Optical properties of semiconducting monolayer transition metal dichalcogenides have received a lot of attention in recent years, following the discovery of the valley selective optical population of either ${\text{K}}_{+}$ or ${\text{K}}_{-}$ valleys at the direct band gap, depending on the polarization of the incoming light. We use group theoretical selection rules, as well as ab initio DFT calculations, to investigate whether this valley selectivity effect is also present in x-ray optical transitions from the flat core level of the transition metal atom to the valence and conduction band K valleys. Valley selectivity is predicted for $s, p_{1/2}$, and $p_{3/2}$ edges in transitions to and from the valence band edges with circularly polarized radiation. Possible novel applications to the diagnostics of valleytronic properties and intervalley dynamics are investigated and the feasibility of ultrafast pump-probe and Kerr rotations experiments with suitable soft-x-ray free-electron laser sources is discussed.

Low power consumption is of great importance for on-chip optical applications of nanolasers. To reduce the lasing threshold, a high quality factor and strong Purcell effect are vital, while the latter is often hindered by the above-diffraction-limit mode volume of photonic cavity, and its improvement generally requires complicated cavity design. We show that by coupling to an off-resonant plasmonic antenna, the lasing threshold of a photonic cavity can be reduced over a wide range of parameters where the plasmon-assisted coherent light-matter interaction dominates over the plasmon-induced dissipation. We develop a semiclassical model of a two-level nanolaser for such a hybrid plasmonic-photonic cavity, which is consistent with the quantum description of the spectral density of a hybrid cavity. The analytical expression of the lasing threshold is derived, which can be utilized to optimize the system parameters associated with cavities designed to obtain the minimum lasing threshold. Through comprehensive study, we find that compared to all-dielectric photonic cavity, a hybrid cavity can have prominent advantages in lasing with lower threshold, narrower emission linewidth, and sustaining the higher-power output of laser field. Our paper demonstrates the possibility of utilizing a hybrid plasmonic-photonic cavity to fabricate room-temperature low-threshold nanolasers.

We consider fixed-point models for topological phases of matter formulated as discrete path integrals in the language of tensor networks. Such zero-correlation length models with an exact notion of topological invariance are known in the mathematical community as state-sum constructions or lattice topological quantum field theories. All of the established ansatzes for fixed-point models imply the existence of a gapped boundary as well as a commuting-projector Hamiltonian. Thus, they fail to capture topological phases without a gapped boundary or commuting-projector Hamiltonian, most notably chiral topological phases in $2+1$ dimensions. In this paper, we present a more general fixed-point ansatz not affected by the aforementioned restrictions. Thus, our formalism opens up a possible way forward towards a microscopic fixed-point description of chiral phases and we present several strategies that may lead to concrete examples. Furthermore, we argue that our more general ansatz constitutes a universal form of topological fixed-point models, whereas established ansatzes are universal only for fixed-points of phases, which admit topological boundaries.

Polar surface and interface play pivotal roles for realizing exotic properties of materials, and search for such polar states is of crucial importance for expanding materials' functionality. Here we report microfocused angle-resolved photoemission spectroscopy of ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$, a member of recently discovered kagome superconductors $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A$ = K, Rb, and Cs) and show evidence for the polar nature of the cleaved surface which is characterized by Cs- and Sb-terminated surfaces with markedly different fermiology. The Cs-terminated surface shows intriguing doubling of V-derived bands at low temperatures associated with the band folding due to the three-dimensional charge density wave (CDW), whereas the Sb-terminated one shows no band doubling or resultant CDW-gap opening indicative of the suppression of bulk-originated CDW due to polar charge. Such polar-surface-dependent band structures must be incorporated for understanding the origin of unconventional superconducting and charge order at the surface of $A{\mathrm{V}}_3{\mathrm{Sb}}_5$.

We explicitly calculate the density-density response function with conserving vertex corrections for anisotropic multiband systems in the presence of impurities including long-range disorder. The direction dependence of the vertex corrections is correctly considered to obtain the diffusion constant which is given by a combination of componentwise transport relaxation times and velocities on the Fermi surface. We also investigate the diffusive density response of various anisotropic systems, propose some empirical rules for the corresponding diffusion constant, and demonstrate that it is crucial to consider the component dependence of the transport relaxation times to correctly interpret the transport properties of anisotropic systems, especially various topological materials with a different power-law dispersion in each direction.

