The magnetic element Mn is generally supposed to be harmful to superconductivity. However, the superconducting transition temperature of ${\mathrm{Ti}}_{1-x}{\mathrm{Mn}}_x$ can be enhanced from 0.4 K (elemental titanium) to about 2.1–2.8 K by doping Mn to the system. Here, we carry out systematic studies on the superconductivity and normal state properties of ${\mathrm{Ti}}_{1-x}{\mathrm{Mn}}_x$ alloys. With the increase of Mn doping in ${\mathrm{Ti}}_{1-x}{\mathrm{Mn}}_x$, we find that the system transforms from hexagonal $\alpha$ phase ($P{6}_3/mmc$) to cubic $\beta$ phase ($Im\overline{3}m$), and the superconducting property changes from filamentary to bulk superconductivity. Thus we argue that the superconductivity in the $\alpha$ phase with dilute Mn doping is not intrinsic; it may be induced by the residual $\beta$ phase embedded in the $\alpha$ phase. Moreover, in ${\mathrm{Ti}}_{0.88}{\mathrm{Mn}}_{0.12}$, we find a positive Hall coefficient with a significant reduction of charge-carrier density, which is in contrast to pure Ti where the Hall coefficient is negative. The specific-heat data of ${\mathrm{Ti}}_{1-x}{\mathrm{Mn}}_x$ with $x=0.12$ can be described by the model of $s$-wave symmetry with a fully opened gap of 0.37 meV. Transport measurements show that it is a type-II superconductor with a relatively large value of Wilson ratio ($R_{\text{W}}=3.1$) in the normal state, which suggests a moderate electron correlation in ${\mathrm{Ti}}_{1-x}{\mathrm{Mn}}_x$ with the $\beta$ phase. The positive correlation between magnetic susceptibility and temperature, and the sudden drop of effective magnetic moment in ${\mathrm{Ti}}_{1-x}{\mathrm{Mn}}_x$ with $x=0.12$ may suggest that the material shows a signature of the existence of spin fluctuations.

Anisotropic magnetic interactions become the origins of intriguing magnetic structures, such as helical and skyrmion structures by the Dzyaloshinskii-Moriya interaction. In general, possible anisotropic exchange interactions are restricted by crystal symmetry. Meanwhile, by lowering the crystal symmetry with light, additional anisotropic magnetic interactions are expected according to its polarization and frequency. In this study, we clarify a relation between anisotropic magnetic interactions and symmetry lowering in insulating magnets irradiated by light. Based on the Floquet formalism, we find that a variety of anisotropic two-spin and three-spin interactions are induced via spin-dependent electric polarizations activated by light irrespective of the presence/absence of the space inversion symmetry; we systematically classify them in the hexagonal point groups, tetragonal point groups, and their subgroups. Our symmetry analyses show that the light-induced two-spin (three-spin) interactions are due to the reduction of the point group to a chiral point group (black and white magnetic point group). We also demonstrate the effect of the light-induced magnetic interactions on the magnetic structures in a triangular unit. Our results will be a symmetry-based reference for the Floquet engineering of magnetic structures.

The $3d^7{\mathrm{Co}}^{2+}$-based insulating magnet ${\mathrm{Na}}_2{\mathrm{Co}}_2{\mathrm{TeO}}_6$ has recently been reported to have strong Kitaev interactions on a honeycomb lattice and is thus being considered as a Kitaev quantum spin liquid candidate. However, due to the existence of other types of interactions, a spontaneous long-range magnetic order occurs. This order is suppressed by applied magnetic fields leading to a succession of phases and ultimately saturation of the magnetic moments. The precise phase diagram, the nature of the phases, and the possibility that one of the field-induced phases is a Kitaev quantum spin liquid phase are still a matter of debate. Here we measured an extensive set of physical properties to build the complete temperature-field phase diagrams to magnetic saturation at 10 T for magnetic fields along the $a$ and $a^{*}$ axes, and a partial phase diagram up to 60 T along $c$. We probe the phases using magnetization, specific heat, magnetocaloric effect, magnetostriction, dielectric constant, and electric polarization, which is a symmetry-sensitive probe. With these measurements, we identify all the previously incomplete phase boundaries and find additional high-field phase boundaries. We find strong magnetoelectric coupling in the dielectric constant and moderate magnetostrictive coupling at several phase boundaries. Furthermore, we detect the symmetry of the magnetic order using electrical polarization measurements under magnetic fields. Based on our analysis, the absence of electric polarization under zero or finite magnetic field in any of the phases or after any combination of magnetic/electric field cooling suggests that a zigzag spin structure is more likely than a triple-Q spin structure at zero field. Finally, we investigate the hysteresis and first- or second-order nature of each phase transition and its entropy changes. With this information, we establish a map of the magnetic phases of this compound and its magnetic, thermodynamic, and magnetoelectric properties, and discuss where spin liquid or other phases may be sought in future studies.

