Although flat-band structures have been the subject of intensive studies in condensed-matter and optical physics due to their eigenstates, which exhibit huge degeneracy and allow for the localization of wave packets, it is not clear how the Liouvillian flat band influences the relaxation dynamics of open quantum systems. To this end, we study the dynamical signatures of the Liouvillian flat band in the scheme of the Lindblad master equation. Considering a chain model with gain and loss, we demonstrate three kinds of Liouvillian band dispersion: (i) a flat band, (ii) a dispersionless band in the real part, and (iii) a dispersionless band in the imaginary part, and we capture their dynamical signatures. When the Liouvillian rapidity spectrum is flat, the particle numbers in different sites relax to their steady-state value with the same decay rate; when the real or imaginary part of the rapidity spectrum is dispersionless, the relaxation behaviors have oscillating or forked characteristics. We also show that the Liouvillian flat band can lead to dynamical localization, which is characterized by a halt in the propagation of local perturbation in the steady state.

Isotope effects on heat conduction and convection have been known for decades. However, whether thermal radiation can be isotopically engineered remains an open question. Here, we predict over three-orders-of-magnitude variation of radiative heat flow with varying isotopic compositions for polar dielectrics at room temperature. We reveal this as an isotope mass effect which induces phonon line shift and broadening that in turn affect phonon-mediated resonant absorption both in the near and far field. In contrast, the isotope effect is negligible for metals and doped semiconductors which largely depend on free carriers. We also discuss the role of temperature with regard to surface mode excitation.

Understanding the interplay between magnetic and electronic degrees of freedom is of profound recent interest in different Eu-based magnetic topological materials. In this paper, we studied the magnetic and electronic properties of the layered Zintl-phase compound ${\mathrm{EuAl}}_2{\mathrm{Ge}}_2$ crystallizing in the trigonal ${\mathrm{CaAl}}_2{\mathrm{Si}}_2$-type structure. We report zero-field neutron diffraction, temperature $T$- and magnetic-field $H$-dependent magnetic susceptibility $\chi (T,H)$, isothermal magnetization $M(T,H)$, heat capacity $C_{\mathrm{p}}(T,H)$, and electrical resistivity $\rho (T,H)$ measurements, together with $T$-dependent angle-resolved photoemission spectroscopy (ARPES) measurements complemented with first-principles calculations. ${\mathrm{EuAl}}_2{\mathrm{Ge}}_2$ undergoes second-order A-type antiferromagnetic (AFM) ordering below $T_{\mathrm{N}}=27.5\left(5\right)$ K, with the Eu moments (${\mathrm{Eu}}^{2+},S=7/2$) aligned ferromagnetically in the $ab$ plane while these layers are stacked antiferromagnetically along the $c$ axis. The critical fields at which all moments become parallel to the field are 37.5(5) and 52.5(5) kOe for $H\parallel ab$ and $H\parallel c$, respectively. The $H=0$ magnetic structure consists of trigonal AFM domains associated with $ab$-plane magnetic anisotropy and a field-induced reorientation of the Eu spins in the domains is also evident at $T=2$ K below the critical field $H_{\text{c}1}=2.5\left(1\right)$ kOe. The $\rho \left(T\right)$ measurements reveal metallic behavior transforming into a slight resistivity increase on cooling towards $T_{\mathrm{N}}$. A pronounced loss of spin-disorder scattering is observed below $T_{\mathrm{N}}$. The ARPES results show that ${\mathrm{EuAl}}_2{\mathrm{Ge}}_2$ is metallic both above and below $T_{\mathrm{N}}$, and the Fermi surface is anisotropic with two hole pockets at the zone center and one small electron pocket at each $\mathrm{M}$ point. In the AFM phase, we directly observe folded bands in ARPES due to the doubling of the magnetic unit cell along the $c$ axis with an enhancement of quasiparticle weight due to the complex change in the coupling between the magnetic moments and itinerant electrons on cooling below $T_{\mathrm{N}}$. The observed electronic structure is well reproduced by first-principles calculations, which also predict the presence of nontrivial electronic states near the Fermi level in the AFM phase with $Z_2$ topological numbers $1;\left(000\right)$.

