arXiv subjects

Ai-Lei He

Publications and source records attributed to Ai-Lei He.

15 recordsLinked to original sources

arXiv2026

Decomposing Fractional Quantum Hall Wave Functions via Operator Contraction Multiplication

We develop a general algebraic scheme to decompose fractional quantum Hall (FQH) wave functions based on the operator contraction multiplication. By introducing fermionic and bosonic operators and establishing three fundamental contraction rules, we achieve an exact decomposition of Laughlin states. This approach naturally extends to multi-component systems by factorizing coupled Jastrow factors via resultants and elementary symmetric polynomials, enabling the first complete decomposition of Halperin states. For Halperin ($2,2,1$) state, we explicitly derive its basic expansion, identify root configurations, and reveal intra- and inter-color squeezing operators, thereby uncovering the underlying generalized Pauli principle. Using this method, we compute orbital entanglement spectra for up to $16$ particles with decomposition dimensions exceeding $10^{11}$, obtaining edge excitation sequences that precisely match chiral Luttinger liquid theory. Our framework breaks through the longstanding limitations of Jack polynomials, provides a unified decomposition for both single- and multi-component FQH states, and opens a new avenue for exploring wave functions for more complex FQH states.

cond-mat.str-el↗

arXiv2026

Alternative $ν+ν$-picture of bosonic fractional Chern insulators at high filling factors in multiple flat-band systems

Most fractional quantum Hall states have been traditionally identified within a single energy band, such as the lowest Landau level or topological flat band. As more particles are introduced, they inevitably populate higher energy bands. Whether the inclusion of multiple topological bands leads to new physics remains an open question. Here, we propose a universal picture applicable at higher filling factors $ν\geq 1$ in bosonic systems: the occupied bands tend to coalesce into an effective single topological band characterized by a total Chern number $\vert C\vert$, the sum of the Chern number of all occupied lower topological flat bands. Using a Kekulé lattice model with two lower flat bands featuring a total Chern number $C=1$, regardless of their specific configurations, we identify the emergence of a $\frac{1}{2}$ fractional Chern insulator (FCI) state at integer filling factor $ν=1$, followed by the Jain sequence states $\frac{2}{3}$ and $\frac{3}{4}$ at filling $ν=\frac{4}{3}$ and $\frac{6}{4}$. That is a $ν+ν$ picture, rather than the generally expected $1+ν^{\prime}$ picture, where $ν^{\prime}$ is the permitted FCI filling factor in the single second topological flat band. Our findings deepen the understanding of FCI states and open avenues for discovering exotic fractional topological phases in multiband systems.

cond-mat.str-el↗

arXiv2025

Square lattice model with staggered magnetic fluxes: zero Chern number topological states and topological flat bands

Staggered magnetic fluxes (SMF) play a crucial role in achieving Chern insulators (CIs), by which a series of CI models have been established on various lattices. In addition, SMF induced higher-order topological insulator (HOTI) in a lattice model has been reported. In this work, we propose a square lattice model with SMF. We find intracellular SMF can induce zero-Chern-number topological insulator (ZCNTI) at quarter filling which hosts topologically protected edge states characterized by the quantized polarization, in analogy to the topological state in two dimensional Su-Schrieffer-Hegger model. When lattice dimerization and intracellular SMF are introduced, there exists HOTI state at half filling. Furthermore, this model hosts topological flat band (TFB) by considering the next-nearest-neighbor hoppings. Several fractional Chern insulator states are investigated when hard-core bosons are filled into this TFB model.

cond-mat.str-el↗

arXiv2024

Magnetically tuned topological phase in graphene nanoribbon heterojunctions

The interplay between topology and magnetism often triggers the exotic quantum phases. Here, we report an accessible scheme to engineer the robust $\mathbb{Z}_{2}$ topology by intrinsic magnetism, originating from the zigzag segment connecting two armchair segments with different width, in one-dimensional graphene nanoribbon heterojunctions. Our first-principle and model simulations reveal that the emergent spin polarization substantially modifies the dimerization between junction states, forming the special SSH mechanism depending on the magnetic configurations. Interestingly, the topological phase in magnetic state is only determined by the width of the narrow armchair segment, in sharp contrast with that in the normal state. In addition, the emergent magnetism increases the bulk energy band gap by an order of magnitude than that in the nonmagnetic state. We also discuss the $\mathbb{Z}$ topology of the junction states and the termination-dependent of topological end states. Our results bring new way to tune the topology in graphene nanoribbon heterostructure, providing a new platform for future one-dimensional topological devices and molecular-scale spintronics.

