arXiv subjects

Wangqian Miao

Publications and source records attributed to Wangqian Miao.

11 recordsLinked to original sources

arXiv2026

Gauge-covariant magnetic Bloch sums for general multiorbital Hofstadter models

We formulate a unified treatment of the Hofstadter problem for general two-dimensional multiorbital Peierls tight-binding Hamiltonians using a gauge-covariant magnetic Bloch-sum basis. The construction retains the full Bravais geometry, arbitrary intracell orbital positions, and the original hopping table, so lattice geometry, orbital embedding, hopping range, and orbital content can all be handled within the same framework. At rational flux $Φ/Φ_0=p/q$, commuting magnetic translations reduce the Peierls Hamiltonian to minimal $qN_{\rm orb}\times qN_{\rm orb}$ blocks. Their dimension depends only on the flux through the primitive cell, even when the fractional orbital coordinates are irrational. Electromagnetic gauge transformations act by unitary conjugation within the construction and do not alter the required magnetic supercell. We derive an explicit sparse matrix in an oblique Landau gauge and establish the associated band counting, spectral redundancy, Chern-number formulation, magnetic spatial constraints, and flux periodicity. Numerical examples include elementary lattices, topological and flat-band models, and a spinful 22-band Wannier Hamiltonian of monolayer $\mathrm{MoS}_2$, demonstrating a direct interface with first-principles electronic-structure calculations. As a complementary representation, we also derive exact generalized Harper equations from the same hopping data and relate them to the finite magnetic-Bloch blocks.

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arXiv2026

Emergence of Topological Electron Crystals in Bilayer Graphene--Mott Insulator Heterostructures

The interplay between strong electron correlation and band topology offers a playground for discovering exotic quantum phases. Here, we predict the emergence of topological electron crystals in a charge-transfer bilayer graphene-Mott insulator heterostructure. In this system, interlayer charge transfer induces a charge-neutral electron-hole bilayer with strong mass asymmetry. While the extreme dilute limit favors a classical triangular dipolar Wigner crystal, we show that increasing the carrier density triggers a critical competition between the Coulomb interaction and the underlying topological band structure of bilayer graphene. This interplay destabilizes the triangular dipolar Wigner crystal and instead stabilizes intrinsic quantum electron crystals with spontaneously formed honeycomb and kagome geometries. Crucially, these new phases can host distinct topological responses including the quantum anomalous and quantum spin Hall effects, which inherit the nonlocal quantum geometry of the bilayer graphene wave functions. Our results establish this artificial heterostructure as a highly tunable platform for mimicking two-dimensional topological solids in a single device.

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arXiv2026

Retarded interaction between opposite chiral edges in anomalous Hall crystals

An anomalous Hall crystal combines spontaneous electronic crystallization with a Chern insulating gap, supporting both chiral edge modes and low-energy electronic phonons. We show that this coexistence produces a distinct dynamical effect from ordinary Chern insulators: transverse bulk phonons can mediate a retarded interaction between counterpropagating chiral edge modes on opposite sides of the sample, realizing a Luttinger-liquid variant with delayed inter-edge coupling. Using microscopic time-dependent Hartree--Fock calculations for rhombohedral pentalayer graphene, we find that lowering the carrier density softens the long-wavelength transverse phonon mode. Near this instability regime, the resulting boundary-projected phonon continuum inevitably overlaps with the edge dispersion, thereby enabling their coupling. A smoking-gun probe is a nonlocal measurement: a drive applied to one edge can induce a response on the other edge, delayed by the transverse phonon time of flight across the sample.

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arXiv2026

Various electronic crystal phases in rhombohedral graphene multilayers

We systematically investigate the emergence of electron crystal phases in rhombohedral multilayer graphene using comprehensive self-consistent Hartree Fock calculations combined with \textit{ab initio} tight binding model. As the carrier density increases, we uncover an isospin cascade sequence of phase transitions that gives rise to a rich variety of ordered states, including electron crystal phases with non-zero Chern numbers. We further show the nearly degeneracy of these topological electron crystals hosting extended quantum anomalous Hall effect (EQAH) in the mean field regime and characterize pressure driven phase transitions. Finally, we discuss the thermodynamic signatures, particularly the behavior of the inverse compressibility, in light of recent experimental observations.

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arXiv2024

Strong Inter-valley Electron-Phonon Coupling in Magic-Angle Twisted Bilayer Graphene

The unusual properties of superconductivity in magic-angle twisted bilayer graphene (MATBG) have sparked enormous research interest. However, despite the dedication of intensive experimental efforts and the proposal of several possible pairing mechanisms, the origin of its superconductivity remains elusive. Here, utilizing angle-resolved photoemission spectroscopy with micrometer spatial resolution, we have revealed flat band replicas in superconducting MATBG, where MATBG is unaligned with its hexagonal boron nitride (hBN) substrate11. These replicas exhibit uniform energy spacing, approximately 150 +- 15 meV apart, indicative of strong electron-boson coupling. Strikingly, these replicas are absent in non-superconducting twisted bilayer graphene (TBG) systems, either when MATBG is aligned to hBN or when TBG deviates from the magic angle. Calculations suggest that the formation of these flat band replicas in superconducting MATBG are attributed to the strong coupling between flat band electrons and an optical phonon mode at the graphene K point, facilitated by inter-valley scattering. These findings, although do not necessarily put electron phonon coupling as the main driving force for the superconductivity in MATBG, unravel the unique electronic structure inherent in superconducting MATBG, thereby providing crucial information for understanding the unusual electronic landscape from which the superconductivity is derived.

