniaxial or interaction term. Furthermore, we look at the fate of the string order when quenching from a topologically nontrivial phase to a trivial phase. Our studies show this depends significantly on the path chosen for quenching; for example, we discover quenches from Néel to Haldane phase which reach a string order greater than their ground state counterparts for the initial or final state at intermediate quench times.

Topological states with quadratic dispersion and multiple-fold band degeneracy have not only fundamentally updated our knowledge of the phases of matter but also become a major cutting-edge research direction in condensed matter physics. Note that the sixfold band degeneracy corresponds to the maximum degeneracy in phononic systems. Remarkably, in this work, based on first-principles calculations, we proposed an authentic material, ${\mathrm{Ta}}_3\mathrm{Sn}$, which hosts phononic nodal points with both quadratic dispersion and maximum band degeneracy, i.e., quadratic contact triple point, quadratic contact Dirac point and sixfold-degenerate point. Furthermore, the corresponding symmetry analysis with the help of the $k·p$ model further deepens the understanding of the relative physics. Evident arc-shaped surface states, originating from the projected phononic nodal points, can strongly benefit the experimental detection. It is hoped that the rich types of phonon points with quadratic dispersion and multiple-fold band degeneracy as well as the surface states can be confirmed in experiments soon.

In this work, we analyze the nonsymmorphic symmetry-group structures for a variety of generalized Kitaev spin chains and ladders with bond alternations, including Kitaev-Gamma chain, Kitaev-Heisenberg-Gamma chain, beyond-nearest-neighbor interactions, and two-leg spin ladders. The symmetry analysis is applied to determine the symmetry-breaking patterns of several magnetically ordered phases in the bond-alternating Kitaev-Gamma spin chains, as well as the dimerization order parameters for spontaneous dimerizations. Our work is useful in understanding the magnetic phases in related models and may provide guidance for the symmetry classifications of mean field solutions in further investigations.

Damping and spin transport in spintronic multilayered systems continues to be a topic of active research. The enhancement of damping in ferromagnet (FM)/spacer layer (SL)/heavy-metal (HM) thin-film systems was studied for ${\mathrm{Co}}_{25}{\mathrm{Fe}}_{75}/\mathrm{SL}/\mathrm{Pt}$ with a nonmagnetic (NM) SL of either Au or Cu with variable thickness, in order to understand the correlation with proximity-induced magnetism (PIM) in the HM. Structural, PIM and magnetic damping measurements were undertaken on the same samples. Specifically, secondary ion mass spectroscopy, element specific x-ray magnetic reflectivity and x-ray magnetic circular dichroism at the Pt and Au $L_3$ edges, and ferromagnetic resonance methods were used. With increasing thickness of a Cu or Au SL directly between the FM and the Pt layer, the Pt PIM and the damping both fall rapidly, with a relationship between damping and PIM that depends on the SL material. The PIM observed in the Au layer showed a complex dependence on the layer thickness, suggesting some hybridization with the Pt. The role of the number and location of interfaces on the damping was demonstrated with the addition of a SL within the Pt layer, which showed that the specific details of the NM/HM interface also affects the damping. The insertion of a Cu SL within the Pt showed a measurable increase in the overall enhancement of the damping while the insertion of a Au SL into Pt had almost no effect on the damping. Together these results demonstrate the role of both PIM and of additional interfaces in the enhancement of damping in FM/HM systems, which is not fully accounted for by existing theory.

The anisotropic spin dynamics in wires based on a [001]-oriented semiconductor quantum well were investigated to determine the effect of applying an in-plane magnetic field both parallel to and perpendicular to the spin-orbit magnetic field, and the interaction between them. In one-dimensional spin motion where the wire width is less than the spin-precession length, it is known that the global spin precession is essentially determined by the spin-orbit induced precession along the wire direction. In this study, our objective is to investigate the nature of anisotropic spin dynamics in such narrow semiconductor wires along various crystal orientations. We proposed an analytic expression for the anisotropic spin-relaxation rates and the Larmor-precession frequencies for the arbitrary magnetic field orientation based on a theoretical understanding of the spin dynamics in the narrow wire structure. This expression describes the interaction between the spin-orbit field and all orientations of the in-plane magnetic field. We experimentally investigated the spin dynamics for lithographically defined 800-nm-width wires oriented along the $\left[\overline{1}10\right]$, [100], and [110] crystal orientations using a [001] GaAs/AlGaAs quantum well. Time-resolved Kerr rotation microscopy measurements indicated that the spin-relaxation time was the longest for the in-plane magnetic field perpendicular to the spin-orbit field, whereas the parallel configuration was found to be the shortest among all the directions. The precession frequency was found to have the opposite symmetry. These relations are well explained by the theoretical considerations developed in this work. Because the Rashba and Dresselhaus spin-orbit fields are mutually orthogonal in the [100] crystal orientation, it is possible to evaluate both spin-orbit coefficients from the precession anisotropy. These findings suggest that it is possible to control the spin state in narrow wires approaching the one-dimensional state and evaluate the spin-orbit coefficient. This has the potential to provide a greater understanding of quantum and topological information in semiconductor one-dimensional wires.