cond-mat.mes-hall↗

arXiv2024

Hyperbolic Fractional Chern insulators

Fractional Chern insulators (FCIs) have attracted intensive attention for the realization of fractional quantum Hall states in the absence of an external magnetic field. Most of FCIs have been proposed on two-dimensional (2D) Euclidean lattice models with various boundary conditions. In this work, we investigate hyperbolic FCIs which are constructed in hyperbolic geometry with constant negative curvature. Through the studies on hyperbolic analogs of kagome lattices with hard-core bosons loaded into topological flat bands, we find convincing numerical evidences of two types of $ν=1/2$ FCI states, {\emph {i.e.}}, the conventional and unconventional FCIs. Multiple branches of edge excitations and geometry-dependent wave functions for both conventional and unconventional $ν=1/2$ FCI states are revealed, however, the geometric degree of freedom in these FCIs plays various roles. Additionally, a center-localized orbital plays a crucial role in the unconventional FCI state.

cond-mat.str-el↗

arXiv2024

Topological flat bands in hyperbolic lattices

Topological flat bands (TFBs) provide a promising platform to investigate intriguing fractionalization phenomena, such as the fractional Chern insulators (FCIs). Most of TFB models are established in two-dimensional Euclidean lattices with zero curvature. In this work, we systematically explore TFBs in a class of two-dimensional non-Euclidean lattices with constant negative curvature, {\emph i.e.,} the hyperbolic analogs of the kagome lattice. Based on the Abelian hyperbolic band theory, TFBs have been respectively found in the heptagon-kagome, the octagon-kagome, the nonagon-kagome and the decagon-kagome lattices by introducing staggered magnetic fluxes and the next nearest-neighbor hoppings. The flatness ratios of all hyperbolic TFB models are more than 15, which suggests that the hyperbolic FCIs can be realized in these TFB models. We further demonstrate the existence of a $ν=1/2$ FCI state with open boundary conditions when hard-core bosons fill into these hyperbolic TFB models.

cond-mat.str-el↗

arXiv2024

Second-order topological insulator in Bilayer borophene

As the novel topological states, the higher-order topological insulators have attracted great attentions in the past years. However, their realizations in realistic materials, in particular in two dimensional systems, remains the big challenge due to the lack of adequate candidates. Here, based on the first-principle calculation and tight-binding model simulations, we identify the currently \emph{existing} bilayer $α_{5}$-phase borophenes as the two-dimensional second-order topological insulators, protected by the $C_{2}$-rotational symmetry. The formation of interlayer B-B covalent bonds, stabilizing the bilayer borophenes and opening the large direct bulk gaps ($\sim 0.55-0.62$ eV) at Fermi level, plays the key roles. The second-order topology is characterized by the bulk quantized quadrupole momentum. Our results enriches the candidates for the second-order topological insulators, and also provide a way to study topological states in borophenes.

cond-mat.mtrl-sci↗

arXiv2022

Magic-angle Twisted Bilayer Systems with Quadratic-Band-Touching: Exactly Flat Bands with High-Chern Number

Studies of twisted moiré systems have been mainly focused on two-dimensional (2D) materials such as graphene with Dirac points and transition-metal-dichalcogenide so far. Here we propose a twisted bilayer of 2D systems which feature stable quadratic-band-touching points and find exotic physics different from previously studied twisted moiré systems. Specifically, we show that exactly flat bands can emerge at magic angles and, more interestingly, each flat band exhibits a high Chern number ($C=\pm 2$). We further consider the effect of Coulomb interactions in such magic-angle twisted systems and find that the ground state supports the quantum anomalous Hall effect with quantized Hall conductivity $2\frac{e^2}{hc}$ at certain filling. Furthermore, the possible physical realization of such twisted bilayer systems will be briefly discussed.

cond-mat.str-el↗

arXiv2022

Topological states in a dimerized system with staggered magnetic fluxes

The bulk-boundary correspondence is a generic feature of topological states of matter, reflecting the intrinsic relation between topological bulk and boundary states. For example, robust edge states propagate along the edges and corner states gather at corners in the two-dimensional first-order and second-order topological insulators, respectively. Here, we report two kinds of topological states hosting anomalous bulk-boundary correspondence in the extended two-dimensional dimerized lattice with staggered flux threading. At $\frac{1}{2}$-filling, we observe isolated corner states with no fractional charge as well as metallic near-edge states in the $\mathcal{C}=2$ Chern insulator states. At $\frac{1}{4}$-filling, we find a $\mathcal{C}=0$ topologically nontrivial state, where the robust edge states are well localized along edges but bypass corners. These robust topological insulating states significantly differ from both conventional Chern insulators and usual high-order topological insulators.

cond-mat.mes-hall↗

arXiv2021

Bosonic fractional Chern insulating state at integer fillings in multi-band system

