The anisotropic nature of $\mathrm{G}{\mathrm{a}}_2{\mathrm{O}}_3$ significantly impacts its device design and performance. However, the understanding of anisotropy is exclusively limited to a few specific crystalline directions. Authors of many studies have been focused on identifying the optimal optoelectronic response direction to enhance device efficiency. In this paper, we thoroughly explore the anisotropic photoelectric properties of $\alpha \text{−}\mathrm{G}{\mathrm{a}}_2{\mathrm{O}}_3$ and $\beta \text{−}\mathrm{G}{\mathrm{a}}_2{\mathrm{O}}_3$ by systematically analyzing three-dimensional carrier distribution and transport behaviors in energy, momentum, and group velocity spaces. Notably, $\alpha \text{−}\mathrm{G}{\mathrm{a}}_2{\mathrm{O}}_3$ and $\beta \text{−}\mathrm{G}{\mathrm{a}}_2{\mathrm{O}}_3$ mainly produce high-energy electrons upon photoexcitation, and the energy range of electrons produced by $\alpha \text{−}\mathrm{G}{\mathrm{a}}_2{\mathrm{O}}_3$ is 0.7 eV narrower than that of $\beta \text{−}\mathrm{G}{\mathrm{a}}_2{\mathrm{O}}_3$, which is beneficial for efficient ballistic transport. Additionally, the electrons in $\alpha \text{−}\mathrm{G}{\mathrm{a}}_2{\mathrm{O}}_3$ are uniformly distributed in initial momentum and group velocity spaces, while the holes exhibit anisotropy. In contrast, both electrons and holes in $\beta \text{−}\mathrm{G}{\mathrm{a}}_2{\mathrm{O}}_3$ show significant anisotropy with distinct aggregation directions. These different spatial distributions can result in anisotropic carrier motion in optoelectronic applications. Furthermore, carriers with long relaxation times and mean free paths exhibit distinct optimal transport directions. Notably, for $\beta \text{−}\mathrm{G}{\mathrm{a}}_2{\mathrm{O}}_3$, the optimal transport direction of electrons deviates from their initial group velocity direction, which may lead to low electron utilization during electrical injection. For $\alpha \text{−}\mathrm{G}{\mathrm{a}}_2{\mathrm{O}}_3$, the optimal transport directions of carriers are consistent with their initial group velocity directions, indicating the potential of realizing the best optoelectronic and electronic devices along these directions. These results provide insights into the anisotropy of photoelectric properties at the atomic and electronic scales, which guide making the best use of carriers in designing $\mathrm{G}{\mathrm{a}}_2{\mathrm{O}}_3$-based devices.

Lead-free chalcogenide perovskites have garnered significant attention in recent years as promising candidates for sustainable, high-performance photovoltaics. These materials present an ideal combination of nontoxic elemental composition, exceptional phase stability, and outstanding optoelectronic properties. However, unlocking their full potential for solar cell applications requires advanced strategies to fine-tune their electronic and optical behavior. In this study, we take ${\mathrm{CaHfS}}_3$—a promising but underexplored candidate—and enhance its performance through strategic substitutions: Ti at the cation site and Se at the anion site. Using state-of-the-art computational techniques, including density functional theory, $GW$ calculations, and the Bethe-Salpeter equation, we reveal how these substitutions transform the material's properties. Our findings highlight that alloyed compounds such as ${\mathrm{CaHfS}}_{3-x}{\mathrm{Se}}_x$ and ${\mathrm{CaHf}}_{1-y}{\mathrm{Ti}}_y{X}_3$ ($X=\mathrm{S}$, Se) are not only phase stable but also feature adjustable direct $G_0{W}_0$@PBE band gaps ($1.29-2.67\mathrm{eV}$), reduced exciton binding energies, and significantly improved polaron mobility. These modifications enable better light absorption, reduced electron-hole recombination, longer exciton lifetimes, and enhanced quantum yield. The Ti-rich Se-based perovskites achieve a spectroscopic-limited maximum efficiency of up to 28.06%, outperforming traditional lead-based halide perovskites. Our results demonstrate that strategic alloying is a powerful tool to supercharge the optoelectronic properties of lead-free chalcogenide perovskites, positioning them as compelling candidates for next-generation photovoltaic technologies.