In resonant inelastic x-ray scattering (RIXS) spectra of ${\mathrm{K}}_2{\mathrm{IrCl}}_6$, the peak for the $j=3/2$ multiplet states shows a splitting that resembles a noncubic crystal-field effect, although the compound is cubic down to 0.3 K. Here we theoretically describe the RIXS spectra concomitantly treating the spin-orbit and vibronic interactions. We found that the dynamic Jahn-Teller effect in the $j=3/2$ multiplet states gives rise to the splitting of the RIXS spectra and the broadening of the spectra in raising the temperature. The validity of the interaction parameters for the simulations is supported by our ab initio calculations. Our results suggest that in cubic iridium compounds, the dynamic Jahn-Teller effect induces the splitting of RIXS spectra without lowering the symmetry.

In recent years, $d^6$ transition-metal corundum oxides $\alpha \text{−}{M}_2{\mathrm{O}}_3$ ($M=\mathrm{Co}$, Rh, Ir) have garnered significant interest due to their notable $p$-type conductivity; however, their electronic properties remain controversial. In this study, we employ first-principles calculations within different functional levels to systematically investigate the geometry and electronic structure of $\alpha \text{−}{M}_2{\mathrm{O}}_3$. Our findings reveal that these oxides have a relatively small difference between the indirect and direct band gap, contradicting previous studies. Additionally, we demonstrate that the band gaps of these oxides are closely associated with the ligand field splitting of the cation M d orbitals and the experimentally observed nonmonotonic trend of the direct band-gap variation can be explained by the orbital-dependent Coulomb and exchange interactions. This study enhances our understanding of how the involvement of $d$ orbitals impacts the band gap of transition-metal oxides.

Topological states in antiferromagnetic (AFM) systems have gained much attention recently. However, general proposals for the realization of a two-dimensional (2D) AFM quantum spin Hall (QSH) insulator are still absent. In this paper, we present a general proposal for 2D AFM QSH insulators by stacking 2D half quantum anomalous Hall insulators in a way that maintains the symmetry of a combination of inversion symmetry and time-reversal symmetry. Depending on the number of stack layers, the obtained AFM QSH insulators can have multiple pairs of dissipationless spin transport channels, revealing the nontrivial implication of high (even) spin Chern numbers ($C_s$). Using two concrete material examples, ${\text{Fe}}_2\text{Br}\text{Mg}\text{P}$ monolayer and TiTe bilayer, we show that both intercalation and van der Waals stacks can be used to realize the proposed AFM QSH insulators. The robustness of the gapless edge states and the topological invariants (high $C_s$) of our AFM QSH insulators have been tested and shown to be robust against diluted magnetic impurities and weak magnetic field. The spin-chirality-spatial locking phenomenon in the edge states and their susceptibility to $z$-direction electric field modulation promote these systems as promising candidates for innovative spintronics applications.

State-of-the-art defect engineering techniques have paved the way to realize unique quantum phases out of pristine materials. Here, through density-functional calculations and model studies, we show that the chain-doped monolayer transition metal dichalcogenides, where $M$ atoms on a single zigzag chain are replaced by a higher-valence transition-metal element $M^{\prime }$ ($M{X}_2/M^{\prime }$), exhibit one-dimensional (1D) bands. These 1D bands, occurring in the fundamental gap of the pristine material, are dispersive along the doped chain but are strongly confined along the lateral direction. This confinement occurs as the bare potential of the dopant chain formed by the positively charged $M^{\prime }$ ions resembles the potential well of a uniformly charged wire. These bands could show unique 1D physics, including another type of Tomonaga-Luttinger liquid behavior, multiorbital Mott insulator physics, and an unusual optical absorption due to the simultaneous presence of the spin-orbit coupling, strong correlation, multiple orbitals, Rashba spin splitting, and broken symmetry. We find the broadening of the half-filled 1D bands with correlation. It is surprising since correlation reduces the effective hopping interactions and in turn reduces the bandwidth. This is interpreted to be due to multiple orbitals forming the single Hubbard band at different points of the Brillouin zone. Furthermore, due to the presence of an intrinsic electric field along the lateral direction, the 1D bands are Rashba spin-split and provide a mechanism for tuning the valley-dependent optical transitions.