We inspect the signatures of dynamical quantum phase transitions driven by quantum quenches acting on a correlated quantum dot embedded between superconducting and metallic reservoirs. Under stationary conditions, the proximity-induced electron pairing, competing with strong Coulomb repulsion, enforces the quantum dot to be either in the singly occupied or BCS-type ground state, depending on its energy level and coupling to the superconducting lead. By means of the time-dependent numerical renormalization group approach, we study the system's time evolution upon traversing the phase boundary between these two states, examining the Loschmidt echo and revealing nonanalytic features in the low-energy return rate, which signal dynamical quantum phase transitions. We also show that these phase transitions are accompanied by the corresponding local extrema in the pairing correlation function and dot's occupation. Since the proposed quench protocols can be realized in a controllable manner, the detection of this dynamical singlet-doublet phase transition should be feasible by performing tunneling spectroscopy measurements.

We study the photoinduced dynamics of the excitonic insulator in the two-orbital Hubbard model on the Penrose tiling by means of the time-dependent real-space mean-field approximation. We show that, with a single-cycle electric-field pulse, the bulk (spatially averaged) excitonic order parameter decreases in the Bardeen-Cooper-Schrieffer (BCS) regime, while it increases in the Bose-Einstein condensate (BEC) regime. This behavior is in common with the excitonic insulator in the square lattice reported previously. To explore the dynamics peculiar to the Penrose tiling, we examine the coordination number dependence of observables and analyze the perpendicular space. In the BEC regime, characteristic oscillations of the electron number at each site are induced by the pulse, which are not observed in normal crystals with single coordination number. On the other hand, the dynamics in the BCS regime is characterized by drastic change in the spatial pattern of the excitonic order parameter. Our results imply that potentially interesting nonequilibrium physics is caused by rich local structural patterns involved in quasicrystals.

Experimental and theoretical studies of the magnetoelectric properties of a series of Fe langasite multiferroics (${\mathrm{Ba}}_3{\mathrm{NbFe}}_3{\mathrm{Si}}_2{\mathrm{O}}_{14}, {\mathrm{Ba}}_3{\mathrm{TaFe}}_3{\mathrm{Si}}_2{\mathrm{O}}_{14}$, and ${\mathrm{Sr}}_3{\mathrm{TaFe}}_3{\mathrm{Si}}_2{\mathrm{O}}_{14}$) with planar triangular spiral magnetic structure and double chiral magnetic order have been carried out. Magnetic field induced electric polarization is observed to emerge in the basal $a{b}^{*}$ plane of the trigonal crystal, depending on both the magnitude (up to 60 T) and orientation of the magnetic field. Remarkably, the induced polarization is very sensitive to the projection of the field onto the $c$ axis, with a sharp increase in polarization found for small deviations of the field from the basal plane and the sign of polarization determined by the direction of the field deviation. At high magnetic fields, the electric polarization behavior changes qualitatively and strongly depends on the magnetic field orientation. A detailed group theoretical analysis of the magnetic and magnetoelectric properties of Fe langasites is presented, and a relationship between the polarization and magnetic order parameters in an external magnetic field is established. We show that, in a magnetic field, the spiral magnetic structure is rotated and canted with respect to the original structure under zero field. The competition between these two processes, rotation and canting, strongly depends on the magnetic field orientation, and determines the polarization behavior. We propose a simplified description of the Fe langasites’ triangular spiral magnetic structure at low temperatures and with saturated moments, characterized by the spiral plane orientation and the field-induced magnetization only. We establish that, at weak fields, the appearance of polarization occurs mainly due to the reorientation of the magnetic spiral (analogous to a spin-flop transition) and could be explained by the inverse Dzyaloshinskii-Moriya interaction. At high fields (above 8 T), the polarization change occurs via canting of the magnetic spiral, owing to Fe-Fe exchange and single-ion contributions.

