arXiv subjects

Junkai Dong

Publications and source records attributed to Junkai Dong.

At least 19 recordsLinked to original sources

arXiv2026

Crystals Caught Doping: Metallic Wigner Crystals in Rhombohedral Graphene

Nearly a century after Wigner's initial proposal, electron crystals are now a topic of intense experimental and theoretical interest. However, most proposed crystalline phases are commensurate and therefore become insulating in the presence of even weak pinning. In this work we discuss when a commensurate Wigner crystal will spontaneously self dope and develop itinerant carriers, giving rise to an incommensurate and thus metallic Wigner crystal (MWC). We develop a general criterion for the instability of the commensurate crystal which involves the competition between the charge gap at commensurability and a ``packing bias'' whose sign selects whether electron or hole doping is preferred. We then apply these insights to rhombohedral multilayer graphene, where calculations for commensurate crystals reveal instabilities towards self-doping. Carrying out self-consistent Hartree-Fock over the landscape of incommensurate crystals reveals the phase diagram, where a broad MWC phase appears directly adjacent to an insulating Wigner crystal phase. Recent observations of an island of reversed Hall conductance near a putative Wigner crystal phase in rhombohedral graphene are naturally explained by our theory.

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arXiv2026

Topological constraint on crystalline current

How much current does a sliding electron crystal carry? The answer to this simple question has important implications for the dynamic properties of the crystal, such as the frequency of its cyclotron motion, and its phonon spectrum. In this work we introduce a precise definition of a sliding crystal and compute the corresponding current $\mathbf{j}_c$ for topological electron crystals in the presence of magnetic field. Our result is fully non-perturbative, does not rely on Galilean invariance, and applies equally to Wigner crystals and (anomalous) Hall crystals. In terms of the electron density $ρ$ and magnetic flux density $ϕ$, we find that $\mathbf{j}_c = e(ρ-Cϕ)\mathbf{v}$. Surprisingly, the current receives a contribution from the many-body Chern number $C$ of the crystal. When $ρ= Cϕ$, sliding crystals therefore carry zero current. The crystalline current fixes the Lorentz force felt by the sliding crystal and the dispersion of low-energy phonons of such crystals. This gives us a simple counting rule for the number of gapless phonons: if a sliding crystal carries nonzero current in a magnetic field, there is a single gapless mode, while otherwise there are two gapless modes. This result can also be understood from anomaly-matching of emanant discrete translation symmetries -- an idea that is also applicable to the dispersion of skyrmion crystals. Our results lead to novel experimental implications and invite further conceptual developments for electron crystals.

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arXiv2026

Controlled localization of anyons in a graphene quantum Hall interferometer

Exchange statistics are a fundamental principle of quantum mechanics, dictating the symmetry of identical particle wavefunctions and thereby enabling emergent phenomena of many-body quantum states. The exchange-induced unitary transformation of both abelian and non-abelian anyonic wavefunctions can be probed using electronic fractional quantum Hall (FQH) interferometers, where quasiparticles propagating along the interfering FQH edge braid with those localized within the interferometer. Here, we add a gate-controlled dot/anti-dot in the center of a bilayer graphene FQH interferometer cavity to tune the number of enclosed anyons. We observe hundreds of controlled phase slips in the diagonal conductance across the interferometer for both abelian and non-abelian states, consistent with discrete changes in the localized quasiparticle population. For abelian anyons, the observed phase slips agree with the theoretically expected value. At half filling, our results suggest the interfering edge carries charge $|e^*/e| = 1/2$ abelian excitations, whereas charge $|e^*/e| = 1/4$ putative non-abelian anyons remain localized in the interferometer cavity. Controlling the population of localized $e/4$ anyons in an interferometer marks a significant milestone towards observing their non-local exchange statistics and building a fault tolerant topological qubit based on non-abelian anyon manipulation.

cond-mat.mes-hall↗

arXiv2025

Quantum Geometry Driven Crystallization: A Neural-Network Variational Monte Carlo Study

Wigner crystals are a paradigmatic form of interaction driven electronic order. A key open question is how Berry curvature and, more generally, quantum geometry reshape crystallization. The discovery of two-dimensional materials with relatively flat bands and pronounced Berry curvature has added fresh urgency to this question. Recent mean-field studies have proposed a topological variant of the Wigner crystal, the anomalous Hall crystal (AHC), with non-zero Chern number. However it remains unclear whether the AHC survives beyond the mean-field approximation. Here, we map out the ground-state phase diagram of the $λ$-jellium model - a simple model whose interaction strength and Berry curvature are independently tunable - using state-of-the-art neural-network variational Monte Carlo. The AHC is found to remain stable against quantum fluctuations. Surprisingly, quantum geometric effects are found to dramatically enhance crystallization. Both the AHC and the standard Wigner Crystal are stabilized at densities up to an order of magnitude above the critical density in the absence of quantum geometry, yet still significantly below the threshold predicted by mean-field theory. These striking results highlight the rich interplay between quantum fluctuations, quantum geometry, and crystallization, providing concrete guidance for experiments and enabling future explorations of fractionalized crystals and chiral superconductors.