The elastic properties, phase stability, and magnetism and correlations among them in all-$d\text{−}\mathrm{metal}$ Heusler compounds, i.e., ${\mathrm{Ni}}_2\mathrm{Mn}T$ ($T=\mathrm{Sc}$, Ti, V, Cr, Y, Zr, Nb, Mo, Hf, Ta, and W) were systematically investigated by first-principles calculations. The results indicated that ${\mathrm{Ni}}_2\mathrm{Mn}T$ compounds were not fully consistent with the conventional atomic preferential occupation rule in the Heusler family. Within the scope of Heusler structures, ${\mathrm{Ni}}_2\mathrm{Mn}T$ compounds containing early transition metal atoms preferred $L{2}_1\text{-type}$ structure, while those with late transition metal atoms were relatively stable in ${\mathrm{Hg}}_2\mathrm{CuTi}\text{−}\mathrm{type}$ structure. In $d\text{−}d$ interatomic hybridization-controlled all-$d\text{−}\mathrm{metal} {\mathrm{Ni}}_2\mathrm{Mn}T$ Heusler compounds, the atomic radius determined the lattice sizes. Owing to the strong couplings among elastic parameters, phonon modes, and electronic structure, the most likely martensitic phase transition could be expected in weakly magnetic ${\mathrm{Ni}}_2\mathrm{Mn}T$ compounds with late transition metal atoms. By applying hydrostatic pressure or imposing chemical pressure via adjusting the composition of Ti in an off-stoichiometric Ni-Mn-Ti system, magnetism was weakened, and the suppressed martensitic phase transition could be re-evoked. In this paper, we also revealed that experimentally observed antiferromagnetism in ${\mathrm{Ni}}_2\mathrm{MnTi}$ originated from the arrest of the atomic diffusion process during the transition from the high-temperature chemically disordered paramagnetic state to the low-temperature chemically and magnetically ordered ferromagnetic state, which resulted in the formation of an intermediate metastable and partially disordered antiferromagnetic phase. Comparatively, ${\mathrm{Ni}}_2\mathrm{Mn}T$ compounds with early transition metals showed better ductility. In representative ${\mathrm{Ni}}_2\mathrm{MnY}$ and ${\mathrm{Ni}}_2\mathrm{MnTa}$, it was found that nondirectional $d\text{−}d$ interatomic hybridization became prevailing and helped establish the metal bonding character, which consequently enhanced the ductility. This paper can provide more insight into understanding the mechanism of martensitic phase transition and the origin of experimental anomalous magnetic states as well as the scheme to design multiple functional magnetic materials with outstanding ductility in the all-$d\text{−}\mathrm{metal}$ Heusler family. Experimentally observed exceptional multicaloric effects in Ni-Mn-based compounds with outstanding mechanical properties make all-$d\text{−}\mathrm{metal}$ Heusler compounds attractive for potential solid-state refrigeration application.

The spin susceptibility is an important probe to characterize the symmetry of the order parameter in unconventional superconductors. Among them, nonunitary triplet superconductors have attracted a lot of attention recently in the context of the search for topological superconductivity. Here, we derive a general formula for the spin susceptibility of nonunitary triplet superconductors within a single-band model of nonmagnetic, centrosymmetric materials with strong spin-orbit coupling. We use it to critically assess experimental claims of nonunitary triplet superconductivity in some materials.

We studied ${\mathrm{Ni}}_{50+x}{\mathrm{Ti}}_{50-x}$ with compositions up to $x=2$, performing ${}^{47}\mathrm{Ti}$ and ${}^{49}\mathrm{Ti}$ nuclear magnetic resonance (NMR) measurements from 4 to 400 K. For large $x$ in this system, a strain glass appears in which frozen ferroelastic nanodomains replace the displacive martensite structural transition. Here, we demonstrate that NMR can provide an extremely effective probe of the strain-glass freezing process, with large changes in NMR line shape due to the effects of random strains which become motionally narrowed at high temperatures. At the same time with high-resolution x-ray diffraction we confirm the lack of structural changes in $x\ge 1.2$ samples, while we show that there is little change in the electronic behavior across the strain-glass freezing temperature. NMR spin-lattice relaxation time ($T_1$) measurements provide a further measure of the dynamics of the freezing process, and indicate a predominantly thermally activated behavior both above and below the strain-glass freezing temperature. We show that the strain-glass results are consistent with a very small density of critically divergent domains undergoing a Vogel-Fulcher-type freezing process, coexisting with domains exhibiting faster dynamics and stronger pinning.

