The one-dimensional Mott metal-insulator transition is a typical strong correlation effect triggered by the Umklapp scattering. However, in a physical system, the Umklapp scattering coexists with the normal scattering, including both forward and backward scattering, which conserves the total momentum of scattered electrons. Therefore, it is not easy to quantify the contribution of the Umklapp scattering in a Mott metal-insulator transition. To resolve this difficulty, we propose to explore these scattering processes separately. We study the contribution of each scattering process in the one-dimensional Hubbard model using the momentum-space density-matrix renormalization group (kDMRG) and bosonization methods. Our kDMRG calculation confirms that the Mott charge gap results from the Umklapp scattering, but the normal scattering processes strongly renormalize its value. Furthermore, we present a scaling analysis of the Mott charge gap in the bosonization theory and show that the interplay between the Umklapp and forward scattering dictates the charge dynamics in the half-filled Hubbard model.

Arrays of Rydberg atoms in the blockade regime realize a wealth of strongly correlated quantum physics, but theoretical analysis beyond the chain is rather difficult. Here we study a tractable model of Rydberg-blockade atoms on the square ladder with a ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ symmetry and at most one excited atom per square. We find $D_4$, ${\mathbb{Z}}_2$, and ${\mathbb{Z}}_3$ density-wave phases separated by critical and first-order quantum phase transitions. A noninvertible remnant of $U\left(1\right)$ symmetry applies to our full three-parameter space of couplings, and its presence results in a larger critical region as well as two distinct ${\mathbb{Z}}_3$-broken phases. Along an integrable line of couplings, the model exhibits a self-duality that is spontaneously broken along a first-order transition. Aided by numerical results, perturbation theory, and conformal field theory, we also find critical ${\mathrm{Ising}}^2$ and three-state Potts transitions, and provide good evidence that the latter can be chiral.

Despite much experimental and theoretical work, the nature of the charge order in the kagome metals belonging to the family of materials ${A\text{V}}_3{\mathrm{Sb}}_5$ ($A=\text{Cs,Rb,K}$) remains controversial. A crucial ingredient for the identification of the ordering in these materials is their response to external perturbations, such as strain or magnetic fields. To this end, we provide a comprehensive symmetry classification of the possible charge orders in kagome materials with a $2\times 2$ increase of the unit cell. Motivated by the experimental reports of time-reversal symmetry breaking and rotational anisotropy, we consider the interdependence of flux and bond orders. Deriving the relevant Landau free energy for possible orders, we study the effect of symmetry-breaking perturbations such as strain and magnetic fields. Our results thus provide a road map for future tests of these intricate orders.

Interfacial coupling between graphene and other two-dimensional materials can give rise to intriguing physical phenomena. In particular, several theoretical studies predict that the interplay between graphene and an antiferromagnetic insulator could lead to the emergence of quantum anomalous Hall phases. However, such phases have not been observed experimentally yet, and further experimental studies are needed to reveal the interaction between graphene and antiferromagnetic insulators. Here, we report the study in heterostructures composed of graphene and the antiferromagnetic insulator ${\mathrm{MnPSe}}_3$. It is found that the ${\mathrm{MnPSe}}_3$ has little impact on the quantum Hall phases apart from doping graphene via interfacial charge transfer. However, the magnetic order can contribute indirectly via a process like Kondo effect, as evidenced by the observed minimum in the temperature-resistance curve between 20 and 40 K, far below the Néel temperature (70 K).

Although $2\mathit{H}\text{−}{\mathrm{NbSe}}_2$ has been discussed as a prototypical charge density wave (CDW) material with strong electron-phonon coupling, its energy gap structure, such as its position and size, has been elusive in spectroscopic measurements. We carefully reinvestigate the spectral change in the scanning tunneling microscopy and spectroscopy (STM/STS) when crossing the CDW transition in temperature and space. In contradiction to previous assignments, our spectroscopy measurements exhibit no significant spectral change across the CDW transition. Density functional theory calculations attribute the absence of the spectral signature to the CDW gap opening at the $M$ point and the $\mathrm{\Gamma }$-point-sensitive tunneling in the STS measurement. As an alternative CDW signature, we identify a strong bias-dependent modulation of local charge density across the Fermi energy which originates from the bonding/antibonding character of bands involved in the CDW gap at the $M$ point. Our findings provide important insights for understanding partially gapped mutliband CDW materials.

Moiré materials have risen to the forefront of physics research because of their ability to realize a disparate set of fascinating physical phenomena in these systems. Besides interesting electronic properties, the moiré pattern has been suggested to be used as a magnifying glass for local strain and dislocations in van der Waals (vdW) systems. Here, we demonstrate the ability to create a custom-designed moiré magnifying glass to probe local atomic lattice rotations directly in tiny-angle twisted bilayer graphene (TBG). In tiny-angle TBG, a moiré periodic network of local subdegree lattice rotations, i.e., the structural reconstruction, occurs due to the vdW interlayer interaction. By introducing a small-period graphene moiré pattern as the magnifying glass, the local subdegree lattice rotations in the underlying tiny-angle TBG are magnified both in structure, i.e., the local moiré periods, and in electronic properties, i.e., energy separations between two low-energy van Hove singularities. Our results unveil the unique magnifying effects of the moiré pattern, and the reported method can be applied to probe the structural reconstruction in any vdW system.