Lattice defects such as stacking faults may obscure electronic topological features of real materials. In fact, defects are a source of disorder that can enhance the density of states and conductivity of the bulk of the system and they break crystal symmetries that can protect the topological states. On the other hand, in recent years, it has been shown that lattice defects can act as a source of nontrivial topology. Motivated by recent experiments on three-dimensional (3D) topological systems such as ${\mathrm{Bi}}_2\mathrm{TeI}$ and ${\mathrm{Bi}}_{14}{\mathrm{Rh}}_3{\mathrm{I}}_9$, we examine the effect of stacking faults on the electronic properties of weak topological insulators (WTIs). Working with a simple model consisting of a 3D WTI formed by weakly-coupled two-dimensional (2D) topological layers separated by trivial spacers, we find that 2D stacking faults can carry their own, topologically nontrivial gapless states. Depending on the WTI properties, as well as the way in which the stacking fault is realized, the latter can form a topologically protected 2D semimetal, but also a 2D topological insulator, which is embedded in the higher-dimensional WTI bulk. This suggests the possibility of using stacking faults in real materials as a source of topologically nontrivial, symmetry-protected conducting states.

Phonons and their interactions are critically important for a variety of energy-relevant applications ranging from low thermal resistance substrates to thermal barrier coatings. Fundamental insights into the nature of phonons and allowed interactions are governed by the underlying symmetries of the crystal lattice. In this paper, we provide a comprehensive and detailed description of lattice dynamics derived from twist symmetries of chiral and achiral crystals—twist dynamics. Phonon bands naturally carry quantized crystal angular momentum derived from rotational phases, which give insights into the nature of band crossings and avoided crossings, selection rules for phonon interactions, and topological band crossing behaviors. Twist dynamics is demonstrated for a variety of materials covering a range of space groups, symmetry operations, twist axis orientations, and constituent elements. Furthermore, twist symmetry offers insights into peculiar features observed in scattering measurements. In this context, we present inelastic neutron scattering measurements for rutile ${\mathrm{TiO}}_2$ and explain them using twist dynamics.

Quantum spin liquid (QSL) is a disordered state of quantum-mechanically entangled spins commonly arising from frustrated magnetic dipolar interactions. However, QSL in some pyrochlore magnets can also come from frustrated magnetic octupolar interactions. Although the key signature for both dipolar and octupolar interaction-driven QSL is the presence of a spin excitation continuum (spinons) arising from the spin quantum number fractionalization, an external magnetic field-induced ferromagnetic order will transform the spinons into conventional spin waves in a dipolar QSL. By contrast, in an octupole QSL, the spin waves carry octupole moments that do not couple, in the leading order, to an external magnetic field or to neutron moments but will contribute to the field dependence of the heat capacity. Here we use neutron scattering to show that the application of a large external magnetic field to ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$, an octupolar QSL candidate, induces an Anderson-Higgs transition by condensing the spinons into a static ferromagnetic ordered state with octupolar spin waves invisible to neutrons but contributing to the heat capacity. Our theoretical calculations also provide a microscopic, qualitative understanding for the presence of octupole scattering at large wave vectors in ${\mathrm{Ce}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ pyrochlore, and its absence in ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$. Therefore, our results identify ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ as a strong candidate for an octupolar $U\left(1\right)$ QSL, establishing that frustrated magnetic octupolar interactions are responsible for QSL properties in Ce-based pyrochlore magnets.