In the context of wave propagation, caustics are usually defined as the envelope of a finite-extent wavefront; folds and cusps in a caustic result in enhanced wave amplitudes. Here, we tackle a related phenomenon, namely, the existence of well-defined beams originating solely from the geometric properties of the corresponding dispersion relation. This directional emission, termed caustic beam, is enabled by a stationary group velocity direction, and has been observed first in the case of phonons. We propose an overview of this “focusing” effect in the context of spin waves excited in soft, thin ferromagnetic films. Based on an analytical dispersion relation, we provide tools for a systematic survey of caustic spin wave beams. Our theoretical approach is validated by time-resolved microscopy experiments using the magneto-optical Kerr effect. Then, we identify two cases of particular interest both from fundamental and applicative perspectives. Indeed, both of them enable broadband excitations (in terms of wave vectors) to result in narrow-band beams of low divergence.

The Landau free energy of a compound that benefits from a linear coupling of an electric field and a magnetic field includes a product of the two fields, one polar and time even and one axial and time odd. Evidently, the coefficient of the product of fields is unchanged by a simultaneous change in the directions of space and time, a symmetry operation labeled anti-inversion. Invariance with respect to anti-inversion is the defining symmetry of the linear magnetoelectric (ME) effect included in 58 of 122 magnetic crystal classes, 19 of which prohibit higher-order (nonlinear) contributions to the free energy. In ME compounds, expectation values of some atomic magnetic tensors are invariant with respect to anti-inversion. An invariance shared by the Dirac monopole (an element of charge allowed in Maxwell's equations that has not been observed) and a Zel'dovich anapole, is also known as a Dirac dipole. From the science of materials perspective, it has been established that Dirac multipoles contribute to the diffraction of x rays and neutrons. We identify Dirac monopoles in bulk magnetic properties of iron tellurate (${\mathrm{Fe}}_2\mathrm{Te}{\mathrm{O}}_6$) and a spin ladder ($\mathrm{Sr}{\mathrm{Fe}}_2{\mathrm{S}}_2\mathrm{O}$). They are visible in the diffraction of light using an iron electric dipole–magnetic dipole absorption event. Both cited compounds present a simple antiferromagnetic configuration of axial dipoles, and their different magnetic crystal classes allow a linear ME effect. However, the Kerr effect is symmetry allowed in the spin ladder and forbidden in iron tellurate. Anapoles are forbidden in iron tellurate and allowed in the spin ladder compound, a difference evident in diffraction patterns fully informed by symmetry. More generally, we identify a raft of Dirac multipoles, and axial multipoles beyond dipoles, visible in future experiments using standard techniques with beams of neutrons or x rays tuned in energy to an iron atomic resonance. ME invariance imposes a phase relationship between nuclear (charge) and magnetic contributions to neutron (x-ray) diffraction amplitudes. In consequence, intensities of Bragg spots in an x-ray pattern do not change when helicity in the primary beam is reversed. A like effect occurs in the magnetic diffraction of polarized neutrons.

We propose a compact and highly efficient scheme for solid-state photonic quantum gates. At the core of our scheme is a $SWA{P}^{\varphi }$ gate based on giant Cooper-pair-based optical nonlinearity we predict in a semiconductor-superconductor structure, selectively introducing a phase to the $|{\mathrm{\Psi }}_{+}\rangle$ Bell state. We theoretically demonstrate this scheme on a practical device based on a superconducting contact coupled to a GaAs/AlGaAs waveguide structure. We model the Cooper-pair-induced nonlinear change of the refractive index showing strong nonlinearities at energies close to the superconducting gap inside a semiconductor band. We calculate the fidelity of the proposed $SWA{P}^{\varphi }$ gate, as well as the sensitivity of the gate to device parameters. As short photon wave packets are crucial for efficient higher-order interactions, we investigate the integrated fidelity for short wave packets with different central wavelengths and bandwidths, providing limiting factors as well as possible optimizations. This theoretically demonstrated concept can pave the way toward practical realizations of scalable photonic quantum circuits.

