Phase transitions with lowering temperature are a manifestation of decreased entropy and within the Landau theoretical framework these are accompanied by the symmetry breaking. Whenever a symmetry is broken weakly or strongly, it leaves its trail and the same may be captured indirectly using renormalization of the quasiparticle excitations. $\mathrm{C}{\mathrm{r}}_2\mathrm{G}{\mathrm{e}}_2\mathrm{T}{\mathrm{e}}_6$, a quasi-two-dimensional magnetic material, provides a rich playground to probe dynamics of the quasiparticle excitations as well as multiple phase transitions with lowering temperature intimately linked with the lattice and spin degrees of freedom. Here, we report in-depth inelastic light scattering measurements on single crystals of $\mathrm{C}{\mathrm{r}}_2\mathrm{G}{\mathrm{e}}_2\mathrm{T}{\mathrm{e}}_6$ as a function of temperature, from 6 to 330 K, and polarization. Our measurements reveal the long as well as short range ordering of the spins below $T_c$ ($\sim 60$ K) and $T^{*}$ ($\sim 180$ K), respectively; setting the stage for broken rotational and time reversal symmetry, gauged via the distinct renormalization of the phonon self-energy parameters along with the mode's intensity. Our measurements also uncovered an intriguing dependence of the interaction strength between discrete state (phonon here) and the underlying continuum, quantified using the Fano asymmetry parameter, as a function of the scattered light polarization. Our results suggest the possibility of tuning the interaction strength using controlled scattered light and symmetry in this 2D magnet.

The discovery of superconductivity in electrides, where partial electrons are localized in lattice interstices, labeled as interstitial anionic electrons (IAEs), introduces a different category known as electride superconductors. Understanding the role of IAEs in electron-phonon coupling (EPC) is crucial for the development of electride superconductors. In this study, we demonstrate that an increased net charge of IAEs enhances EPC in 12 $\mathrm{L}{\mathrm{i}}_8{\mathrm{H}}_n$ ($n=4–7$) electrides, exhibiting cubic/tetragonal symmetry and diverse IAEs topologies. First-principles calculations reveal a nearly linear rise in the EPC constant with the net charge of IAEs. This increase stems from the excitation effect of IAEs on Li $2p$ electrons and their collaborative involvement in the formation of Cooper pairs, facilitated by Li-derived low/medium-frequency phonons. This mechanism is prominently illustrated in $Pm\text{−}3m \mathrm{L}{\mathrm{i}}_8{\mathrm{H}}_4$, featuring a $T_{\mathrm{c}}$ of 40.3 K, where Li atoms exhibit compressing and stretching vibrations, inducing IAEs dimerization and the strongest local EPC interaction. Conversely, hydrogen atoms in $\mathrm{L}{\mathrm{i}}_8{\mathrm{H}}_n$ electrides primarily regulate the net charge and topology of IAEs. Our findings bear significant implications for the advancement of electride superconductors.

Exceptional points (EPs) have been widely studied in quantum mechanics, condensed-matter physics, optics, and photonics. However, their potential in acoustics has only recently been recognized due to the rapid development of acoustic metamaterials. This paper proposes a method for achieving EP conditions in acoustic resonators by lowering their symmetry and enabling resonant-mode interaction. The formation of EPs is predicted through direct numerical simulation supported by coupled-mode theory and resonant state expansion. These findings have significant implications for the design and optimization of acoustic metamaterials for applications such as acoustic sensing and noise reduction.

Liouville theorem (L theorem) reveals robust incompressibility of the distribution function in phase space, given arbitrary potentials. However, its quantum generalization, Wigner flow, is compressible, i.e., L theorem is only conditionally true (e.g., for perfect Harmonic potential). We develop quantum L theorem (rigorous incompressibility) for arbitrary potentials (interacting or not) in Hamiltonians. Haar measure, instead of symplectic measure $dp\wedge dq$ used in Wigner's scheme, plays a central role. The argument is based on general measure theory, independent of specific spaces or coordinates. Comparison of classical and quantum is made: for instance, we address why Haar measure and metric preservation do not work in the classical case. Applications of the theorems in statistics, topological phase transition, ergodic theory, etc., are discussed.

We investigate the Andreev reflection in a normal metal/charge-$4e$ superconductor junction. Compared with the electron-hole conversion in normal charge-$2e$ superconductors, here four electrons participate simultaneously, enriching the possibility of conversion ways. Using the nonequilibrium Green's function method, we obtain a four-particle-type Landauer-Büttiker formula with generalized charge-$4e$ anomalous Green's function to describe it. We then calculate and clarify the behavior of the Andreev coefficient and the conductance contributed by it, showing features like the unconventional position of the peak structure and the emerging plateau inside the superconducting gap. Our research makes up the blank of research for transport property of charge-$4e$ superconductors and can serve as a hallmark for future experimental verifications.