We study the doping and temperature dependencies of temporal and spatial spin stiffnesses of the Hubbard model within the mean-field approach for incommensurate magnetic order. We show that the frequency dependence of temporal spin stiffness within the considered mean-field approach is crucial to obtain small values of correlation length, comparable to those observed in cuprates. Using the obtained spin stiffnesses, we obtain the temperature and doping dependencies of the correlation length within the large-$N$ limit of the respective nonlinear sigma model. In agreement with the experimental data on ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ we obtain short-range magnetic order with a relatively small correlation length at $0.1\lesssim x\lesssim 0.2$, and a magnetically ordered ground state in the narrow doping region $0.05\lesssim x\lesssim 0.1$. The latter state may correspond to the spin-frozen state, observed in the experimental data on ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$.

The study of nonreciprocal phenomena has long captivated interest in both Hermitian and non-Hermitian systems. The superconducting diode effect (SDE) is a nonreciprocal phenomenon characterized by unequal critical charge supercurrents flowing in opposite directions in Hermitian superconducting systems. In this study, we introduce an SDE driven by non-Hermiticity in a superconducting quantum interference device (SQUID) under an external magnetic flux, which we refer to as the non-Hermitian SDE. Non-Hermiticity is introduced by coupling one of the two Josephson junctions to a gapless electron reservoir, introducing phase decoherence. Remarkably, we find that an emergent non-Hermitian Fermi-Dirac distribution can give rise to an SDE in the non-Hermitian SQUID. We analyze the behavior of the SDE under both direct current and alternating current biases, highlighting the appearance of direction-dependent critical currents and asymmetric Shapiro steps as hallmarks of the SDE. Our findings not only reveal an experimentally accessible mechanism for non-Hermitian SDE but also open avenues for investigating nonreciprocal phenomena in non-Hermitian systems.

Symmetry-breaking phenomena are identifiable in numerous strongly correlated systems including high-temperature superconductors. However, identification of these exotic states and understanding their interplay with superconductivity in topological materials remains limited. Here we employ cryogenic scanning tunneling microscopy to reveal coexistent charge and pair density waves (CDWs and PDWs) in topological monolayer $1T^{\prime }\text{−}{\mathrm{MoTe}}_2$. The two orders are modulated unidirectionally and share the same periodicity of five unit cells or a wave vector near (0, 0.4)$\pi /b$ ($b$ is the lattice constant along the zigzag Mo chains). Importantly, the PDW features a two-gap superconductivity below a transition temperature of around 6.0 K and induces a unique secondary particle-hole-symmetric CDW at twice its wave vector. Combining these results and our density functional calculations, we elucidate that the two unidirectional orders are driven by nesting behaviors between electron and hole pockets. Our findings establish monolayer $1T^{\prime }\text{−}{\mathrm{MoTe}}_2$ as a topological paradigm to explore multiple preexisting symmetry-breaking states.

Inspired by experiments on the magnetic field induced phases of the spin-orbit coupled two dimension ($2\text{D}$) Mott insulator $\alpha \text{−}{\mathrm{RuCl}}_3$, we study some general aspects of gapped $Z_2$ quantum spin liquids (QSL) enriched by lattice translation symmetry. We show that there are 12 distinct such phases with different implementations of translation symmetry. In some of these phases the vison excitations of this QSL may form topological Chern bands. We explore a phenomenological description of a putative $Z_2$ QSL as a candidate ground state at intermediate magnetic fields in $\alpha \text{−}{\mathrm{RuCl}}_3$. This state has broad continuum spectra in neutron scattering, a “bosonic” thermal Hall signal that goes to zero at zero temperature, and is naturally proximate to a zigzag magnetic ordered state, all of which are also seen in $\alpha \text{−}{\mathrm{RuCl}}_3$. On general grounds, continuum scattering will also be seen at multiple points in the Brillouin zone in this state.