The recent measurement of the de Haas–van Alphen effect in the spin-triplet superconductor ${\mathrm{UTe}}_2$ [D. Aoki et al., J. Phys. Soc. Jpn. 91, 083704 (2022)] supports cylindrical electron and hole Fermi surfaces, which implies that ${\mathrm{UTe}}_2$ is trivial as a 3D time-reversal-invariant topological superconductor. Inspired by this observation, we investigate the possible realization of a topological crystalline superconductor protected by the crystalline symmetry of ${\mathrm{UTe}}_2$. We examine Majorana surface states protected by mirror and twofold rotational symmetries for all symmetry-allowed odd-parity pairing states with time-reversal symmetry and clarify the corresponding topological invariants. It is found that topological crystalline superconductivity can be realized for all irreducible representations of odd-parity pairing states of ${\mathrm{UTe}}_2$, even for cylindrical Fermi surfaces.

Rank-2 toric code (R2TC), a prototypical archetype of the discrete rank-2 symmetric gauge theory, has properties that differ from those of the standard toric code. Specifically, it features a blending of UV and IR in its ground state, restricted mobility of its quasiparticles, and variations in the braiding statistics of its quasiparticles based on their position. In this paper, we investigate various aspects of ${\mathbb{Z}}_N$ rank-2 gauge theory in $(2+1)$-dimensional spacetime. Firstly, we demonstrate that $U\left(1\right)$ rank-2 gauge theory can arise from $U\left(1\right)\times U\left(1\right)$ rank-1 gauge theory after condensing the gauge charges in a specific way. This construction scheme of $U\left(1\right)$ rank-2 gauge theory carries over to the ${\mathbb{Z}}_N$ case simply by Higgsing $U\left(1\right)$ to ${\mathbb{Z}}_N$, after which the resulting rank-2 gauge theory can be tuned to the R2TC. The holonomy operators of R2TC are readily identified using this scheme and are given clear physical interpretation as the pair creation/annihilation of various monopoles and dipoles. Explicit tensor network construction of the ground states of R2TC is given as two copies of the ground states of Kitaev's toric code that are “sewn together” according to the condensation scheme. In addition, through a similar anyon condensation protocol, we present a double semion version of rank-2 toric code whose flux excitations exhibit restricted mobility and semionic statistics. Finally, we identify the generalized discrete symmetries of the R2TC, which are much more complex than typical 1-form symmetries. They include conventional and unconventional 1-form symmetries, such as framed 1-form symmetries and what we call sublattice 1-form symmetries. Using these, we interpret the R2TC's unique properties (UV/IR mixing, position-dependent braiding, etc.) from the modern perspective of generalized spontaneous symmetry breaking and 't Hooft anomalies.

Topological crystalline insulators from the ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Se}$ family host textbook Dirac surface states that are nearly electron-hole symmetric and isotropic in momentum space. The high mobility of charge carriers possible in these materials allows one to reach the quantum limit at reasonably achievable magnetic fields. We exploit this advantage to combine magnetooptical Landau level spectroscopy, Shubnikov–de Haas transport measurement, and consistent modeling of the two experiments to precisely extract the band parameters of the topological states of this system along with their $g$ factor. We find an enhanced $g$ factor with field dependence compared with bulk states. This information is vital to the realization and understanding of novel quantized Hall effect, stemming from the mirror protected valley-degenerate Dirac states of this material family.

Rashba-type spin-orbit coupling is a long-term active topic due to its superiority of magnetic-field-free control of the electron spin. However, numerous Rashba-related works focus on improving the magnitude of the spin splitting that exhibits the traditional in-plane spin polarization. Very few studies concern manipulating the direction of the spin splitting, such as the generation of out-of-plane spin polarization especially in nonmagnetic materials. Intriguingly, this research field has recently become very appealing owing to its great prospects in high-density and energy-efficient spintronic applications. Here, we report a prominent out-of-plane spin polarization in the two-dimensional Dion-Jacobson (DJ) perovskite and reveal that it is the physical origin of the large Rashba spin splitting observed in both experiments and theoretical calculations. Consequently, the spin-split band structures of the studied system must be interpreted by a proposed three-dimensional Rashba model, with the spin polarization mainly along the out-of-plane direction. Moreover, the temperature-dependent Rashba spin splitting shows that both static and dynamical Rashba effects contribute to the total spin splitting, where the out-of-plane spin polarization always dominates the overall splitting. Such a robust generation of this unconventional spin component indicates the significant influence of the in-plane asymmetric crystal field on the spin-orbit interactions. It is worth emphasizing that it is this out-of-plane spin splitting, not the commonly considered in-plane ones, responsible for the reported large band splitting in DJ perovskites. These results present that the studied system may serve as a type of spin source material to explore the attractive out-of-plane spin polarization, which is highly desired for high-density magnetic switching as well as field-free spin-based computing. It also suggests that crystal symmetry engineering can be a promising strategy to manipulate the spin polarization.