The anomalous Hall effect, typically observed in ferromagnetic metals, can also manifest in certain noncollinear antiferromagnetic materials. However, studying the cubic kagome antiferromagnet ${\mathrm{Mn}}_{3}X$ ($X=\mathrm{Ir}$, Pt, Rh), which was theoretically predicted to exhibit the anomalous Hall effect, has proven challenging due to the extremely small measured values. In this study, we validate these theoretical predictions by successfully measuring a remarkable anomalous Hall conductivity in the cubic kagome antiferromagnet ${\mathrm{Mn}}_3\mathrm{Sb}$, reaching up to $308{\mathrm{\Omega }}^{-1}\mathrm{c}{\mathrm{m}}^{-1}$. Combining these results with those obtained from the hexagonal kagome antiferromagnet ${\mathrm{Mn}}_{3}Z$ ($Z=\mathrm{Sn}$, Ge), our findings contribute to a comprehensive understanding of the anomalous Hall effect in noncollinear antiferromagnetic materials, leading to further advancements in the research on the functions and control of cluster multipoles.

We develop a theory of heat transfer induced by thermal charge fluctuations in two-dimensional electron double layers. We consider pristine systems comprised of identical layers and focus on the regime of sufficiently high temperatures and interlayer distances $d$, where the relevant charge fluctuations may be described using the hydrodynamic approach. In this limit heat transfer is dominated by the plasmon resonances. For systems with Galilean-invariant electron dispersion the interlayer thermal conductance $\varkappa$ is proportional to the kinematic viscosity of the electron liquid and decreases as $1/d^4$. In the absence of Galilean invariance $\varkappa \propto \sigma /d^3$, where $\sigma$ is the intrinsic conductivity of the liquid. This strong enhancement can be traced to a drastically different broadening of plasmon resonances in systems with and without Galilean invariance.

Degenerate states in condensed matter are frequently the cause of unwanted fluctuations, which prevent the formation of ordered phases and reduce their functionalities. Removing these degeneracies has been a common theme in materials design, pursued, for example, by strain engineering at interfaces. Here we explore a nonequilibrium approach to lift degeneracies in solids. We show that coherent driving of the crystal lattice in bi- and multilayer graphene boosts the coupling between two doubly degenerate modes of $E_{1u}$ and $E_{2g}$ symmetry, which are virtually uncoupled at equilibrium. New vibronic states result from anharmonic driving of the $E_{1u}$ mode to large amplitudes, boosting its coupling to the $E_{2g}$ mode. The vibrational structure of the driven state is probed with time-resolved Raman scattering, which reveals laser-field-dependent mode splitting and enhanced lifetimes. We expect this phenomenon to be generally observable in many materials systems, affecting the nonequilibrium emergent phases in matter.

We theoretically study the Aharonov-Bohm effect manifestation in the interaction of a moving nonrelativistic electron and a tubular electron beam with electromagnetic eigenmodes in a semiconductor nanotube with dielectric filling placed in a coaxial dc magnetic field. The calculations are performed taking into account the effect of delay of electromagnetic waves and collisions of electrons in a nanotube. First, we have shown that collisions of electrons lead to a significant transformation of the eigenmode spectrum of the structure under study in comparison with the collisionless case. In particular, dissipative (leaky) modes with phase velocities greater than the speed of light in vacuum appear in the spectrum. It has been established that the number of branches with negative (anomalous) dispersion in the eigenmode spectrum oscillates when changing the number of magnetic flux quanta in a nanotube with a period equal to one magnetic flux quantum. Second, an analysis of the expressions for the power of energy loss of a single moving electron and the rate of increase in the kinetic instability of an electron tubular beam due to their interaction with the studied eigenmodes showed that these quantities also oscillate when changing the number of magnetic flux quanta. These oscillations are the result of the Aharonov-Bohm effect.