The existence of bound states induced by local impurities coupled to an insulating host depends decisively on the global topological properties of the host's electronic structure. In this context, we consider magnetic impurities modeled as classical unit-length spins that are exchange coupled to the spinful Haldane model on the honeycomb lattice. We investigate the spectral flow of bound states with the coupling strength $J$ in both the topologically trivial and Chern-insulating phases. In addition to conventional $k$-space topology, an additional, spatially local topological feature is available, based on the space of impurity-spin configurations forming, in case of $R$ impurities, an $R$-fold direct product of two-dimensional spheres. Global $k$-space and local $S$-space topology are represented by different topological invariants, the first ($k$-space) Chern number and the $R\mathrm{th}$ ($S$-space) spin-Chern number. We demonstrate that there is a local $S$-space topological transition as a function of $J$ associated with a change in the spin-Chern number and work out the implications of this for the $J$-dependent local electronic structure close to the impurities and, in particular, for in-gap bound states. The critical exchange couplings' dependence on the parameters of the Haldane model, and thus on the $k$-space topological state, is obtained numerically to construct local topological phase diagrams for systems with $R=1$ and 2 impurity spins.

Kagome materials have recently drawn great attention due to the interplay between nontrivial band topology, electron correlations, and Van Hove singularities related many-body orders. Here we report three new vanadium-based kagome metals, ${\mathrm{TiV}}_6{\mathrm{Sn}}_6$, ${\mathrm{ZrV}}_6{\mathrm{Sn}}_6$, and ${\mathrm{HfV}}_6{\mathrm{Sn}}_6$, and conduct a comprehensive investigation of their structural, magnetic, and electrical transport properties. All three compounds exhibit large unsaturated magnetoresistances and multiband Hall effects at low temperatures, indicating the existence of multiple highly mobile carriers. Both the diagonal and off-diagonal resistivity show quantum oscillations with nontrivial Berry phases and high quantum mobilities. First-principles calculations together with quantum oscillation analyses suggest the Van Hove singularities at the $M$ point for the three compounds all located in close vicinity of the Fermi level, and there also exist multiple topological nontrivial band crossings, including a nodal ring and a massive Dirac cone. Our work extends the kagome ${AM}_6{\mathit{\text{X}}}_6$ family and paves the way for searching possible Van Hove physics in the V kagome lattice.

We investigate the crossover from an ordinary Van Hove singularity (OVHS) to a higher order Van Hove singularity (HOVHS) in a model applicable to Bernal bilayer graphene and rhombohedral trilayer graphene in a displacement field. At small doping, these systems possess three spin-degenerate Fermi pockets near each Dirac point $K$ and $K^{\prime }$; at larger doping, the three pockets merge into a single one. The transition is of Lifshitz type and includes Van Hove singularities. Depending on system parameters, there are either three separate OVHS or a single HOVHS. We model this behavior by a one-parameter dispersion relation, which interpolates between OVHS and HOVHS. In each case, the diverging density of states triggers various electronic orders (superconductivity, pair density wave, valley polarization, ferromagnetism, spin, and charge density wave). We apply parquet renormalization group (pRG) technique and analyze how the ordering tendencies evolve between OVHS and HOVHS. We report rich system behavior caused by disappearance/reemergence and pair production/annihilation of the fixed points of the pRG flow.

Recent findings indicate that orbital angular momentum (OAM) has the capability to induce the intrinsic orbital Hall effect (OHE), which is characterized by orbital Chern number in the orbital Hall insulator. Unlike the spin-polarized channel in the quantum anomalous Hall insulator, the OAM is valley locked, posing challenges in manipulating the corresponding edge state. Here we demonstrate the sign-reversal orbital Chern number through strain engineering by combing the $k·p$ model and first-principles calculation. Under the manipulation of strain, we observe the transfer of nonzero OAM from the valence band to the conduction band, aligning with the orbital contribution in the electronic structure. Our investigation reveals that electrons and holes with OAM exhibit opposing trajectories, resulting in a reversal of the orbital Hall conductivity. Furthermore, we explore the topological quantum state between the sign-reversible OHE.