Two dimensional moiré systems have recently emerged as a platform in which the interplay between topology and strong correlations of electrons play out in nontrivial ways. Among these systems, twisted double bilayer graphene (TDBG) is of particular interest as its topological properties may be tuned via both twist angle and applied perpendicular electric field. In this system, energy gaps are observed at half filling of particular bands, which can be associated with correlated spin polarized states. In this work, we investigate the fate of these states as the system is doped away from this filling. We demonstrate that, for a broad range of fractional fillings, the resulting ground state is partially valley polarized, and supports multiple broken symmetries, including a textured spin order indicative of skyrmions, with a stripe ordering that spontaneously breaks $C_3$ symmetry. Experimental signatures of this state are discussed.

Structural phase transitions in ${\mathrm{VO}}_2$ and consequent changes in its physical properties have been cornerstones in the development of condensed matter physics, not only in terms of the spectacular insulator-metal transition in the archetypical monoclinic (M1)-rutile (R) phase transition but also in closely related structure types achieved by minor perturbations of the pure system by the application of pressure or doping. In this context, the most investigated phenomenon is the triclinic (T)-monoclinic (M2)-rutile (R) phase transition. The present work, using single-crystal and powder x-ray diffraction measurements on ${\mathrm{Al}}^{3+}, {\mathrm{Cr}}^{3+}$, and ${\mathrm{Fe}}^{3+}$ doped samples, reveals a common structural behavior independent of the nature of the dopant ion. The structures of the different phases can be described in terms of V chains, characterized by different extents of V-V dimerization and tilt. The systematic structural evolution of the V chains across the T-M2-R transitions allows us to define microscopic order parameters combining the extents of dimerization and tilt to describe the T-M2 and M2-R phase transitions, which in turn help us establish that the T-M2 transition remains first-order throughout the composition range, contrary to the current belief.

In lithium fluoride (LiF), a self-trapped exciton (STE) forms when a fluoride ion (${\mathrm{F}}^{-}$) leaves its lattice site; the resulting anion vacancy traps the excited electron, becoming an $F$-center, while the displaced ${\mathrm{F}}^{-}$ moves to a nearby interstitial position, pairs with a neighboring fluoride ion to create an ${\mathrm{F}}_2^{-}$ molecular dimer, and localizes the hole as an $H$-center. Because the vacancy and the interstitial dimer sit next to each other, the self-trapped electron and hole remain nearest-neighbor partners. Here we present a comprehensive ab initio study of the structure and dynamics of STEs in LiF, focusing on their formation, stability, and dissociation processes. Using density functional theory with hybrid functionals and a supercell approach, we confirm that the $H$-center within the STE preferentially aligns along the $\langle 111\rangle$ direction, as determined via the Delta self-consistent field method. By employing the nudged elastic band method, we calculate migration barriers and reveal that the hopping barrier for the $H$-center remains nearly constant across different scenarios, including free $H$-center diffusion, the $H$-center orbiting around the $F$-center, and $H$-center separation during STE dissociation. This consistency stems from the weak interaction between the $F$ and $H$-centers in the STE, as indicated by the small energy difference between the STE configuration and the configuration where the $H$-center and the $F$-center are infinitely separated ($\mathrm{\Delta }{E}_{\text{STE-Free}}=0.064$ eV), suggesting that these centers behave almost as free entities after dissociation. Our results demonstrate that STE dissociation is energetically competitive with orbiting events at room temperature, leading to long-lived free electron-hole pairs. These findings provide crucial insights into exciton behavior in LiF, shedding light on the interplay between electronic localization and lattice distortions, which govern its optical and radiation response properties.