We set forth the structural and magnetic properties of the frustrated spin-$5/2$ triangle lattice antiferromagnet ${\mathrm{Na}}_3\mathrm{Fe}{\left({\mathrm{PO}}_4\right)}_2$ examined via x-ray diffraction, magnetization, heat capacity, and neutron diffraction measurements on the polycrystalline sample. No structural distortion was detected from the temperature-dependent x-ray diffraction down to 12.5 K, except a systematic lattice contraction. The magnetic susceptibility at high temperatures agrees well with the high-temperature series expansion for a spin-$5/2$ isotropic triangular lattice antiferromagnet with an average exchange coupling of $J/k_{\mathrm{B}}\simeq 1.8$ K rather than a one-dimensional spin-$5/2$ chain model. This value of the exchange coupling is consistently reproduced by the saturation field of the pulse field magnetization data. It undergoes a magnetic long-range order at $T_{\mathrm{N}}\simeq 10.4$ K. Neutron diffraction experiments elucidate a collinear antiferromagnetic ordering below $T_{\mathrm{N}}$ with the propagation vector $k=(1,0,0)$. An intermediate value of frustration ratio ($f\simeq 3.6$) reflects moderate frustration in the compound which is corroborated by a reduced ordered magnetic moment of $\sim 1.52{\mu }_{\mathrm{B}}$ at 1.6 K, compared to its classical value ($5{\mu }_{\mathrm{B}}$). Magnetic isotherms exhibit a change of slope envisaging a field induced spin-flop transition at $H_{\mathrm{SF}}\simeq 3.2$ T. The magnetic field vs temperature phase diagram clearly unfold three distinct phase regimes, reminiscent of a frustrated magnet with in-plane ($XY$-type) anisotropy.

The research on emergent particles in condensed matters has been attracting tremendous interest, and recently it is extended to magnetic systems. Here, we study the emergent particles stabilized by the symmetries of type-IV magnetic space groups (MSGs) based on our classification of emergent particles in 230 gray space groups [Yu et al., Sci. Bull. 67, 375 (2022)]. Type-IV MSGs feature a special time reversal symmetry $\left\{\mathcal{T}\right|{\mathit{t}}_0\}$, namely, the time reversal operation followed by a half lattice translation, which significantly alters the symmetry conditions for stabilizing the band degeneracies. In this work, based on symmetry analysis and modeling, we present a complete classification of emergent particles in type-IV MSGs by studying all possible (spinless and spinful, essential and accidental) particles in each of the 517 type-IV MSGs. Particularly, the detailed correspondence between the emergent particles and the type-IV MSGs that can host them are given in easily accessed interactive tables, where the basic information of the emergent particles, including the symmetry conditions, the effective Hamiltonian, the band dispersion, and the topological characters, can be found. According to the established encyclopedia, we find that several emergent particles that are previously believed to exist only in spinless systems will occur in spinful systems here, and vice versa, due to the $\left\{\mathcal{T}\right|{\mathit{t}}_0\}$ symmetry. Our work not only deepens the understanding of the symmetry conditions for realizing emergent particles but also provides specific guidance for searching and designing materials with target particles.

We study the lattice dynamics effects on the phase stability and magnetocrystalline anisotropy (MCA) energy of ${\mathrm{CaCu}}_5$-type ${\mathrm{YCo}}_5$ at finite temperatures using first-principles calculations based on density functional theory (DFT). Harmonic lattice dynamics (HLD) calculations indicate that ${\mathrm{YCo}}_5$ with 56 full valance electrons is dynamically unstable and this instability can be cured by reducing the number of electrons ($N_e$). Crystal orbital Hamilton population analysis reveals that the observed phonon instability originates from the large population of antibonding states near the Fermi level, which is dominated by the Co atoms in the honeycomb layer. The antibonding state depopulates with decreasing $N_e$, resulting in stable phonons for hole-doped ${\mathrm{YCo}}_5$ with $N_e\le 55$. We then evaluate the temperature-dependent MCA energy using both HLD and ab initio molecular dynamics (AIMD) methods. For the pristine ${\mathrm{YCo}}_5$, we observe a very weak temperature decay of the MCA energy, indicating a small effect of lattice dynamics. Also, the MCA energies evaluated with AIMD at all target temperatures are larger than that of the static hexagonal lattice at 0 K, which is mainly attributed to the structural distortion driven by soft phonon modes. In the hole-doped ${\mathrm{YCo}}_5$, where the distortion is suppressed, a considerable temperature decay in MCA energy is obtained both in HLD and AIMD methods, showing that lattice dynamics effects on MCA energy are non-negligible.