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arXiv2025

$λ$-Jellium Model for the Anomalous Hall Crystal

The jellium model is a paradigmatic problem in condensed matter physics, exhibiting a phase transition between metallic and Wigner crystal phases. However, its vanishing Berry curvature makes it ill-suited for studying recent experimental platforms that combine strong interactions with nontrivial quantum geometry. These experiments inspired the anomalous Hall crystal (AHC) -- a topological variant of the Wigner crystal. The AHC spontaneously breaks continuous translation symmetry but has a nonzero Chern number. In this work, we introduce $λ-$jellium, a minimal extension of the two-dimensional jellium model. Its Berry curvature distribution is controlled by a single parameter, $λ$, where $λ=0$ corresponds to the standard jellium model. This setup facilitates the systematic exploration of Berry curvature's impact on electron crystallization. The phase diagram of this model, established using self-consistent Hartree Fock calculations, reveals several interesting features: (i) The AHC phase occupies a large region of the phase diagram. (ii) Two distinct Wigner crystal phases, the latter enabled by quantum geometry, and two distinct Fermi liquid phases are present. (iii) A continuous phase transition separates the AHC and one of the WC phases. (iv) In some parts of the AHC phase, the lattice geometry is non-triangular, unlike in the classical Wigner crystal. In addition to elucidating the physics of correlated electrons with nonzero Berry curvature, we expect that the simplicity of the model makes it an excellent starting point for more advanced numerical methods.

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arXiv2025

Phonons in Electron Crystals with Berry Curvature

Recent advances in 2D materials featuring nonzero Berry curvature have inspired extensions of the Wigner crystallization paradigm. This paper derives a low-energy effective theory for such quantum crystals, including the anomalous Hall crystal (AHC) with nonzero Chern number. First we show that the low frequency dispersion of phonons in AHC, despite the presence of Berry curvature, resembles that of the zero field (rather than finite magnetic field) Wigner crystal due to the commutation of translation generators. We explain how key parameters of the phonon theory such as elastic constants and effective mass can be extracted from microscopic models, and apply them to two families of models: the recently introduced $λ$-jellium model and a model of rhombohedral multilayer graphene (RMG). In the $λ$-jellium model, we explore the energy landscape as crystal geometry shifts, revealing that AHC can become `soft' under certain conditions. This causes transitions in lattice geometry, although the quantized Hall response remains unchanged. Surprisingly, the Berry curvature seems to enhance the effective mass, leading to a reduction in phonon speed. For the AHC in RMG, we obtain estimates of phonon speed and shear stiffness. We also identify a previously overlooked `kineo-elastic' term in the phonon effective action that is present in the symmetry setting of RMG, and leads to dramatic differences in phonon speeds in opposite directions. We numerically confirm these predictions of the effective actions by time-dependent Hartree-Fock calculations.

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arXiv2025

hBN alignment orientation controls moiré strength in rhombohedral graphene

Rhombohedral multilayer graphene hosts a rich landscape of correlated symmetry-broken phases, driven by strong interactions from its flat band edges. Aligning to hexagonal boron nitride (hBN) creates a moiré pattern, leading to recent observations of exotic ground states such as integer and fractional quantum anomalous Hall effects. Here, we show that the moiré effects and resulting correlated phase diagrams are critically influenced by a previously underestimated structural choice: the hBN alignment orientation. This binary parameter distinguishes between configurations where the rhombohedral graphene and hBN lattices are aligned near 0° or 180°, a distinction that arises only because both materials break inversion symmetry. Although the two orientations produce the same moiré wavelength, we find their distinct local stacking configurations result in markedly different moiré potential strengths. Using low-temperature transport and scanning SQUID-on-tip magnetometry, we compare nearly identical devices that differ only in alignment orientation and observe sharply contrasting sequences of symmetry-broken states. Theoretical analysis reveals a simple mechanism based on lattice relaxation and the atomic-scale electronic structure of rhombohedral graphene, supported by detailed modeling. These findings establish hBN alignment orientation as a key control parameter in moiré-engineered graphene systems and provide a framework for interpreting both prior and future experiments.