Using symmetry analysis and a semiclassical Boltzmann equation, we theoretically explore the planar Hall effect (PHE) in three-dimensional materials. We demonstrate that PHE is a general phenomenon that can occur in various systems regardless of band topology. Both the Lorentz force and Berry curvature effects can induce significant PHE, and the leading contributions of both effects linearly depend on the electric and magnetic fields. The Lorentz force and Berry curvature PHE coefficient possess only antisymmetric and symmetric parts, respectively. Both contributions respect the same crystalline symmetry constraints but differ under time-reversal symmetry. Remarkably, for topological Weyl semimetals, the Berry curvature PHE coefficient is a constant that does not depend on the Fermi energy, while the Lorentz force contribution linearly increases with the Fermi energy, resulting from the linear dispersion of the Weyl point. Furthermore, we find that the PHE in topological nodal line semimetals is mainly induced by the Lorentz force, as the Berry curvature in these systems vanishes near the nodal line. Our study not only highlights the significance of the Lorentz force in PHE, but also reveals its unique characteristics, which will be beneficial for determining the Lorentz force contribution experimentally.

Quantum anomalous Hall states, or Chern insulators (CIs), have been investigated in various lattice models by introducing staggered magnetic fluxes. Considering long-distance hopping terms, some topological flat band (TFB) models have been proposed based on CI models. In this work, we construct a ruby lattice with staggered fluxes threading hexagons and find that staggered fluxes give rise to higher-order topological insulators (HOTIs) and TFBs. At $1/3$ filling, this model supports the phase transition from a CI with Chern number 2 to a HOTI phase by tuning the staggered fluxes. This HOTI can be identified based on the gapped edge state, robust corner state, and quantized topological invariants. Simultaneously, we find the best TFB with a flatness ratio of about 18 at $1/6$ filling. Furthermore, we explore fractional Chern insulator states when hard-core bosons and interacting spinless fermions fill into these TFB models.

For decades, it has remained an open question whether two dopants in the $t\text{−}J$ model bind in the strongly correlated regime of small spin couplings versus hopping, $J\ll t$. Here, we investigate this problem in Bethe lattice structures with Ising coupling $J_z$, and mainly focus on the case of a coordination number equal to 4. The special geometry circumvents subtle effects in regular lattices, but importantly still contains the nontrivial dependency on the rotational symmetry and particle statistics. It furthermore allows us to reach numerical convergence, and we conclusively answer whether binding occurs or not. In particular, we find that the rotationally symmetric $s$ waves unbind below $J_z\simeq 0.3t$, which we unveil is tied to Pauli blocking of symmetrical hole configurations. This is further substantiated by the fact that holes in a bosonic spin environment shows strong, superlinear binding at low $J_z/t$. Additionally, higher rotational fermionic $p$ and $d$ waves partially overcome the blocking, are perfectly degenerate, and bind for all $J_z/t$. In the strongly correlated regime of $J_z\ll t$, this binding occurs sublinearly with scaling $\sim t{(J_z/t)}^{3/2}$.

In contemporary physics, especially in condensed-matter physics, fermionic topological order and its protected edge modes is one of the most important objects. In this work, we propose a systematic construction of the cylinder partition corresponding to the fermionic fractional quantum Hall effect and a general mechanism for obtaining the candidates of the protected edge modes. In our construction, when the underlying conformal field theory has $Z_2$ duality defects corresponding to the fermionic $Z_2$ electric particle, we show that the fractional quantum Hall partition function has a fermionic T duality. This duality is analogous to (hopefully the same as) the dualities in the dual resonance models, typically known as supersymmetry, and it provides a renormalization-group (RG) theoretical understanding of the topological phases. We also introduce a modern understanding of bulk topological degeneracies and topological entanglement entropy. This understanding is based on the traditional tunnel problem and the recent conjecture of correspondence between bulk RG flow and boundary conformal field theory. Our formalism provides an intuitive and general understanding of the modern physics of topologically ordered systems in the traditional language of RG and fermionization, and it may serve as a complement to more mathematical physical frameworks such as fermionic category theories.