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arXiv2024

Universal Moiré-Model-Building Method without Fitting: Application to Twisted MoTe$_2$ and WSe$_2$

We develop a comprehensive method to construct analytical continuum models for moiré systems directly from first-principle calculations without any parameter fitting. The core idea of this method is to interpret the terms in the continuum model as a basis, allowing us to determine model parameters as coefficients of this basis through Gram-Schmidt orthogonalization. We apply our method to twisted MoTe$_2$ and WSe$_2$ with twist angles ranging from 2.13$^\circ$ to 3.89$^\circ$, producing continuum models that exhibit excellent agreement with both energy bands and wavefunctions obtained from first-principles calculations. We further propose a strategy to integrate out the higher-energy degrees of freedom to reduce the number of the parameters in the model without sacrificing the accuracy for low-energy bands. Our findings reveal that decreasing twist angles typically need an increasing number of harmonics in the moiré potentials to accurately replicate first-principles results. We provide parameter values for all derived continuum models, facilitating further robust many-body calculations. Our approach is general and applicable to any commensurate moiré materials accessible by first-principles calculations.

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arXiv2024

Artificial moiré engineering for an ideal BHZ model

We demonstrate that (001) grown Cd3As2 thin films with a superlattice-patterned gate can potentially realize the moiré Bernevig-Hughes-Zhang (BHZ) model. Our calculations identify the parameterization region necessary to achieve topological flat mini-bands with a C4z symmetric and a C6z symmetric potential. Additionally, we show that a spin-polarized state can serve as the minimal platform for hosting the moiré induced quantum anomalous Hall effect, supported by Hartree Fock interaction kernel analysis and self-consistent mean field calculations.

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arXiv2024

Engineering the in-plane anomalous Hall effect in Cd$_3$As$_2$ thin films

We predict two topological phase transitions for cadmium arsenide (\ce{Cd3As2}) thin films under in-plane magnetic field, taking advantage of a four-band $k\cdot p$ model and effective $g$ factors calculated from first principles. Film thickness, growth direction and in-plane Zeeman coupling strength can all serve as control parameters to drive these phase transitions. For (001) oriented \ce{Cd3As2} thin films, a two dimensional Weyl semimetal phase protected by $C_{2z}\mathcal{T}$ symmetry can be realized using an in-plane magnetic field, which has recently been reported in our companion paper. We then put forth two pathways to achieve in-plane anomalous Hall effects (IPAHE). By either introducing a trigonal warping term or altering the growth orientation, the emergent $C_{2z} \mathcal{T}$ symmetry can be broken. Consequently, in the clean limit and at low temperatures, quantized Hall plateaus induced by in-plane Zeeman fields become observable.

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arXiv2024

Moiré optical phonons dancing with heavy electrons in magic-angle twisted bilayer graphene

Electron-phonon coupling in magic-angle twisted bilayer graphene is an important but difficult topic. We propose a scheme to simplify and understand this problem. Weighted by the coupling strength with the low-energy heavy electrons ($f$ orbitals), several moiré optical phonons are singled out which strongly couple to the flat bands. These modes have localized envelopes in the moiré scale, while in the atomic scale they inherit the monolayer oscillations like the Kekulé pattern. They flip the flavor of $f$ orbitals, helping stabilize some symmetry-breaking orders. Such electron-phonon couplings are incorporated into an effective extended Holstein model, where both phonons and electrons are written as moiré scale basis. We hope this model will inspire some insights guiding further studies about the superconductivity and other correlated effects in this system.

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arXiv2023

Zeeman field-induced two-dimensional Weyl semimetal phase in cadmium arsenide

We report a topological phase transition in quantum-confined cadmium arsenide (Cd3As2) thin films under an in-plane Zeeman field when the Fermi level is tuned into the topological gap via an electric field. Symmetry considerations in this case predict the appearance of a two-dimensional Weyl semimetal (2D WSM), with a pair of Weyl nodes of opposite chirality at charge neutrality that are protected by space-time inversion (C2T) symmetry. We show that the 2D WSM phase displays unique transport signatures, including saturated resistivities on the order of h/e^2 that persist over a range of in-plane magnetic fields. Moreover, applying a small out-of-plane magnetic field, while keeping the in-plane field within the stability range of the 2D WSM phase, gives rise to a well-developed odd integer quantum Hall effect, characteristic of degenerate, massive Weyl fermions. A minimal four-band k.p model of Cd3As2, which incorporates first-principles effective g factors, qualitatively explains our findings.

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arXiv2023

Truncated atomic plane wave method for the subband structure calculations of Moiré systems

We propose a highly efficient and accurate numerical scheme named Truncated Atomic Plane Wave (TAPW) method to determine the subband structure of Twisted Bilayer Graphene (TBG) inspired by BM model. Our method utilizes real space information of carbon atoms in the moiré unit cell and projects the full tight binding Hamiltonian into a much smaller subspace using atomic plane waves. We present accurate electronic band structures of TBG in a wide range of twist angles together with detailed moiré potential and screened Coulomb interaction at the first magic angle using our new method. Furthermore, we generalize our formalism to solve the problem of low frequency moiré phonons in TBG.

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