We address an issue of how to accurately include the self-energy effect of the screened electron-electron Coulomb interaction in phonon-mediated superconductors from first principles. In the Eliashberg theory for superconductors, self-energy is usually decomposed using the $2\times 2$ Pauli matrices in the electron-hole space. We examine how the diagonal (${\sigma }_0$ and ${\sigma }_3$) components resulting in the quasiparticle correction to the normal state, $Z$ and $\chi$ terms, behave in the homogeneous electron gas in order to establish a norm of treating those components in real metallic systems. Within the $G_0{W}_0$ approximation, we point out that these components are nonanalytic near the Fermi surface but their directional derivatives and resulting corrections to the quasiparticle velocity are, nevertheless, well defined. Combined calculations using the $G_0{W}_0$ approximation and Eliashberg equations show us that the effective mass and pairing strength strikingly depend on both $Z$ and $\chi$ in different manners. The calculations without the numerically demanding $\chi$ term is thus shown to be incapable of describing the homogeneous electron gas limit. This result poses a challenge to accurate first-principles Eliashberg theory.

We study the full counting statistics (FCS) and symmetry-resolved entanglement entropies of integer and fractional quantum Hall states. For the filled lowest Landau level of spin-polarized electrons on an infinite cylinder, we compute exactly the charged moments associated with a cut orthogonal to the cylinder's axis. This yields the behavior of FCS and entropies in the limit of large perimeters: in a suitable range of fluctuations, FCS is Gaussian and entanglement spreads evenly among different charge sectors. Subleading charge-dependent corrections to equipartition are also derived. We then extend the analysis to Laughlin wave functions, where entanglement spectroscopy is carried out assuming the Li-Haldane conjecture. The results confirm equipartition up to small charge-dependent terms, and are then matched with numerical computations based on exact matrix product states.

High-pressure optical-absorption measurements performed on polycrystalline $\mathrm{Co}{\left(\mathrm{I}{\mathrm{O}}_3\right)}_2$ samples were used to characterize the influence of pressure on the electronic $d–d$ transitions associated with ${\mathrm{Co}}^{2+}$ and the fundamental band gap of $\mathrm{Co}{\left(\mathrm{I}{\mathrm{O}}_3\right)}_2$. The results shed light on the electron-lattice coupling and show that $\mathrm{Co}{\left(\mathrm{I}{\mathrm{O}}_3\right)}_2$ exhibits an unusual behavior because the compression of Co–O bond distances is not coupled to pressure-induced changes induced in the unit-cell volume. Experimental results on the internal $d–d$ transitions of ${\mathrm{Co}}^{2+}$ have been explained based on changes in the constituent $\mathrm{Co}{\mathrm{O}}_6$ octahedral units using the semiempirical Tanabe-Sugano diagram. Our findings support that the high-spin ground state $\left({}^{4}T_1\right)$ is very stable in $\mathrm{Co}{\left(\mathrm{I}{\mathrm{O}}_3\right)}_2$. We have also determined the band-gap energy of $\mathrm{Co}{\left(\mathrm{I}{\mathrm{O}}_3\right)}_2$ and its pressure dependence which is highly nonlinear. According to density-functional theory band-structure calculations, this nonlinearity occurs because the bottom of the conduction band is dominated by I-5p orbitals and the top of the valence band by Co-3d and O-2p orbitals, and because the Co–O and I–O bond lengths exhibit different pressure dependences.

The thermodynamic uncertainty relation, quantifying a trade-off among average current, the associated fluctuation (precision), and entropy production (cost), has been formulated at nonequilibrium steady state in various stochastic systems. Herein, we study the thermodynamic uncertainty relation in generic thermoelectric heat engines under periodic control protocols, by uncovering the underlying Berry-phase-like contribution. We show that our thermodynamic uncertainty relation breaks the seminal steady-state results, originating from the nonvanishing geometric effect. Furthermore, by deriving the consequent trade-off relation binding efficiency, power, and constancy, we prove that the periodically driven thermoelectric heat engines can generally outperform the steady-state analogies. The general bounds are illustrated by an analytically solvable two-terminal single quantum dot heat engine under the periodic modulation. Our work provides a geometric framework in bounding and optimizing a wide range of periodically driven thermoelectric thermal machines.

We consider a bosonic two-legged ladder whose two-band energy spectrum can be tuned in the presence of a uniform gauge field, to four distinct scenarios: degenerate or nondegenerate ground states with gapped or gapless energy bands. We couple the ladder to two baths at different temperatures and chemical potentials and analyze the efficiency and power generated in the linear as well as nonlinear response regime. Our results, obtained with the Green's function method, show that the maximum performance efficiency and generated power are strongly dependent on the type of the underlying energy spectrum. We also show that the ideal scenario for efficient energy conversion, as well as power generation, corresponds to the case in which the spectrum has a gap between the bands, and the ground state is degenerate.