The engineering of desired magnetoelectronic properties in artificially created $3d/4d$-based perovskite heterostructures via interfacial exchange coupling and octahedral distortions is an effective strategy for developing high-performance spintronic devices. In this study, we have demonstrated the manipulation of magnetic anisotropy and metal-insulator transition (MIT) in the $4d$-based ferromagnetic metal $\mathrm{SrRu}{\mathrm{O}}_3$ (SRO) by interfacing it with a $3d$-based antiferromagnetic (AFM) orthoferrite $\mathrm{LaFe}{\mathrm{O}}_3$ (LFO). The temperature- and field-dependent magnetization data reveal a systematic enhancement of magnetic anisotropy by increasing the thickness of the AFM LFO layer. Using the Stoner-Wohlfarth model, we have highlighted the pivotal role of interfacial exchange interaction in the development of magnetic anisotropy in the heterostructures. More importantly, magnetotransport measurements reveal a low-temperature upturn in resistivity that can be systematically tuned by varying the thickness of the LFO layer, emphasizing the crucial role of interfacial coupling governed by quantum interference and strong electron-electron interactions (EEIs). By evaluating the quantum correction to the sheet conductance in the two-dimensional limit, it is found that spin-orbit interaction (SOI) dominantly contributes to negative magnetoconductance in the weak field regime via the weak antilocalization effect. We emphasize that the observed MIT might be caused by a change in the oxygen octahedral rotation pattern leading to an alteration of the local hybridization. These results in a $3d/4d$ heterostructure feature the importance of the interfacial buffer layer and open a feasible route to tune the magnetic anisotropy and MIT via interfacial exchange coupling, SOI, and EEI.

The complex magnetic behavior of double-perovskite oxides (${\mathrm{A}}_2{\mathrm{BB}}^{\prime }{\mathrm{O}}_6$) with rare-earth (RE) element A and transition metal (TM) elements B-${\mathrm{B}}^{\prime }$ is determined by the interactions between intra- and interatomic magnetic moments. The peculiar magnetism in these systems stems from the interplay between spin, orbit, and lattice degrees of freedom. This study comprehensively investigates the role of spin-orbit entangled $J_{\text{eff}}=1/2$ moments of the Kramers ion ${\mathrm{Nd}}^{3+}$ on the magnetic ground state of a B-site ordered ferrimagnetic (FiM) double-perovskite oxide, ${\mathrm{Nd}}_2{\mathrm{FeCrO}}_6$. Furthermore, employing microscopic techniques like $\mu \mathrm{SR}$ (muon spin rotation and relaxation) and neutron diffraction, we gained insight into the origin of low-temperature anomalies in the magnetic ground state of the system. The DC magnetization data encompass the first transition at critical temperature $T_{\text{N}}=250$ K, followed by a negative magnetization below 15 K. The temperature-dependent neutron diffraction shows a commensurate magnetic ordering below 250 K, forming a ferrimagnetic ground state, supported by theoretical calculations. In addition, a sharp drop in initial muon asymmetry confirms the transition from a disordered state to a long-range-ordered state at 250 K. Interestingly, the thermal evolution of the dynamic muon spin-relaxation rate (${\lambda }_L$) reveals a transition at two temperatures, at 250 K and $\approx 11$ K, suggesting a low-$T$ ordering at the A site. The heat-capacity data show that ${\mathrm{Nd}}^{3+}$ hosts the ground-state doublet (pseudospin-1/2) at low temperatures. Our analysis of neutron diffraction, heat capacity, and $\mu \mathrm{SR}$ results suggests that the correlation between the ${\mathrm{Nd}}^{3+}$ doublet and the complex interaction between Nd-TM moments gives rise to the observed low-temperature anomaly.