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arXiv2025

Higher vortexability: zero field realization of higher Landau levels

The rise of moiré materials has led to experimental realizations of integer and fractional Chern insulators in small or vanishing magnetic fields. At the same time, a set of minimal conditions sufficient to guarantee a Abelian fractional state in a flat band were identified, namely "ideal" or "vortexable" quantum geometry. Such vortexable bands share essential features with the lowest Landau level, while excluding the need for more fine-tuned aspects such as flat Berry curvature. A natural and important generalization is to ask if such conditions can be extended to capture the quantum geometry of higher Landau levels, particularly the first (1LL), where non-Abelian states at $ν= 1/2,2/5$ are known to be competitive. The possibility of realizing these states at zero magnetic field , and perhaps even more exotic ones, could become a reality if we could identify the essential structure of the 1LL in Chern bands. In this work, we introduce a precise definition of 1LL quantum geometry, along with a figure of merit that measures how closely a given band approaches the 1LL. We apply the definition to identify two models with 1LL structure -- a toy model of double bilayer twisted graphene and a more realistic model of strained Bernal graphene.

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arXiv2025

Simulating the non-unitary Yang-Lee conformal field theory on the fuzzy sphere

The fuzzy sphere method has enjoyed great success in the study of (2+1)-dimensional unitary conformal field theories (CFTs) by regularizing them as quantum Hall transitions on the sphere. Here, we extend this approach to the Yang-Lee CFT-the simplest non-unitary CFT. We use an Ising quantum-Hall ferromagnet Hamiltonian with a transverse field and an imaginary longitudinal field, the latter breaks the Hermiticity of the Hamiltonian and thus the unitarity of the associated quantum field theory. Non-unitary conformal field theories-particularly the Yang-Lee CFT-pose significant challenges to conventional fuzzy sphere approaches. To overcome these obstacles, here we utilize a different method for determining critical points that requires no a priori knowledge of CFT scaling dimensions. Our method instead leverages the state-operator correspondence while utilizing two complementary criteria: the conformality of the energy spectrum and its consistency with conformal perturbation theory. We also discuss a new finite-size scaling on the fuzzy sphere that allows us to extract conformal data more reliably, and compare it with the conventional analysis using the (1+1)-dimensional Yang-Lee problem as an example. Our results show broad agreement with previous Monte-Carlo and conformal bootstrap results. We also uncover one previously unknown primary operator and several operator product expansion coefficients.

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arXiv2024

Nonlocal Moments in the Chern Bands of Twisted Bilayer Graphene

Twisted bilayer graphene (TBG) has elements in common with two paradigmatic examples of strongly correlated physics: quantum Hall physics and Hubbard physics. On one hand, TBG hosts flat topological Landau-level-like bands which exhibits quantum anomalous Hall effects. On the other hand, these bands have concentrated charge density and show signs of extensive entropy resembling local moments. The combination of these features leads to a question: can decoupled moments emerge in an isolated topological band, despite the lack of exponentially localized Wannier states? In this work, we answer the question affirmatively by proposing a minimal model for these bands in TBG that combines topology and charge concentration at the AA sites, leading to analytic wavefunctions that closely approximate those of the BM model with realistic parameters. Importantly, charge concentration also leads to Berry curvature concentration at $\Gamma$, generating a small parameter $s$ that yields analytic tractability. We show that, rather surprisingly, the model hosts nearly decoupled flavor moments without any extra degrees of freedom. These moments are non-local due to topology-enforced power-law tails, yet have parametrically small overlap. We further develop a diagrammatic expansion in which the self energy can be computed exactly to leading order in $s^2$ in the fluctuating moment regime. At charge neutrality, we find a "Mott semimetal", with large flavor entropy and a Mott gap everywhere in the BZ except for the vicinity of the $\Gamma$ point. Away from neutrality, the Mott semimetal gaps out in a spectrally imbalanced manner, with one Mott band having zero $Z_k$ at the $\Gamma$ point. The model accurately reproduces results from finite temperature thermodynamic measurements, leads to new experimental predictions, and resolves the problem of the emergence of Hubbard physics in isolated topological bands.

