We report an experimental study of carrier density ($n$), displacement field, and twist angle (θ) dependence of temperature ($T$)-linear resistivity in twisted double-bilayer graphene (TDBG). For a large twist angle ($\theta >1.5^{\circ }$) where correlated insulating states are absent, we observe a $T$-linear resistivity (with a slope on the order of $\sim 10\mathrm{\Omega }/\mathrm{K}$) over a wide range of carrier densities, and its slope decreases with increasing $n$, which is in agreement with the acoustic phonon scattering model semiquantitatively. The slope of $T$-linear resistivity is nonmonotonically dependent on the displacement field with a single peak structure. For a device with $\theta \sim 1.{23}^{\circ }$ at which correlated states emerge, the slope of $T$-linear resistivity is found to be a maximum ($\sim 100\mathrm{\Omega }/\mathrm{K}$) at the boundary of the halo structure where phase transition occurs, with signatures of continuous phase transition, Planckian dissipation, and diverging effective mass. These observations are in line with quantum critical behaviors, which might be due to symmetry-breaking instability at the critical points. Our results shed new light on correlated physics in TDBG and other twisted moiré systems.

A theory is developed to describe the singlet dark state (usually labeled $S_1$ or $2A_g$) of polyenes and carotenoids. The properties of this state explain the nonemissive properties of linear polyenes, it is responsible for the photoprotection properties of carotenoids in light harvesting complexes, and because of its triplet-pair character, it is thought to be the cause of singlet fission in polyene-type systems. The theory described here assumes that in principle this state is a linear combination of singlet triplet-pairs and a singlet charge-transfer exciton. Crucially, these components only couple when the triplet pair occupies neighboring C-C dimers, such that an electron transfer between the triplets creates a nearest-neighbor singlet charge-transfer excitation. This local coupling stabilizes the $2A_g$ state and induces a nearest-neighbor attraction between the triplets. In addition, because of the electron-hole Coulomb attraction in the exciton, the increased probability that the electron-hole pair occupies neighboring dimers enhances the triplet-triplet attraction: the triplet pair is “slaved” to the singlet exciton. The theory also predicts that as the Coulomb interaction is increased, the $2A_g$ state evolves from a predominately charge-transfer exciton with a small component of triplet-pair character to a state predominately composed of a triplet pair with some exciton character. Above a critical Coulomb interaction there is a decoupling of the triplet-pair and exciton subspaces, such that the $2A_g$ state becomes entirely composed of unbound spin-correlated triplet pairs. The predictions of this theory of a triplet-pair binding energy in carotenoids of ca. 0.4 eV are consistent with density matrix renormalization group calculations of the Pariser-Parr-Pople (or extended Hubbard) model. It also predicts that the single-triplet component of the $2A_g$ state in carotenoids is ca. 50%.

We present a study of the nonlinear optical response of twisted bilayer graphene. We discuss the contribution of the Berry phase to the nonlinearity when inversion symmetry is broken, thus underlining the interplay between band and real-space geometry, and nonlinear response. We also highlight an effect that is characteristic of extreme nonlinear optics, namely the generation of harmonics in disguise. This effect emerges in twisted bilayer graphene at relatively moderate field strengths because of the much reduced bandwidth. Our findings contribute to the understanding of the link between geometry and optical properties, as well as of the extreme nonlinear optical regime in twisted bilayer graphene.

Machine-learning generative methods for material design are constructed by representing a given chemical structure, either a solid or a molecule, over appropriate atomic features, generally called structural descriptors. These must be fully descriptive of the system, must facilitate the training process, and must be invertible, so that one can extract the atomic configurations corresponding to the output of the model. In general, this last requirement is not automatically satisfied by the most efficient structural descriptors, namely the representation is not directly invertible. Such a drawback severely limits our freedom of choice in selecting the most appropriate descriptors for the problem, and thus our flexibility to construct generative models. In this paper, we present an optimization method capable of inverting the local many-body descriptors of the chemical environment, back to a Cartesian representation. This is not a global inversion scheme, but it allows one to find the Cartesian representation of variations of known structures, such as those produced by molecular distortions. The algorithm, which is implemented together with the bispectrum representation, is demonstrated for a number of molecules with different bonding structures and atomic species. The scheme presented here thus represents a convenient approach to the local inversion of structural descriptors, enabling the construction of structural generative models.

Valley-related multiple Hall effect in two-dimensional (2D) lattice is a fundamental transport phenomenon in the fields of condensed matter physics and materials science. Most proposals for its realization are limited to toy models or extrinsic effects. Here, based on a tight-binding model and first-principles calculations, we report the discovery of intrinsic valley-related multiple Hall effect in the 2D organometallic lattice of NbTa-benzene. Protected by the breaking of both time-reversal and inversion symmetry, NbTa-benzene exhibits large valley polarization spontaneously in both the conduction and valence bands, guaranteeing the anomalous valley Hall effect. Simultaneously, because of the exchange interaction and strong spin-orbit coupling, intrinsic band inversion occurs at one valley, which ensures the valley-polarized quantum anomalous Hall (QAH) effect, thus presenting the extraordinary valley-related multiple Hall effect in nature. In addition, it can be transformed into the phase with a ferrovalley or the QAH effect solely through strain engineering. These insights are not only useful for the fundamental research in valley-related physics but also enable a wide range of device applications.