Experimental observations of anisotropic tightly bound excitons in black phosphorene, and correlated phenomena such as room-temperature magnetically active edges in phosphorene nanoribbons (PNRs), sparked discussions on the controversial screening of the Coulomb interaction in phosphorene-based materials. In this way, we investigate the first-principles electronic screening of the long-range Coulomb interaction in black phosphorene from bulk to nanoribbon by employing ab initio calculations in conjunction with the constrained random-phase approximation. The bands near the Fermi energy ($E_F$) are predominantly $p_z$ orbital characters, and due to the puckering, they are not well separated from the other bands with $s, p_x$, and especially $p_y$ characters. This proximity in energy levels increases the contribution of $p_x/p_y\to p_z$ transitions to the polarization function and significantly alters the Coulomb parameters. In semiconducting systems, the on-site Coulomb interaction values (Hubbard $U$) range from 4.1 to 6.5 eV and depend on the correlated subspace, electronic structure, nanoribbon's width, and edge passivation. We find an anisotropic behavior of long-range Coulomb interaction along the zigzag and armchair directions in black phosphorene at the static limit. Our long-range interaction has revealed a nonconventional screening in semiconducting nanoribbons. We have discovered that screening actually enhances the electron-hole interaction for separations larger than a critical distance $r_c$, which is contrary to what was previously seen in conventional semiconductors. This unique “antiscreening” region helps to explain the large experimentally extrapolated exciton binding energies of PNRs. In unpassivated zigzag nanoribbons, due to a metallic screening channel stemming from quasi-flat-edge bands at $E_F$, we find $U/W_b>1$ (the bandwidth $W_b$) and large gradient of intersite Coulomb interactions, making them correlated materials. We have investigated the instability of the paramagnetic state of bare zigzag PNRs toward ferromagnetism using a Stoner model based on the calculated Hubbard $U$ parameters.

A model for the effective permittivity of a doped single-walled carbon nanotube (CNT) thin film in the optical range is proposed. The permittivity of CNT walls is calculated from the quantum theory of $\pi$-electron transitions. The contributions from $\sigma$ electrons and ultraviolet $\pi$ plasmon are taken into account phenomenologically using experimental data obtained for graphene and CNT film. These contributions lead to an enhancement of the depolarization effect thereby strongly suppressing the transverse response of the CNTs. They also cause a decrease in both the frequency and height of the absorption peak associated with the azimuthal intersubband plasmon in doped CNTs. This eliminates the existing discrepancy between experimental and previous theoretical data. The azimuthal plasmon response is studied in a bundle of doped CNTs.

The intrinsic superlattice magnetic topological insulators of ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$(${\mathrm{Bi}}_2{\mathrm{Te}}_3{)}_n$ ($n=0,1,2...$) provides a promising material platform for the realization of diverse exotic topological quantum states, such as quantum anomalous Hall effect and axion-insulator state. All these quantum states are sensitively dependent on the complex interplay and intertwinement of their band topology, magnetism, and defective structural details. Here, we report a comprehensive real-space investigation on the magnetic ordering states of ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$(${\mathrm{Bi}}_2{\mathrm{Te}}_3{)}_n$ using cryogenic magnetic force microscopy. The ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$(${\mathrm{Bi}}_2{\mathrm{Te}}_3{)}_n$ crystals exhibit a distinctive magnetic evolution from A-type antiferromagnetic to ferromagnetic states via the increased ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ intercalation layers. The magnetic field- and temperature-dependent phase evolution behaviors of ${\mathrm{MnBi}}_6{\mathrm{Te}}_{10}$ and ${\mathrm{MnBi}}_8{\mathrm{Te}}_{13}$ are comparatively investigated to obtain the complete $H-T$ phase diagrams. The combination impact of the intrinsic and defect-mediated interlayer coupling on their magnetic states were further discussed. Our results pave a possible way to realize more exotic quantum states via the tunable magnetic configurations in the artificial-stacking ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$(${\mathrm{Bi}}_2{\mathrm{Te}}_3{)}_n$ multilayers.

Revealing the fine electronic structure is critical for understanding the underlying physics of low-dimensional materials. Angle-resolved photoemission spectroscopy (ARPES) is a powerful experimental technique for mapping out the experimental electronic structure. By reducing the photon energy (e.g., to 6 eV) using laser sources, a greatly improved momentum resolution can be achieved, thereby providing opportunities for “zooming in” the fine electronic structure and even revealing the previously unresolvable bands near the Brillouin zone center. Here, by using quasi-one-dimensional material CuTe as an example, we demonstrate the unique capability of laser-based ARPES in revealing the fine electronic structures of “hidden” charge density wave induced shadow bands near the Brillouin zone center, which are previously unresolvable using synchrotron light sources. The observation of the shadow bands reveals the CDW phase from the aspect of band folding, and the unpredicted CDW band hybridization strongly modifies the electronic structure and Fermi surface, which suggests that such hybridization must be taken into account for studying the CDW transition. Moreover, the ultrafast nonequilibrium carrier dynamics are captured by time-resolved ARPES, revealing the relaxation dynamics through electron-phonon scattering. Our work demonstrates the advantages of laser-based ARPES in zooming in the fine electronic structures, as well as capturing the ultrafast dynamics of low-dimensional materials.