With the aim to understand the role of the constraints in the thermalization of quantum systems, we study the dynamics of a family of kinetically constrained models arising through duality from the XXZ spin chain. We find that integrable and nonintegrable deformations around the stochastic point give rise to ground state phase transitions between localised and delocalised phases, which in turn determine the nature of the relaxation dynamics at finite energy densities. While in the delocalised phase thermalization is fast and homogeneous, in the localised phase relaxation is slow, temporal autocorrelations exhibit plateaus indicative of metastability, and the growth of entanglement is heterogeneous in space. Furthermore, by considering relaxation from initial product states, we demostrate that this slow thermalization can be rationalised directly from the presence of constraints in the dynamics.

We introduce a model of Dirac fermions in $2+1$ dimensions with a semimetallic, a quantum spin-Hall insulating (QSHI), and an $s$-wave superconducting (SSC) phase. The phase diagram features a multicritical point at which all three phases meet as well as a QSHI-SSC deconfined critical point. The QSHI and SSC orders correspond to mutually anticommuting mass terms of the Dirac Hamiltonian. Based on this algebraic property, SO(5) symmetric field theories have been put forward to describe both types of critical points. Using quantum Monte Carlo simulations, we directly study the operator that rotates between QSHI and SSC states. The results suggest that it commutes with the low-energy effective Hamiltonian at criticality but has a gap in the ordered phases. This implies an emergent SO(5) symmetry at both the multicritical and the deconfined critical points.

We investigate electronic states in a two-dimensional network consisting of interacting quantum wires, a model adopted for twisted bilayer systems. We construct general operators which describe various scattering processes in the system. In a twisted bilayer structure, the moiré periodicity allows for generalized umklapp scatterings, leading to a class of correlated states at certain fractional fillings. We identify scattering processes which can lead to an insulating gapped bulk with gapless chiral edge modes at fractional fillings, resembling the quantum anomalous Hall effect recently observed in twisted bilayer graphene. Finally, we demonstrate that the description can be useful in predicting spectroscopic and transport features to detect and characterize the chiral edge modes in the moiré-induced correlated states.

We show that the chiral modes in circular graphene $pn$ junctions provide an advantage for spin manipulation via spin-orbit coupling compared to semiconductor platforms. We derive the effective Hamiltonian for the spin dynamics of the junction's zero modes and calculate their quantum phases. We find a sweet spot in parameter space where the spin is fully in-plane and radially polarized for a given junction polarity. This represents a shortcut to singular spin configurations that would otherwise require spin-orbit coupling strengths beyond experimental reach.

The Dice lattice structure is similar to the graphene honeycomb lattice, but with an imbalance atom in each hexagon center giving rise to a dispersionless flat band, which intersects the pseudopsin $S=1$ Dirac bands through the Dirac point. In this work, we report a theoretical study on the thermopower of the Dice lattice by focusing on the role of the flat band and comparison with the graphene case. Based on the Chebyshev polynomials Green's function method, we show that an extra pair of thermopower peaks near the band center appear in the Dice lattice compared to the graphene counterpart due to the presence of the flat band. In the relatively high temperature regime, the emergent thermopower peaks exhibit an unconventional dependence on temperature and disorder contrary to the Mott's relation, and the origin is ascribed to the extreme narrow bandwidth of the broadened flat band. We also discuss the enhancement of the thermopower by introducing an energy gap in the Dice lattice.

We have theoretically studied phonon-mediated spin-flip processes of electrons in a GaAs double quantum dot (DQD) holding two spins, under a phonon temperature gradient over the DQD. Transition rates of interdot phonon-assisted tunnel processes and intradot spin-flip processes involving spin triplet states are formalized by the electron-phonon interaction accompanied with the spin-orbit interaction. The calculations of the spin-flip rates and the occupation probabilities of the spin-states in the two-electron DQD with respect to the phonon temperature difference between the dots are quantitatively consistent with our previous experiment. This theoretical study on the temperature gradient effect onto spins in coupled QDs would be essential for understanding spin-related thermodynamic physics.

The Casimir-Polder interaction between the Jahn-Teller $X_3$ molecule with the linear $E\otimes e$ problem and a gyrotropic medium is considered. Due to the interaction, the molecule plane is reoriented perpendicularly to the interface surface to lift degeneracy of circular motion of molecule nuclei. A direct consequence of the broken rotational symmetry is the appearance of the orbital magnetic moment and accumulation of the topological Berry phase.

We report on a detailed investigation of the shell-filling sequence in electrostatically defined elliptic bilayer graphene quantum dots (QDs) in the regime of low charge carrier occupation, $N\le 12$, by means of magnetotransport spectroscopy and numerical calculations. We show the necessity of including both short-range electron-electron interaction and wave-function-dependent valley $g$-factors for understanding the overall fourfold shell-filling sequence. These factors lead to an additional energy splitting at half filling of each orbital state and different energy shifts in out-of-plane magnetic fields. Analysis of 31 different bilayer graphene (BLG) QDs reveals that both valley $g$-factor and electron-electron interaction-induced energy splitting increase with decreasing QD size, validating theory. However, we find that the electrostatic charging energy of such gate-defined QDs does not correlate consistently with their size, indicating complex electrostatics. These findings offer significant insights for future BLG QD devices and circuit designs.