Usually the Josephson current is driven by the superconducting phase difference $\phi$ between two superconducting leads. Here we propose an anomalous Josephson current between two Majorana nanowires, which can be driven by both the superconducting phase difference $\phi$ and the orientation difference $\varphi$ between the Zeeman fields in two Majorana wires. We show that the orientation of the Zeeman field acts as an effective superconducting phase under appropriate conditions, which provides a new signature of Majorana zero modes. Due to the presence of Majorana zero modes, the anomalous Josephson current is $4\pi$ periodic in both $\phi$ and $\varphi$. When both $\phi$ and $\varphi$ are periodically varying, we predict the existence of peaks in the average Josephson current, which are the analog to Shapiro steps in the ac Josephson effect. Similarly, the existence of Majorana zero modes can be confirmed by the missing of odd peaks. The findings provide a scheme to experimentally verify the $4\pi$-periodic Josephson effect, as well as a platform to realize the anomalous Josephson junction.

We study the anomalous Hall effect on the antiferromagnetic coloring-triangular lattice with a coplanar magnetic configuration in the presence of a spin-orbit interaction. The effect of the spin-orbit coupling is included at an effective level as a rotation of the electronic spin as the electrons hop from site to site. Our result reveals that a finite Hall conductivity in the planar ${120}^{\circ }$ structure takes place if a finite spin-orbit coupling is present. A quantized Hall conductivity occurs at global band gaps resulting from the topologically nontrivial band structure.

We compute the resistivity anisotropy in the nematic phase of FeSe from the static solution of the multiorbital Boltzmann equation. By introducing disorder at the level of the microscopic multiorbital model we show that even elastic scattering by localized impurities may lead to nontrivial anisotropic renormalization of the electronic velocities, challenging the usual understanding of transport based only on cold- and hot-spots effects. Our model takes into account both the $xz/yz$ and the recently proposed $xy$ nematic ordering. We show that the latter one has a crucial role in order to reproduce the experimentally measured anisotropy, providing a direct fingerprint of the different nematic scenarios on the bulk transport property of FeSe.

We report the numerical discovery of a Luther-Emery liquid with pair-density-wave (PDW) correlations from doping either (i) a spin-one Haldane chain or (ii) a two-leg ladder in the rung-singlet phase in which the doped charges occupy a single leg. We model these systems using a generalized Kondo model. The itinerant electrons are correlated and described by the $t\text{−}J$ model, and are further coupled to a spin-$1/2$ Heisenberg model through the Kondo coupling $J_K$. When the density of electrons $x$ is one, the Mott insulator is in a Haldane phase or in a rung-singlet phase depending on whether $J_K$ is negative or positive. Upon doping, a pair-density-wave with $\mathbf{Q}=\pi$ can emerge for both signs of $J_K$. In the $J_K\to -\infty$ limit, the model reduces to the recently proposed type II $t-J$ model. We also identify a composite order parameter for the superconductor, which can be understood as a Cooper pair formed by two nearby fermionic spin-polarons. Our model and the predicted PDW phase can be experimentally realized by doping $S=1$ chains formed by ${\mathrm{Ni}}^{2+}$ in a solid-state system or a two-leg ladder of fermionic cold atoms with a potential bias between legs, which preferentially dopes carriers into a single leg. Long-range order of the PDW can be achieved in quasi-one-dimensional system with finite interwire coupling.

The PXP model is paradigmatic in the field of quantum many-body scars. This model has a number of zero-energy eigenstates that is exponentially large in system size. Lower bounds on the number of zero-energy eigenstates are obtained for both open and periodic (zero- and $\pi$-momentum sectors) boundary conditions. These bounds are found to be tight up to system sizes accessible by numerical exact diagonalization and can be expected to be tight in general. In addition to previous results, separate lower bounds are obtained for the spatial inversion-symmetric and inversion-antisymmetric symmetry sectors. Furthermore, the derivations improve on previous ones as they are free of assumptions.

The recent higher-order topological insulators (HOTIs) encoded with the tight-binding model (TBM) have been demonstrated beyond traditional bulk-edge correspondence, which shows the exotic capability of sound manipulation. However, the current waveguide resonator model with weak tunability in hopping controls has been used as the most common method to construct the TBM directly in a realistic acoustic system. Here, we present another carrier and methodology to realize the TBM based on split-ring resonators (SRRs) coupling in a realistic physical platform and construct a second-order topological insulator (SOTI) based on it, where the hopping and frequencies of the topological corner states can be easily tuned by adjusting the coupling strength of the SRRs. Numerical analysis and experimental measurement demonstrated zero-dimensional topological corner states in this acoustic resonant system. The findings provide a more flexible method for tunable acoustic HOTIs realization.