The normal-conducting state of the superconductor ${\mathrm{UTe}}_2$ is studied by entropy analysis for magnetic fields along the $b$ axis, obtained from magnetization using the relation ${(\partial M/\partial T)}_B={(\partial S/\partial B)}_T$. We observe a strong increase in entropy with magnetic field due to metamagnetic (MM) fluctuations (spatially uniform, $Q=0$). The field dependence is well described by the Hertz-Millis-Moriya theory for quantum criticality of itinerant MM. Notably, the lower bound of the quantum-critical region coincides well with the position of the minimum in the superconducting transition temperature $T_c\left(B\right)$. Hence, our results suggest that $Q=0$ fluctuations reinforce the superconductivity.

The discovery of hybrid-order topological insulators (TIs), where the first- and second-order topologies are obtained independently in different complete band gaps, further refines the classification of topological phases. In the electronic system, simultaneous measurements of the edge and corner states in two complete bulk gaps are difficult due to the fermionic band filling. In this paper, we demonstrate a non-Hermiticity-induced acoustic hybrid-order TI, incorporating on-site losses within the two-dimensional anisotropic Su-Schrieffer-Heeger (SSH) model. The robust one-dimensional edge states and zero-dimensional corner states are observed independently in different bulk band gaps. Interestingly, by taking advantage of the mutual effect between on-site non-Hermiticity and coupling anisotropy, the corner states are always captured in the middle bulk bandgap, and the directions of edge states are controllable in multiband. Our work provides a route to design the acoustic devices with multifrequency and multidirectional sound transport, and paves the way to explore various exotic non-Hermiticity-induced topological phases.

We calculate the thermal Hall conductivity ${\kappa }_{xy}$ for the columnar valence bond solid phase of a two-dimensional frustrated antiferromagnet. In particular, we consider the square lattice spin-$1/2J_1\text{−}{J}_2$ antiferromagnetic Heisenberg model with an additional Dzyaloshinskii-Moriya interaction between the spins and in the presence of an external magnetic field. We concentrate on the intermediate parameter region of the $J_1\text{−}{J}_2$ model, where a quantum paramagnetic phase is stable, and consider a Dzyaloshinskii-Moriya vector pattern associated with the couplings between the spins in the ${\mathrm{CuO}}_2$ planes of the ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_6$ compound. We describe the columnar valence bond solid phase within the bond-operator formalism, which allows us to map the Heisenberg model into an effective interacting boson model written in terms of triplet operators. The effective boson model is studied within the harmonic approximation, and the triplon excitation bands of the columnar valence bond solid phase are determined. We then calculate the Berry curvature and the Chern numbers of the triplon excitation bands and, finally, determine the thermal Hall conductivity due to triplons as a function of the temperature. We find that the Dzyaloshinskii-Moriya interaction yields a finite Berry curvature for the triplon bands, but the corresponding Chern numbers vanish. Although the triplon excitations are topologically trivial, the thermal Hall conductivity of the columnar valence bond solid phase in the square lattice antiferromagnet is finite at low temperatures. Our results complement a previous study by Samajdar et al., Phys. Rev. B 99, 165126 (2019) concerning the thermal Hall effect due to spinons of a spin-liquid phase on a square lattice. We also comment on the relations of our results with a no-go condition for a thermal Hall effect previously derived for ordered magnets by Katsura et al., Phys. Rev. Lett. 104, 066403 (2010).

The lacunar spinel ${\mathrm{GaNb}}_4{\mathrm{Se}}_8$ is a tetrahedral cluster Mott insulator where spin-orbit coupling on molecular orbitals and Jahn-Teller energy scales are competitive. ${\mathrm{GaNb}}_4{\mathrm{Se}}_8$ undergoes a structural and antipolar ordering transition at ${\mathrm{T}}_Q=50$ K that corresponds to a quadrupolar ordering of molecular orbitals on ${\mathrm{Nb}}_4$ clusters. A second transition occurs at ${\mathrm{T}}_M=29$ K, where local distortions on the ${\mathrm{Nb}}_4$ clusters rearrange. We present a single crystal x-ray diffraction investigation for these phase transitions and solve the crystal structure in the intermediate $T_M<T<T_Q$ and low $T<T_M$ temperature phases. The intermediate phase is a primitive cubic $\mathrm{P}{2}_{1}3$ structure with a staggered arrangement of ${\mathrm{Nb}}_4$ cluster distortions. A symmetry mode analysis reveals that the transition at ${\mathrm{T}}_Q$ is continuous and described by a single Jahn-Teller active distortion mode. In the low temperature phase, the symmetry of ${\mathrm{Nb}}_4$ clusters is further reduced and a staggered arrangement of intercluster dimers is formed, suggesting a valence bond solid magnetic state.