Synthetic Antiferromagnets (SAFs) have gained significant attention in the field of spintronics due to their high precession frequency and small stray field. Surface acoustic waves (SAWs) have been proved to generate spin current via spin-rotation coupling (SRC). In this work, we investigate the spin wave resonance driven by SAWs via SRC in a Py/Ru/Py/Cu compensated SAF with a nearly zero magnetostriction coefficient, which is composed of two ferromagnetic layers with equal thicknesses separated by a thin nonmagnetic Ru spacer layer. We use the Vector Network Analyzer to measure the transmission parameters $S_{21}$ and $S_{12}$ of the SAW devices. By manipulating the magnitude and direction of the external magnetic field H, both acoustic mode and optic mode can be clearly observed, causing a prominent acoustic attenuation that is significantly connected with the frequency of the SAW and the angle between H and the wave vector k of the SAW. Remarkably, the angle dependence of the acoustic attenuation intensity and the transmission nonreciprocity of our devices are substantially different from that caused by Magnetoelastic Coupling. We believe that the findings can promote the further development of magnetoacoustic devices.

Topological phases of matter have been extensively studied in artificial crystals and metamaterials. Recent advances in non-Hermitian topology have revealed unique phenomena such as the non-Hermitian skin effect (NHSE). While spin and valley degrees of freedom (DoFs) have been widely explored, orbital DoFs, which can generate distinct topological effects, remain understudied in non-Hermitian systems, particularly in the context of point-gap topology. Here, we theoretically and numerically investigate the orbital NHSE in a one-dimensional zigzag Su-Schrieffer-Heeger acoustic crystal. We demonstrate the NHSE for both $p_x$ and $p_y$ orbital modes through unidirectional nearest-neighbor couplings and show that the NHSE direction can be reversed by tuning the bonding angle. Furthermore, by introducing third-nearest-neighbor unidirectional couplings, we achieve an orbital bipolar NHSE, where $p_x$ and $p_y$ modes localize at opposite boundaries within the same frequency range. These findings, supported by theoretical calculations and numerical simulations, highlight the unique role of orbital DoFs in non-Hermitian systems and provide new mechanisms for controlling wave localization. Our work paves the way for exploring orbital-induced phenomena in higher-dimensional and multiorbital systems.

Measurement-induced phase transitions (MIPTs) in monitored quantum dynamics are nonequilibrium phase transitions between quantum-chaotic (volume-law entangled) and entanglement-suppressed, area-law phases. Here we reveal how monitored dynamics are situated within the framework of general far-from-equilibrium, quantum condensed-matter physics. Measurement-induced heating effects scramble the distribution function in generic (interacting) monitored fermion systems, and this enables a simplified symmetry-based description of the dynamics. We demonstrate the equivalence of the Keldysh technique with the conventional Statistical-Mechanics Model for circuits, resulting from a doubled Hilbert-space (Choi-Jamiołkowski) mapping. We illustrate this using the monitored dynamics of interacting fermions with a conserved charge, deriving a unified effective-field theory that captures all phases and phase transitions. The noninteracting counterpart in one-dimensional space only has an area-law phase, with no MIPT. This was explained via an effective nonlinear sigma model replica field theory possessing a very large symmetry. We show that other phases and phase transitions emerge when the replica symmetry is reduced by interactions. The reduced symmetry combines a replica permutation symmetry and charge-conservation within each replica. The former and its spontaneous breaking govern the MIPT, which can be recognized via a separatrix in the renormalization-group flow. The replica-resolved charge conservation dictates the “charge-sharpening” transition between two kinds of dynamics, where the global charge information is either hidden or reconstructible from the measurements. The field theory explains why the charge-sharpening transition should occur only in the volume-law phase. Our framework provides a template for other classes of MIPTs and situates these within the arena of nonequilibrium condensed-matter physics.