The integer quantum Hall state occurs when the Landau levels are fully occupied by the fermions, while the fractional quantum Hall state usually emerges when the Landau level is partially filled by the strongly correlated fermions or bosons. Here, we report two fractional Chern insulating states of the hard-core bosons in a multi-band lattice model hosting topological flat bands with high Chern number. The previously proposed $ν=1/3$ fractional Chern insulating state inherited from the high Chern number $C=2$ of the lowest topological flat band is revisited by the infinite density matrix renormalization group algorithm. In particular, we numerically identify a bosonic $1/2$-Laughlin-like fractional Chern insulating state at the integer fillings. We show two lower topological flat bands jointly generate an effective $C=1$ Chern band with half-filling. Furthermore, we find a strictly particle-hole-like symmetry between the $ν$ and $3-ν$ filling in our model. These findings extend our understanding of quantum Hall states and offer a new route to realize the novel fractional states in the system with multi-bands and high-Chern numbers.

cond-mat.str-el↗

arXiv2020

Non-Abelian Fractional Chern Insulator in Disk Geometry

Non-Abelian (NA) fractional topological states with quasi-particles obeying NA braiding statistics have attracted intensive attentions for both its fundamental nature and the prospect for topological quantum computation. To date, there are many models proposed to realize the NA fractional topological states, such as the well-known Moore-Read quantum Hall states and the Non-Abelian fractional Chern insulators (NA-FCIs). Here, we investigate the NA-FCI in disk geometry with three-body hard-core bosons loaded into a topological flat band. This stable $ν= 1$ bosonic NA-FCI is characterized by the edge excitations and the ground-state angular momentum. Based on the generalized Pauli principle and the Jack polynomials, we successfully construct a trial wave function for the NA-FCI. Moreover, a $ν= 1/2$ Abelian FCI state emerges with the increase of the on-site interaction and it can be identified with the help of the trial wave function as well. Our findings not only lead to an optimal wave function for the NA-FCI, but also directly provide an effective approach for future researches on paired topological states.

cond-mat.str-el↗

arXiv2019

Quasicrystalline Chern Insulators

Chern insulator or quantum anomalous Hall state is a topological state with integer Hall conductivity but in absence of Landau level. It had been well established on various two-dimensional lattices with periodic structure. Here, we report similar Chern insulators can also be realized on the quasicrystal with $5$-fold rotational symmetry. Providing the staggered flux through plaquettes, we propose two types of quasicrystalline Chern insulators. Their topological characterizations are well identified by the robustness of edge states, non-zero real-space Chern number, and quantized conductance. We further find the failure of integer conductivity but with quantized Chern number at some special energies. Our study therefore provide a new opportunity to searching topological materials in aperiodic system.

cond-mat.mes-hall↗

arXiv2019

Fractional Chern Insulators in Singular Geometries

The fractional quantum anomalous Hall (FQAH) states or fractional Chern insulator (FCI) states have been studied on two-dimensional (2D) flat lattices with different boundary conditions. Here, we propose the geometry-dependent FCI/FQAH states that interacting particles are bounded on 2D singular lattices with arbitrary $n$-fold rotational symmetry. Based on the generalized Pauli principle, we construct trial wave functions for the singular-lattice FCI/FQAH states with the aid of an effective projection approach, and compare them with the exact diagonalization results. High wave-function overlaps show that the singular-lattice FCI/FQAH states are certainly related to the geometric factor $β$. More interestingly, we observe some exotic degeneracy sequences of edge excitations in these singular-lattice FCI/FQAH states, and provide an explanation that two branches of edge excitations mix together.

cond-mat.str-el↗

arXiv2017

Chern Insulators on Singular Geometries

Topological quantum states have been proposed and investigated on two-dimensional flat surfaces or lattices with different geometries like the plane, cylinder and torus. Here, we study quantum anomalous Hall (QAH) or Chern insulator (CI) states on two-dimensional singular surfaces (such as conical and helicoid-like surfaces). Such singular geometries can be constructed based on the disk geometry and a defined unit sector with $n$-fold rotational symmetry. The singular geometry induces novel and intriguing features of CI/QAH states, such as in-gap and in-band core states, charge fractionalization, and multiple branches of edge excitations.

cond-mat.mes-hall↗

arXiv2015

Wave Functions for Fractional Chern Insulators on Disk Geometry

Recently, fractional Chern insulators (FCIs), also called fractional quantum anomalous Hall (FQAH) states, have been theoretically established in lattice systems with topological flat bands. These systems exhibit similar fractionalization phenomena as the conventional fractional quantum Hall (FQH) systems. Using the mapping relationship between the FQH states and the FCI/FQAH states, we construct the many-body wave functions of the fermionic FCI/FQAH states on the disk geometry with the aid of the generalized Pauli principle (GPP) and the Jack polynomials. Compared with the ground state by exact diagonalization method, the wave-function overlap is higher than $0.97$ even when the Hilbert space dimension is as large as $3\times10^6$. We also use the GPP and the Jack polynomials to construct edge excitations for the ferminoic FCI/FQAH states. The quasi-degeneracy sequences of fermionic FCI/FQAH systems reproduce the prediction of the chiral Luttinger liquid theory, complementing the exact diagonalization results with larger lattice sizes and more particles.

cond-mat.str-el↗