We discuss the two-channel Kondo lattice model where a single localized spin per unit cell is coupled to two different conduction electron orbitals per unit cell. The calculation is done using the bond fermion formalism. For a Hamiltonian which is symmetric under exchange of the conduction channels we find a spontaneous breaking of this symmetry, i.e., the Kondo singlets are formed almost exclusively between the localized spin and only one of the two conduction orbitals. In addition to this channel-ferromagnetic phase we also find a channel-antiferromagnetic phase where the preferred conduction electron orbital alternates between sublattices. The parameter which determines the transition between these phases is the interchannel hybridization.

We show that classical Heisenberg antiferromagnets on the breathing kagome lattice can be a platform to realize a zero-field topological order of the scalar spin chirality which can be viewed as a miniature skyrmion crystal (SkX) of discrete form with a small number of spins in its magnetic unit cell. In the model, a third nearest-neighbor (NN) antiferromagnetic interaction along the bond direction $J_3$ and the breathing bond alternation characterized by the ratio of the NN interaction for large triangles to that for small ones, $J_1^{\prime }/J_1$, are essential. It is found by means of Monte Carlo simulations that a commensurate triple-$\mathbf{Q}$ state appearing for relatively strong $J_3$ at zero field is the noncoplanar state with the SkX structure in the breathing case of $J_1^{\prime }/J_1\ne 1$, while in the uniform case of $J_1^{\prime }/J_1=1$, it is a collinear state favored by thermal fluctuations. The origin of this chiral order and experimental implications of our result are also discussed.

The superconducting transition temperature ($T_c$) of single-layer graphene coupled to an indium oxide (InO) film, a low carrier-density superconductor, is found to increase with decreasing carrier density and is largest close to the average charge neutrality point in graphene. Such an effect is very surprising in conventional BCS superconductors. We study this phenomenon both experimentally and theoretically. Our analysis suggests that the InO film induces random electron and hole doped puddles in the graphene. The Josephson effect across these regions of opposite polarity enhances the Josephson coupling between the superconducting clusters in InO, along with the overall $T_c$ of the bilayer heterostructure. This enhancement is most effective when the chemical potential of the system is tuned between the charge neutrality points of the electron and hole doped regions.

${\mathrm{Mn}}_3{\mathrm{O}}_4$ represents a model system for probing geometrically frustrated magnetism, and studying the magnetic behavior of the material under high pressure could yield new insights into the magnetostructural coupling and structurally driven magnetic ordering transitions that are otherwise not observable at ambient pressure. We report here a systematic study of the crystal and magnetic structures of ${\mathrm{Mn}}_3{\mathrm{O}}_4$ at high pressure up to 37 and 20 GPa using x-ray and neutron powder diffraction techniques, respectively. We find that upon compression, the crystal structure transforms from the initial tetragonal hausmannite phase of $I{4}_1/amd$ symmetry into the orthorhombic ${\mathrm{CaMn}}_2{\mathrm{O}}_4$-type ($Pbcm$ symmetry) phase via the intermediate orthorhombic ${\mathrm{CaTi}}_2{\mathrm{O}}_4$-type ($Bbmm$ symmetry) phase. In the tetragonal phase, the application of pressure, $P>2$ GPa, leads to the suppression of low-temperature incommensurate and commensurate antiferromagnetic (AFM) orders with a propagation vector $k=\left(0,\sim 0.5,0\right)$, and the expansion of the Yafet-Kittel-type ferrimagnetic phase, becoming the only ground state. As a result, the magnetic ordering temperature $T_{\mathrm{N}}$ increases rapidly, from ∼43 K at $P=0\mathrm{GPa}$ to ∼100 K at $P=10\mathrm{GPa}$. In the orthorhombic ${\mathrm{CaMn}}_2{\mathrm{O}}_4$-type phase, the AFM ordering on the sublattice of ${\mathrm{Mn}}^{3+}$ spins with a propagation vector $k=\left(1/2,0,0\right)$ occurs below $T_{\mathrm{N}}=275\mathrm{K}$ for $P=20\mathrm{GPa}$. This value of $T_{\mathrm{N}}$ is about six times greater than that obtained at ambient pressure for the tetragonal phase, indicating a strong pressure enhancement of the magnetic ordering temperature in ${\mathrm{Mn}}_3{\mathrm{O}}_4$. These experimental observations have been complemented by density functional theory calculations, which shed light on the underlying mechanisms of the structurally coupled magnetic phenomena in geometrically frustrated magnetic systems under high pressure.