The flat band is a key ingredient for the realization of interesting quantum states for functionalities. In this paper, we investigate the conditions for the flat band in both monolayer and bilayer graphene under periodic strain. We find topological nearly flat bands with homogeneous distribution of Berry curvature in both systems. The quantum metric of the nearly flat band closely resembles that for Landau levels. For monolayer graphene, the strain field can be regarded as an effective gauge field, while for Bernal-stacked ($\mathit{AB}$-stacked) bilayer graphene, its role is beyond the description of a gauge field. We also provide an understanding of the origin of the nearly flat band in monolayer graphene in terms of the Jackiw-Rebbi model for Dirac fermions with sign-changing mass. In this paper, we suggest strained graphene as a promising platform for strongly correlated quantum states.

We demonstrate that level crossings at the Fermi energy serve as robust indicators for higher-order topology in two-dimensional superconductors of symmetry class D. These crossings occur when the boundary condition in one direction is continuously varied from periodic to open, revealing the topological distinction between opposite edges. The associated Majorana numbers acquire nontrivial values whenever the system supports two Majorana zero modes distributed at its corners. Owing to their immunity to perturbations that break crystalline symmetries, Fermi level crossings are able to characterize a wide range of higher-order topological superconductors. By directly identifying the level-crossing points from the bulk Hamiltonian, we establish the correspondence between gapped bulk and Majorana corner states in higher-order phases. In the end, we illustrate this correspondence using two toy models. Our findings suggest that Fermi level crossings offer a possible avenue for characterizing higher-order topological superconductors in a unifying framework.

We introduce a general mechanism for obtaining Weyl points in a stack of two-dimensional (2D) quasicrystals, which can be extended to any stack of aperiodic layers. We do so by driving a topological phase transition with the vertical crystal momentum as the tuning parameter, which leads to gap closures at the critical points sourcing Berry curvature. To illustrate, we use a simple 3D generalization of the Qi-Wu-Zhang model defined on a Penrose quasicrystal. The presence of Weyl points is established via the local Chern marker, projected band structure, and density of states. Interestingly, we uncover an analog of Fermi arcs in the quasicrystalline setting, which we deem Fermi-Bragg arcs, densely distributed lines connecting the band degeneracies and indexed by the Bragg peaks. Signatures of such surface states in quantum oscillations and the prospect of a fully quasicrystalline Weyl system are also discussed. The flexibility of our proposal brings opportunities for realizing other gapless topological phases in aperiodic systems, paving the way for a significantly expanded role for topological band theory.

A recent paper [Lee et al., J. Kor. Cryst. Growth Cryst. Technol. 33, 61 (2023)] provides some experimental indications that ${\mathrm{Pb}}_{10-x}{\mathrm{Cu}}_x{\left({\mathrm{PO}}_4\right)}_6\mathrm{O}$ with $x\approx 1$, coined LK-99, might be a room-temperature superconductor at ambient pressure. Our density-functional theory (DFT) calculations show lattice parameters and a volume contraction with $x$, very similar to experiment. The DFT electronic structure shows ${\mathrm{Cu}}^{2+}$ in a $3d^9$ configuration with two flat Cu bands crossing the Fermi energy. This puts ${\mathrm{Pb}}_9\mathrm{Cu}{\left({\mathrm{PO}}_4\right)}_6\mathrm{O}$ in an ultracorrelated regime and suggests that, without doping, it is a Mott or charge-transfer insulator. If doped, such an electronic structure might support flat-band superconductivity or a correlation-enhanced electron-phonon mechanism, whereas a diamagnet without superconductivity appears to be rather at odds with our results.

This paper examines the relaxation dynamics of a two-dimensional Coulomb glass lattice model with high disorder. The study aims to investigate the effects of disorder and Coulomb interactions on glassy dynamics by computing the eigenvalue distribution of the linear dynamical matrix using the mean-field approximation. The findings highlight the significance of the single-particle density of states (DOS) as the main controlling parameter affecting the relaxation at intermediate and long times. For the model with unscreened Coulomb interactions, our results indicate that the depletion of the DOS near the Fermi level leads to logarithmic decay at intermediate times. As the relaxation progresses to longer times, a power-law decay emerges, with the exponent approaching zero as the disorder strength increases, suggesting the manifestation of logarithmic decay at high disorders. The effects of screening of interactions on the dynamics are also studied at various screening and disorder strengths. The findings reveal that screening leads to the filling of the gap in the density of states, causing deviation from logarithmic decay at intermediate disorders. Moreover, in the strong disorder regime, the relaxation dynamics are dominated by disorder, and even with screened Coulomb interactions, the electronic relaxation remains similar to the unscreened case. The time at which crossover to exponential decay occurs increases with increasing disorder and interaction strength.