We consider a quantum ring of a certain radius $R$ built from a sheet of the $\alpha \text{−}{T}_3$ lattice and solve for its spectral properties in the presence of an external magnetic field. The energy spectrum consists of a conduction band, a valence band, and a zero-energy flat band, all having a number of discrete levels which can be characterized by the angular momentum quantum number $m$. The energy levels in the flat band are infinitely degenerate irrespective of the value of $\alpha$. We reveal a twofold degeneracy of the levels in the conduction band as well as in the valence band for $\alpha =0$ and $\alpha =1$. However, the $m=0$ level for $\alpha =1$ is an exception. Corresponding to an intermediate value of $\alpha$, namely, $0<\alpha <1$, the energy levels become nondegenerate. The scenario for the degeneracy of the energy levels remains unaltered when the ring is threaded by a magnetic flux which is an integer multiple of the flux quantum. We comment on the energy levels which are relevant for low-energy physics by studying their radius dependence in the presence of a magnetic field. We also calculate the persistent current, which exhibits quantum oscillations as a function of the magnetic field with a period of one flux quantum at a particular Dirac point, which is often referred to as a valley. The total persistent current comprising the contributions from both the valleys is zero in the cases corresponding to $\alpha =0$ and $\alpha =1$. However, the total current oscillates with a periodicity of one flux quantum for any intermediate value of $\alpha$. We also explore the effect of a mass term (that breaks the sublattice symmetry) in the Hamiltonian. In the absence of a magnetic field, the energy levels in the flat band become dispersive, except for the $m=0$ level in the case of $\alpha =1$. In the presence of the field, each of the flat band levels becomes dispersive for any $\alpha \ne 0$. Finally, we also see the effect of the mass term on the behavior of the persistent current, which shows a periodicity of one flux quantum, but the total current remains finite for all values of $\alpha$.

Majorana fermions that emerge on the surface of topological superconductors are charge neutral but can have higher-rank electric multipoles by allowing for time-reversal and crystalline symmetries. Applying the general classification of these multipoles, we show that the spin current of Majorana fermions is driven by spatially nonuniform dynamic strains on the surface of a 3D topological crystalline superconductor. We find that the frequency dependence of the Majorana spin current reflects the energy dispersion of Majorana fermions. Our results provide new dynamics of Majorana fermions characterized by crystalline and superconducting symmetries.

We investigate the electron-hole two-stream instability (or Coulomb drag) in bilayer graphene in the hydrodynamic regime, accounting for the effects of temperature, initial drift velocity, magnetic field, and collisions. We put in evidence a purely electrostatic mechanism leading to current relaxation, giving rise to a well-defined dc longitudinal conductivity $\propto T^{3/2}$. Due to competition between electrostatic and collisional processes, two distinct transport regimes are identified. An analysis on the Hall conductivity revealed that the two-stream instability effects also correct the most recent results obtained within the linear response theory.

We have carried out temperature-dependent x-ray diffraction and Raman scattering experiments on powder ${\mathrm{Cs}}_3{\mathrm{Bi}}_2{\mathrm{Br}}_9$. Trigonal to monoclinic structural transition at around 95 K is discussed and shown to be driven by the incomplete soft mode. We propose that the anharmonic scattering of phonons due to the nucleation of the new phase leads to the incomplete soft mode. Raman scattering experiments demonstrate the origin of the soft mode to the rocking motions of Br atoms that participate to form $\mathrm{Bi}{\mathrm{Br}}_6$ octahedra, which correlates with the reported theoretical calculations. Some of the Raman mode frequencies exhibit anomalous temperature dependence due to strong anharmonic phonon-phonon coupling. Temperature-dependent x-ray diffraction analysis estimates the volume thermal expansion coefficient in the trigonal phase to be $13.4\times {10}^{-5}{\text{K}}^{-1}$. In the trigonal phase, the broadening of the full width at half maximum (FWHM) with the increase in temperature for $E_g$ and $A_{1g}$ modes are mostly accompanied by the decaying of one optical phonon into two acoustic phonons. The volume thermal expansion rather than anharmonic phonon-phonon interaction dominates the frequency shift for the Raman modes in the trigonal phase. In the monoclinic phase, the strength of four phonon processes to the frequency shift and linewidth broadening is much smaller than that for three phonon processes.

In this study, the formation of a large in-plane nuclear field, known as the anomalous Hanle effect, in a self-assembled quantum dot was studied from both experimental and theoretical aspects. Time-resolved measurements of photoluminescence revealed that the buildup time of the nuclear field increased with increasing applied transverse magnetic field strength. Further, we found that inversion of the circular polarization degree of photoluminescence due to the excitation helicity reversal was completed on a timescale at least three orders of magnitude faster than the nuclear field buildup time. Accordingly, we reconsidered the previously proposed model for the anomalous Hanle effect. The alternatively developed model successfully explains the experimental results, suggesting that the in-plane component of the major principal axis of nuclear quadrupole interaction is essential for the generation of the anomalous Hanle effect.