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arXiv2024

Anomalous Hall Crystals in Rhombohedral Multilayer Graphene II: General Mechanism and a Minimal Model

We propose a minimal "three-patch model" for the anomalous Hall crystal (AHC), a topological electronic state that spontaneously breaks both time-reversal symmetry and continuous translation symmetry. The proposal for this state is inspired by the recently observed integer and fractional quantum Hall states in rhombohedral multilayer graphene at zero magnetic field. There, interaction effects appear to amplify the effects of a weak moiré potential, leading to the formation of stable, isolated Chern bands. It has been further shown that Chern bands are stabilized in mean field calculations even without a moiré potential, enabling a realization of the AHC state. Our model is built upon the dissection of the Brillouin zone into patches centered around high symmetry points. Within this model, the wavefunctions at high symmetry points fully determine the topology and energetics of the state. We extract two quantum geometrical phases of the non-interacting wavefunctions that control the stability of the topologically nontrivial AHC state. The model predicts that the AHC state wins over the topological trivial Wigner crystal in a wide range of parameters, and agrees very well with the results of full self-consistent Hartree-Fock calculations of the rhombohedral multilayer graphene Hamiltonian.

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arXiv2024

Anomalous Hall Crystals in Rhombohedral Multilayer Graphene I: Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field

Recent experiments on rhombohedral pentalayer graphene flakes with a substrate induced moiré potential have identified both Chern insulators and fractional Quantum Hall states in the absence of an applied magnetic field. Surprisingly, these states are observed in strong displacement fields where the effects of the moiré lattice are weak, and seem to be readily accessed without fine-tuning. To address these experimental puzzles we study an interacting model of electrons in this geometry, first within the self-consistent Hartree-Fock (SCHF) approximation. We find an isolated Chern band with Chern number $|C|=1$, that moreover is relatively flat and shows good quantum geometry. Exact diagonalization and density matrix renormalization group methods at fractional filling establish the presence of fractional quantum anomalous Hall (FQAH) states. The $|C|=1$ band in SCHF is remarkably robust to varying microscopic parameters, and is also found in the $N_L=4$ and $N_L=6$ layer systems. Remarkably, it appears stable even to switching off the moiré potential, pointing to spontaneous breaking of translation symmetry. We term this topological crystalline state the ``anomalous Hall crystal" (AHC), and argue that it constitutes a general mechanism for creating stable Chern bands in rhombohedral graphene. Our work elucidates the physics behind the recent rhombohedral pentalayer graphene observations, predicts the appearance of the same phase in other systems, and opens the door to studying the interplay between electronic topology and spontaneous translation symmetry breaking.

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arXiv2024

Constraints on real space representations of Chern bands

A Chern band is characterized by a Wannier obstruction indicating the absence of a basis of complete, orthogonal, and exponentially-localized states. Here, we study the properties of real space bases of a Chern band obtained by relaxing either exponential localization or orthogonality and completeness. This yields two distinct real space representations of a band with Chern number $C$: (i) a basis of complete orthogonal Wannier states which decay as power-law and (ii) a basis of exponentially-localized overcomplete non-orthogonal coherent states. For (i), we show that the power-law tail only depends on the Chern number and provide an explicit gauge choice leading to the universal asymptotic $w({\boldsymbol r}) \approx \frac{C e^{-i C φ_{\boldsymbol r}}}{2π|{\boldsymbol r}|^2}$ up to a normalized Bloch-periodic spinor. For (ii), we prove a rigorous lower bound on the spatial spread that can always be saturated for ideal bands. We provide an explicit construction of the maximally localized coherent state by mapping the problem to a dual Landau level problem where the Berry curvature and trace of the quantum metric take the roles of an effective magnetic field and scalar potential, respectively. Our coherent state result rigorously bounds the spatial spread of any localized state constructed as a linear superposition of wavefunctions within the Chern band. Remarkably, we find that such bound does not generically scale with the Chern number and provide an explicit example of an exponentially localized state in a Chern $C$ band whose size does not increase with $|C|$. Our results show that band topology can be encoded in a real space description and set the stage for a systematic study of interaction effects in topological bands in real space.

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arXiv2023

Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe$_2$

The pursuit of exotic phases of matter outside of the extreme conditions of a quantizing magnetic field has been a long standing quest of solid state physics. Recent experiments have observed spontaneous valley polarization and fractional Chern insulators (FCIs) in zero magnetic field in twisted bilayers of MoTe$_2$, at partial filling of the topological valence band ($ν=-2/3$ and $-3/5$). We study the topological valence band at $\textit{half}$ filling, using exact diagonalization and density matrix renormalization group calculations. We discover a composite Fermi liquid (CFL) phase even at zero magnetic field that covers a large portion of the phase diagram centered around twist angle ${\sim}3.6^\circ$. The CFL is a non-Fermi liquid phase that shows metallic behavior despite the absence of Landau quasiparticles. We discuss experimental implications including the competition between the CFL and a Fermi liquid, which can be tuned with a displacement field. The topological valence band has excellent quantum geometry over a wide range of twist angles and a small bandwidth that is, remarkably, reduced by interactions for a range of angles. These key properties are responsible for stabilizing the exotic quantum Hall phases we find at zero field. Finally, we present an optical signature involving "extinguished" optical responses as a means to identify Chern bands with ideal quantum geometry.