The SU(2)-symmetric three-component spin-boson model (also Bose-Kondo model) exhibits different behavior of quantum phase and phase transition from its widely studied single-component counterpart. In this paper we proposed and theoretically studied a model of two separated spins coupled to a common bosonic bath. For our SU(2)-symmetric model, the stable fixed point representing the nonclassical phase and an unstable fixed point corresponding to the transition between the strong-coupling and nonclassical phases can be continuously tuned by the distance between the two spins. Thus the fixed-point collision and annihilation (FPCAA) could be achieved by simply changing the distance. We also studied in detail variations of the values of the two fixed points above as the distance is changed. Our work is essential for realization of FPCAA in such systems and paves the way for studying related physics such as deconfined criticality and quasiuniversality.

We show how to compute the orbital magnetization, as the first-order change of the energy due to an homogeneous magnetic field, within the projector augmented-wave (PAW) formalism of density functional theory, for systems with periodic boundary conditions. To accomplish this, magnetic translation symmetry is invoked together with a perturbative treatment of the density operator, yielding well-posed expressions that account fully for all PAW terms. The terms may be computed in a standard PAW implementation using density functional perturbation theory to compute the necessary wave-function derivatives, rather than the finite-difference approach that has been used previously. In order to obtain nontrivial magnetization, we also impose nuclear magnetic dipole moments on atomic sites of interest, which gives direct access to the chemical shielding, as measured in nuclear magnetic resonance spectroscopy. The resulting expressions have been implemented and tested, and results are shown both for atoms and solids.

Recent observations of superconductivity in moire graphene have led to an intense interest in that system, with subsequent studies revealing a more complex phase diagram including correlated insulators and ferromagnetic phases. Here we propose an alternate system, electrostatically patterned bilayer graphene, in which a supermodulation is induced via metallic gates rather than the moire effect. We show that, by varying either the gap or the modulation strength, bilayer graphene can be tuned into the strongly correlated regime. Further calculations show that this is not possible in monolayer graphene. We present a general technique for addressing Coulomb screening of the periodic potential and demonstrate that this system is experimentally feasible.

We demonstrate the existence of a conceptually distinct topological pumping phenomenon in one-dimensional chains undergoing topological adiabatic cycles. Specifically, for a stack of two semi-infinite chains cycled in opposite directions and coupled at one edge by a gapping potential, we derive a higher-order bulk-boundary correspondence that relates the bulk Chern number associated with the adiabatic cycle of a single infinite chain and the number of electrons transferred between the semi-infinite chains. The relation is formulated using the relative index of two projections and proven using $K$-theoretic calculations. The phenomenon is exemplified using the Rice-Mele model and possible experimental implementations with classical and quantum degrees of freedom are discussed.

We manipulate the coupling effect between interdot tunneling and the external control field to study the optical diffractive property in a quantum dot molecule (QDM) system. Based on the density matrix approach, an analytical relation is obtained for the optical susceptibility, which shows tunneling-induced transparency (TIT) in the absorption spectra. We propose an innovative optoelectronic device called tunneling-induced grating, which operates based on the diffraction of the forward-transmitted probe laser light. The diffraction integrals for the far-field regime (i.e., Fraunhofer diffraction) are numerically solved, and the effect of interdot tunneling coupling strength on the diffraction patterns is studied. It is shown that the transmission is increased under tunneling-induced quantum coherence. The weak probe light can be diffracted into higher-order directions upon applying a standing-wave control field. The optimal parametric condition for maximum first- and second-order diffractions is obtained. The results find the potential applications in quantum information processing devices, such as all-optical grating and switches at low light levels.