Magnetic frustration in metallic rare- earth lanthanides ($Ln$) with $4f$ electrons is crucial for producing interesting magnetic phases with high magnetic anisotropy where intertwined charge and spin degrees of freedom lead to novel phenomena. Here we report on the magnetic, thermodynamic, and electrical transport properties of ${\mathrm{TbAuAl}}_4{\mathrm{Ge}}_2$. Tb ions form two-dimensional triangular lattice layers which stack along the crystalline $c$ axis. The magnetic phase diagram reveals multiple nearly degenerate ordered states upon applying field along the magnetically easy $ab$-plane before saturation. The magnetoresistance in this configuration exhibits intricate field dependence that closely follows that of the magnetization while the specific heat reveals a region of highly enhanced entropy, suggesting the possibility of a nontrivial spin textured phase. For fields applied along the $c$ axis (hard axis), we find linear magnetoresistance over a wide range of fields. We compare the magnetic properties and magnetoresistance with an isostructural ${\mathrm{GdAuAl}}_4{\mathrm{Ge}}_2$ single crystal. These results identify ${\mathrm{TbAuAl}}_4{\mathrm{Ge}}_2$ as an environment for complex quantum spin states and pave the way for further investigations of the broader $Ln{\mathrm{AuAl}}_4{\mathrm{Ge}}_2$ family of materials.

We present a single-crystal neutron diffraction study on the Shastry-Sutherland lattice system ${\mathrm{TbB}}_4$ at zero magnetic field and under pulsed high magnetic fields up to 35 T applied along the crystallographic $c$ axis. While our results confirm the magnetic structures at zero field as well as those at the half- and full-magnetization plateaus, they offer insight into the $2/9$- and $1/3$-magnetization plateaus observed in this system. A stripe model of polarized 4-spin plaquettes whose stripe density proportionally increases with the macroscopic magnetization is in full agreement with the neutron diffraction data. Equally well-suited alternative models exist which explain the observed Bragg peaks being inherently limited in a pulsed high magnetic field experiment. We discuss the different intensity distributions in $Q$ space which can be used to distinguish these models in future experiments.

Multiband superconductors can host collective excitations with marked differences with respect to their single-band counterpart. We first study the spectrum of collective amplitude fluctuations in a clean two-band superconductor, showing that the spectral weight of the Higgs mode rapidly deviates from the naive extension of the single band case as the interband coupling is turned on. These results are then used to critically analyze the nonlinear optical response in ${\mathrm{MgB}}_2$, providing an explanation for the apparently contradictory results of recent experiments, pointing towards a selective relevance either of the Leggett mode or of the amplitude fluctuations at twice the lower gap. By using exact numerical simulations and realistic estimates of disorder we compute the relative contribution of the quasiparticle, amplitude, and phase fluctuations to the nonlinear optical response. We show that at low pumping frequency only the resonance at twice the smaller gap emerges, as due to the BCS response, while the Leggett mode dominates only in a narrow range of higher pumping frequencies matching its low-temperature value. Our findings provide a fresh perspective on the potential of nonlinear THz spectroscopy to detect collective modes in other multiband systems, such as iron-based superconductors.

The spin coherence times of 69 triplet defect centers in 45 different 2D host materials are calculated using the cluster-correlation expansion method with parameters of the spin Hamiltonian obtained from density-functional theory. Several of the triplets are found to exhibit extraordinarily large spin coherence times making them interesting for quantum information processing. The dependence of the spin coherence time on various factors, including the hyperfine coupling strength, the dipole-dipole coupling, and the nuclear $g$ factors, are systematically investigated. The analysis shows that the spin coherence time is insensitive to the atomistic details of the defect center and rather is dictated by the nuclear-spin properties of the host material. Symbolic regression is then used to derive a simple expression for the spin coherence time, which is validated on a test set of 55 doublet defects unseen by the regression model. The simple expression permits order-of-magnitude estimates of the spin coherence time without expensive first-principles calculations.

Nanoscale shear bands formed in many energetic molecular crystals upon shock compression [including 1,3,5-trinitro-$s$-triazine (RDX)] are considered as a defect-free mechanism for formation and growth of hot spots which control detonation initiation. Using classical molecular dynamics, we predict the formation of similar nanoscale shear bands in the α-RDX crystal subjected to quasistatic isothermal uniaxial compression indicating a common mechanism of shear strain localization under both shock and quasistatic conditions. In the framework of the Ginzburg-Landau phenomenology coupled with the coarse-grained (CG) Helmholtz free energy of the crystal from first principles, we explore the thermodynamics of stress-induced lattice transformations under quasistatic uniaxial load. We show that the shear banding exhibits a critical behavior associated with a first-order structural phase transition with bands of localized twinning strain as transient microstructure. Analysis of the CG Helmholtz free energy suggests that the stress-induced core softening of the effective intermolecular interaction is a fundamental mechanism for a structural phase transition leading to the nanoscale shear bands.