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arXiv2022

Untwisting moiré physics: Almost ideal bands and fractional Chern insulators in periodically strained monolayer graphene

Moiré systems have emerged in recent years as a rich platform to study strong correlations. Here, we will discuss a simple, experimentally feasible setup based on periodically strained graphene that reproduces several key aspects of twisted moiré heterostructures -- but without introducing a twist. We consider a monolayer graphene sheet subject to a $C_2$-breaking periodic strain-induced psuedomagnetic field (PMF) with period $L_M \gg a$, along with a scalar potential of the same period. This system has {\it almost ideal} flat bands with valley-resolved Chern number $\pm 1$, where the deviation from ideal band geometry is analytically controlled and exponentially small in the dimensionless ratio $(L_M/l_B)^2$ where $l_B$ is the magnetic length corresponding to the maximum value of the PMF. Moreover, the scalar potential can tune the bandwidth far below the Coulomb scale, making this a very promising platform for strongly interacting topological phases. Using a combination of strong-coupling theory and self-consistent Hartree fock, we find quantum anomalous Hall states at integer fillings. At fractional filling, exact diagonaliztion reveals a fractional Chern insulator at parameters in the experimentally feasible range. Overall, we find that this system has larger interaction-induced gaps, smaller quasiparticle dispersion, and enhanced tunability compared to twisted graphene systems, even in their ideal limit.

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arXiv2022

Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers

Motivated by the higher Chern bands of twisted graphene multilayers, we consider flat bands with arbitrary Chern number $C$ with ideal quantum geometry. While $C>1$ bands differ from Landau levels, we show that these bands host exact fractional Chern insulator (FCI) ground states for short range interactions. We show how to decompose ideal higher Chern bands into separate ideal bands with Chern number $1$ that are intertwined through translation and rotation symmetry. The decomposed bands admit an $SU(C)$ action that combines real space and momentum space translations. Remarkably, they also allow for analytic construction of exact many-body ground states, such as generalized quantum Hall ferromagnets and FCIs, including flavor-singlet Halperin states and Laughlin ferromagnets in the limit of short-range interactions. In this limit, the $SU(C)$ action is promoted to a symmetry on the ground state subspace. While flavor singlet states are translation symmetric, the flavor ferromagnets correspond to translation broken states and admit charged skyrmion excitations corresponding to a spatially varying density wave pattern. We confirm our analytic predictions with numerical simulations of ideal bands of twisted chiral multilayers of graphene, and discuss consequences for experimentally accessible systems such as monolayer graphene twisted relative to a Bernal bilayer.

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arXiv2022

Dirac electron under periodic magnetic field: Platform for fractional Chern insulator and generalized Wigner crystal

We propose a platform for flat Chern band by subjecting two-dimensional Dirac materials -- such as graphene and topological insulator thin films -- to a periodic magnetic field, which can be created by the vortex lattice of a type-II superconductor. As a generalization of the $n=0$ Landau level, the flat band of Dirac fermion under a nonuniform magnetic field remains at zero energy, exactly dispersionless and topologically protected, while its local density of states is spatially modulated due to the magnetic field variation. In the presence of short-range repulsion, we find fractional Chern insulators emerge at filling factors $ν=1/m$, whose ground states are generalized Laughlin wavefunctions. We further argue that generalized Wigner crystals may emerge at certain commensurate fillings under a highly nonuniform magnetic field in the form of a flux line lattice.

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arXiv2021

Averaging over moduli in deformed WZW models

WZW models live on a moduli space parameterized by current-current deformations. The moduli space defines an ensemble of conformal field theories, which generically have $N$ abelian conserved currents and central charge $c > N$. We calculate the average partition function and show that it can be interpreted as a sum over 3-manifolds. This suggests that the ensemble-averaged theory has a holographic dual, generalizing recent results on Narain CFTs. The bulk theory, at the perturbative level, is identified as $U(1)^{2N}$ Chern-Simons theory coupled to additional matter fields. From a mathematical perspective, our principal result is a Siegel-Weil formula for the characters of an affine Lie algebra.

hep-th↗