The ternary gallium-rich ${\mathrm{Y}}_2{\mathrm{Co}}_3{\mathrm{Ga}}_9$-type compound, ${\mathrm{Ce}}_2{\mathrm{Rh}}_3{\mathrm{Ga}}_9$ and its non-$4f$-electron isostructural counterpart ${\mathrm{La}}_2{\mathrm{Rh}}_3{\mathrm{Ga}}_9$ have been successfully synthesized using the conventional arc-melting method. The physical properties were determined by means of x-ray powder diffraction (XRD), magnetic susceptibility $\chi \left(T\right)$, isothermal magnetization $M$($B$), specific heat $C_p\left(T\right)$, electrical resistivity $\rho \left(T\right)$, and thermopower $S$ ($T$) measurements. In addition, a first-principles density functional theory (DFT) investigations have been used to further explore the thermophysical and electron structure properties. The XRD crystal structure determination at room temperature has revealed that both compounds have the orthorhombic ${\mathrm{Y}}_2{\mathrm{Co}}_3{\mathrm{Ga}}_9$-type crystal structure, with the space group Cmcm. $\chi \left(T\right), C_p\left(T\right)$, and $\rho \left(T\right)$ measurements performed in a wide temperature range reveal that ${\mathrm{La}}_2{\mathrm{Rh}}_3{\mathrm{Ga}}_9$ is a weakly interacting, nonmagnetic metal with $\gamma =7.5\mathrm{mJ}/\mathrm{La}\text{−}\mathrm{mol}{\mathrm{K}}^2$. On the other hand, for ${\mathrm{Ce}}_2{\mathrm{Rh}}_3{\mathrm{Ga}}_9$ the same measurements, plus $S$ ($T$) uncover the features usually found in the heavy-fermion Kondo lattice class of materials with a strong impact of the crystal field effect (CEF). The characteristic parameters estimated for this material, such as Kondo temperature and the Sommerfeld coefficient, are respectively $T_K=14.7\mathrm{K}$ and $\gamma =100\mathrm{mJ}/\mathrm{Ce}\text{−}\mathrm{mol}{\mathrm{K}}^2$. Additionally, at low temperatures, the Ce-based compound is found to exhibit the $-\ln T$ behavior of the ratio $C_p\left(T\right)/T$, without exhibiting any phase transition down to 1.9 K. Also, the measurements of $\rho \left(T\right)$ performed down to 0.4 K showed no anomaly that might evidence the presence of a phase transition. Such a low-$T$ logarithmic upturn in specific heat, together with the observed enhancement in the thermodynamic effective mass of the fermionic quasiparticles, as well as an anomalous power law temperature dependence of the $\rho \left(T\right) \sim {\rho }_{\text{el-el}}{T}^{1.5}$ signals Fermi liquid breakdown, likely connected to the presence of a quantum critical point at $T \to 0\mathrm{K}$. The remarkably large values of the slope $S\left(T\right)/T$ have also been noted for the low-$T$ regime.

We use the generalized Bloch theorem formalism of A. Alase et al. [Phys. Rev. Lett. 117, 076804 (2016)] to analyze simple one-dimensional tight-binding lattice systems connected by Hermitian bonds (all with the same hopping parameter $t$), but containing one bond impurity which can be either Hermitian or non-Hermitian. We calculate the band structure, the bulk-boundary correspondence indicator [$D_L\left(\epsilon \right)$], and analyze the eigenvalues of the lattice translation operator ($z$) for each eigenstate. From the $z$ values the generalized Brillouin zone can be reconstructed. If the impurity is Hermitian (and $\mathcal{PT}$-symmetric), then we find a parameter regime in which two localized edge states separate from the tight-binding band. We then simulate a non-Hermitian impurity by keeping hopping in one direction of the bond impurity the same as the rest of the tight-binding system and varying only its reciprocal. Again, we find a region with localized edge states, but in this case the energy eigenvalues are purely imaginary. We also find that in this case the two zero energy eigenvectors coalesce, hence this system is an exceptional line. We then perform an interpolative scan between the above two scenarios and find that there is an intermediate region exhibiting a non-Hermitian skin effect. In this region a macroscopic fraction of states acquire complex energy eigenvalues and exhibit localization toward the impurity. Our numerical results are supported by a detailed analysis of the solutions of the boundary-impurity equation.