We show that the classical (mean-field) description of far from equilibrium superconductivity is exact in the thermodynamic limit for local observables but breaks down for global quantities, such as the entanglement entropy or Loschmidt echo. We do this by solving for and comparing exact quantum and exact classical long-time dynamics of a BCS superconductor with interaction strength inversely proportional to time and evaluating local observables explicitly. Mean field is exact for both normal and anomalous averages (superconducting order) in the thermodynamic limit. However, for anomalous expectation values, this limit does not commute with adiabatic and strong coupling limits and, as a consequence, their quantum fluctuations can be unusually strong. The long-time steady state of the system is a gapless superconductor whose superfluid properties are only accessible through energy resolved measurements. This state is nonthermal but conforms to an emergent generalized Gibbs ensemble. Our study clarifies the nature of symmetry-broken many-body states in and out of equilibrium and fills a crucial gap in the theory of time-dependent quantum integrability.

We construct quasi-one-dimensional topological and nontopological three-band lattices with a tunable band gap and winding number of the flat band. Using full multiband mean field (MF) and exact density matrix renormalization group (DMRG) calculations, we show explicitly how the band gap affects pairing and superconductivity (SC) in a Hubbard model with attractive interactions. We obtain excellent agreement between MF and DMRG calculations. The SC weight $D_s$ on the gapped topological, $W\ne 0$, flat band increases linearly with interaction strength $U$ for low values and with a slope that depends on the details of the compact localized state at $U=0$. As $U\to 0$ for the gapped nontopological flat band ($W=0$), $D_s$ decays with a power law faster than quadratically but slower than exponentially. In the gapless case (flat band touching the band above it), we find at low $U$ (for both $W=0$ and $W\ne 0$) that $D_s\propto U^{\phi }$, with $\phi <1$. In other words, $D_s$ increases faster than linearly for low $U$, thus favoring SC at weak interaction more than the gapped case. Our results reestablish that the BCS mean field and quantum metric alone are insufficient to characterize SC at weak coupling.

Here, we report on the low-energy excitations within the paramagnetic spin-orbit insulator ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7{\mathrm{F}}_2$ studied via resonant inelastic x-ray scattering, ab initio quantum chemical calculations, and model Hamiltonian simulations. This material is a unique $d^4 {\mathrm{Ir}}^{5+}$ analog of ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$ that forms when F ions are intercalated within the SrO layers spacing the square lattice ${\mathrm{IrO}}_6$ bilayers of ${\mathrm{Sr}}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$. Due to the large distortions about the ${\mathrm{Ir}}^{5+}$ ions, our computations demonstrate that a large single-ion anisotropy yields an $S=1$ ($L\approx 1, J\approx 0$) ground-state wave function. Weakly coupled, excitonic modes out of the $S_z=0$ ground state are observed and are well described by a phenomenological spin-orbit exciton model previously developed for $3d$ and $4d$ transition metal ions. The implications of our results regarding the interpretation of previous studies of hole-doped iridates close to $d^4$ fillings are discussed.

Localization phenomena and the quantum phase transition are two core concepts of low-dimensional condensed-matter physics. The localization transition problem related to vortex line pinning in superconductors can be studied by mapping it to a real-complex non-Hermitian problem. Its relation to the quantum phase transition has to be discerned. We explore these two phase transitions induced by interactions rather than by the disorder in non-Hermitian systems. It is shown that the phase diagram is divided into the classical and quantum regimes by a characteristic temperature. The classical regime contains topological localization transitions and a tricritical point which connects the first-order phase transition line to the second-order transition line. The quantum regime is a nonchaotic and first-order phase transition. In such a quantum regime, the relaxation time does not always satisfy the bound on chaos. We show that the oscillation phase transition line due to quantized Matsubara frequencies can give an index similar in structure to the quantum oscillation in an imaginary magnetic field, which makes the first-order quantum phase diagram behave as a quantum critical phase diagram.