The ab initio electromagnetic theory of Fano resonances in resonant plasmonic nanostructures and metamaterials, developed by Gallinet and Martin [Phys. Rev. B 83, 235427 (2011)], is generalized to the case of double Fano resonances. A system is considered in which two uncoupled nonradiative modes interfere with a broad radiative mode driven by incident electromagnetic radiation. Feshbach-Fano partitioning formalism is employed to recover the formula for the double Fano resonance spectral line shape suggested by Fano phenomenologically in his original work, and derive the exact microscopic expressions for the parameters governing the optical response of the system.

Acoustic phonons have recently been posited as playing an integral role in explaining the half-quantized thermal Hall effect in $\alpha \text{−}{\mathrm{RuCl}}_3$. Therefore, we present much needed inelastic x-ray scattering measurements of its acoustic phonon dispersion, along with calculations using the frozen-phonon method. We also discuss a temperature study which conclusively shows a first-order structural transition to a non-$C2/m$ space group at low temperature. Together these results are an important backbone for future theoretical and experimental studies of $\alpha \text{−}{\mathrm{RuCl}}_3$.

Composite fermions (CFs), exotic quasiparticles formed by pairing an electron and an even number of magnetic flux quanta, emerge at high magnetic fields in an interacting electron system, and can explain phenomena such as the fractional quantum Hall state (FQHS) and other many-body phases. CFs possess an effective mass $\left(m_{\text{CF}}\right)$ whose magnitude is inversely related to the most fundamental property of a FQHS, namely its energy gap. We present here experimental measurements of $m_{\text{CF}}$ in ultrahigh quality two-dimensional electron systems confined to GaAs quantum wells of varying thickness. An advantage of measuring $m_{\text{CF}}$ over gap measurements is that mass values are insensitive to disorder and are therefore ideal for comparison with theoretical calculations, especially for high-order FQHS. Our data reveal that $m_{\text{CF}}$ increases with increasing well width, reflecting a decrease in the energy gap as the electron layer becomes thicker and the in-plane Coulomb energy softens. Comparing our measured masses with available theoretical results, we find significant quantitative discrepancies, highlighting that more rigorous and accurate calculations are needed to explain the experimental data.

We analytically derived an explicit condition for high-contrast plasmonic modulation and switchable routing in coupled graphene waveguides consisting of two coupled gated graphene sheets sandwiching a gyrotropic medium. The analytical condition intuitively predicts that by manipulating the graphene chemical potential and the gyration of the in-between medium we can combine robustness of the plasmonic routing to the deviation of design and material parameters due to imperfect fabrication and harsh environment with the extreme high contrast. Also, it predicts broadband tunability of the high-contrast plasmonic routing. The intuitive analytical condition reveals that the high contrast is achievable at a resonance gyration due to a magnetic resonance of nonreciprocal directional coupling. The magnetic resonance of nonreciprocity breaks a currently held preconception that the stronger magnetic field induces the stronger magnetically induced nonreciprocity. Numerical simulations demonstrate the robustness of the magnetic resonance of nonreciprocity and its tunability over a one-octave spanning spectral range. In practice, the chemical potential and the gyration can be manipulated by controlling the gate voltage of the graphene and the external magnetic field, respectively. Our findings would provide a robust and broadband tunable tool for high-contrast plasmonic modulator and switchable router and for probing of ultrafast magnetization dynamics.

We consider the fate of the Wigner crystal state in a two-dimensional system of massive Dirac electrons as the effective fine structure constant $\alpha$ is increased. In a Dirac system, larger $\alpha$ naively corresponds to stronger electron-electron interactions, but it also implies a stronger interband dielectric response that effectively renormalizes the electron charge. We calculate the critical density and critical temperature associated with quantum and thermal melting of the Wigner crystal state using two independent approaches. We show that at $\alpha \gg 1$, the Wigner crystal state is best understood in terms of logarithmically interacting electrons, and that both the critical density and the melting temperature approach a universal, $\alpha$-independent value. We discuss our results in the context of recent experiments in twisted bilayer graphene near the magic angle.

We develop an analytic model for an ideal polyyne ring which describes the induced terahertz (THz) gap in the molecular spectrum due to the Stark effect. This simple model can also be used to describe an odd-dimered cyclocarbon which has undergone a spontaneous symmetry-breaking event (due to the Jahn-Teller effect) as an effective dipole across an ideal ring. We show that both the size of the gap and the strength of optical transitions across it can be modulated by varying the external electric field strength. A THz emission scheme based on optical excitation is proposed, thus paving the way for tunable THz emitters based on $\mathrm{cyclo}\left[n\right]\mathrm{carbon}$.