While the quantum spin Hall effect leverages two-dimensional topological states to manipulate spin without dissipation, layertronics extends this paradigm to three dimension by enabling control over the layer degree of freedom. Topological materials incorporating screw dislocations exhibit the capability for simultaneous manipulation of both electronic spin and layer degrees of freedom. In this work, the electronic transport properties of a multilayer Kane-Mele model with screw dislocations is studied theoretically. Numerical simulations of a screw dislocation reveal that dissipationless quantum spin Hall edge states propagate not only at the outer boundaries of the structure but also along the screw dislocation itself, working as layer-spin filter. In detail, (i) the spin-up and spin-down carriers starting from the same source layer flow to different drain layers along the topological channels, respectively. (ii) The spin of carriers flowing into a given drain layer is determined by the input source layer. Moreover, we found that the transmission coefficient and spin polarization remain robust against Anderson disorder. Under magnetic disorder, spin flip and backscattering occur, suppressing the transmission coefficient while maintaining nearly unchanged spin polarization. Finally, the layer- and spin-resolved transport properties in a device with two screw dislocations are investigated as well. We have developed an innovative methodology to modulate electron transport with simultaneous layer and spin resolution.

Phononic higher-order topology has been discovered in several crystalline materials in recent years. However, studies on the properties related to applications of phonon higher-order topological states, especially their transport characteristics, remain scarce. In this work, we demonstrate the existence of phononic higher-order topological phases characterized by fractional quadrupole topological numbers in AB-stacked bilayer $2\mathrm{H}\text{−}{\mathrm{MoTe}}_2$ ($\mathrm{AB}\text{−}2\mathrm{H}\text{−}{\mathrm{MoTe}}_2$) and AB-stacked bilayer $2\mathrm{H}\text{−}{\mathrm{WTe}}_2$ ($\mathrm{AB}\text{−}2\mathrm{H}\text{−}{\mathrm{WTe}}_2$). Phononic topological corner states are found in nanodisks of $\mathrm{AB}\text{−}2\mathrm{H}\text{−}{\mathrm{MoTe}}_2$ and $\mathrm{AB}\text{−}2\mathrm{H}\text{−}{\mathrm{WTe}}_2$. Using the nonequilibrium Green's function method, we calculate the phonon transmission spectra near the frequencies of corner states and reveal that transmission peaks emerge when the frequencies between incident phonons and corner states match, indicating that the phonon topological corner states can serve as efficient transmission channels. Our work deepens the understanding of phononic higher-order topology and provides theoretical support for future applications of higher-order topological phases.

Sixteen second-order Raman modes of monolayer ${\mathrm{MoSe}}_2$ are observed and analyzed by experiment and calculation, respectively, for four laser energies from 2.33–2.60 eV. The Raman peaks labeled by ${\mathrm{P}}_i$ ($i=1,2,3,4$) at $280\text{–}320{\mathrm{cm}}^{-1}$ and ${\mathrm{S}}_i$ ($i=1,2,3$) at $400\text{–}480{\mathrm{cm}}^{-1}$ are newly analyzed quantitatively by the first-principles calculation using qr²-code. The ${\mathrm{P}}_i$ bands are assigned to the second-order combination modes of TA (LA) and ${\mathrm{E}}_{\mathrm{TO}}^{\prime }\left({\mathrm{E}}_{\mathrm{LO}}^{\prime }\right)$, while the ${\mathrm{S}}_i$ bands are assigned to the 2LA mode with different phonon wave vectors, which is explained by the combination of two-phonon density of states and electron-phonon coupling calculations. The overlapped Raman peak of the first-order mode ${\mathrm{E}}^{\prime }$ and the second-order mode ${\mathrm{S}}_1$ can be identified separately using helicity-dependent Raman spectroscopy. The mode assignments are further confirmed by space-group analysis and helicity-dependent selection rule.