arXiv subjects

Fengcheng Wu

Publications and source records attributed to Fengcheng Wu.

At least 19 recordsLinked to original sources

arXiv2026

Supermoir\'e Reconstruction and Topological Mosaics in Twisted Trilayer WSe$_2$ and MoTe$_2$

We investigate lattice relaxation and band structures of helical and alternating twisted trilayer WSe$_2$ and MoTe$_2$ using machine-learning force fields and large-scale ab initio calculations. Interference between the two bilayer moir\'e lattices generates a supermoir\'e lattice that, upon relaxation, reconstructs into a few dominant domain types with locally commensurate bilayer moir\'e lattices. Because the systems lack $C_{2z}$ symmetry, domains otherwise related by this symmetry become energetically and topologically distinct, unlike in twisted trilayer graphene. Band structure calculations show that the topmost valence bands originate from the $K$ ($K'$) valleys and carry domain-dependent valley Chern numbers. The resulting supermoir\'e lattice hosts a mosaic of topologically inequivalent domains, offering a platform for exploring correlated and topological physics.

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arXiv2026

Chiral superconductors and competing states across a Lifshitz transition in rhombohedral pentalayer graphene

Rhombohedral multilayer graphene hosts a distinctive low-energy electronic structure in which strong Coulomb interactions and nontrivial quantum geometry intertwine to generate exotic quantum states. Recent experiments reported signatures of chiral superconductivity in electron-doped rhombohedral multilayer graphene within the spin- and valley-polarized regime. Here we map the normal-state fermiology surrounding chiral superconductivity in rhombohedral pentalayer graphene. Quantum oscillation measurements reveal an electrically controlled Lifshitz transition between a simply-connected circular quarter-metal Fermi surface and an annular quarter-metal Fermi surface. The Lifshitz boundary itself shifts with perpendicular magnetic field, consistent with the strongly momentum-dependent orbital magnetic moment of the low-energy band. Approaching the transition from either side, the electron effective mass becomes strongly enhanced, implying the formation of a nearly dispersionless band bottom and a strongly reduced kinetic-energy scale. This singular electronic structure produces a regime of exceptionally strong instability in which chiral superconductivity competes with Wigner crystalline phases and reentrant quantum Hall states. In particular, two superconducting regions with signatures of orbital time-reversal-symmetry breaking lie on opposite sides of the Lifshitz boundary and have comparable transition temperatures, yet the annular-side state is suppressed by a substantially smaller perpendicular magnetic field. Our calculation finds comparable chiral pairing tendencies on the two parent Fermi surfaces while producing a much lower orbital-Zeeman pair-breaking scale and an additional finite-momentum pairing tendency for the annular state. These results identify Fermi-surface topology as a key control parameter for chiral superconductivity in rhombohedral graphene.

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arXiv2026

Quantum-Geometric Design of Lattice Generalized Landau Levels

We design lattice models with tailored quantum geometry, including generalized Landau levels (LLs) satisfying the integrated trace condition and higher-Chern bands with ideal quantum geometry. Our models with $N=2$, $3$, and $4$ sublattices include a generalized Haldane model ($N=2$ honeycomb lattice model) with Gaussian-decaying hoppings realizable in twisted bilayer MoTe$_2$, and $N \geq 3$ models with exponentially decaying hoppings. Exact diagonalization reveals fractional Chern insulators in the generalized zeroth LL bands of all three models, a Moore-Read state in the generalized first LL band of the $N=4$ model, and various interaction-driven topological phases$\unicode{x2013}$including integer and fractional anomalous Hall crystals and a multicomponent Halperin state$\unicode{x2013}$in the ideal higher-Chern band of the $N=3$ model. Informed by quantum geometry, our work provides a pathway for lattice realizations of Landau-level and beyond-Landau-level physics.

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arXiv2026

Supermoir\'e Chern mosaic in helical trilayer WSe2

Helically twisted multilayers offer access to moir\'e physics beyond the single-superlattice paradigm, yet their correlated and topological transport properties remain largely unexplored in semiconductor moir\'e materials. Here we report magnetotransport measurements of helical trilayer WSe2, in which two coupled moir\'e patterns relax into a supermoir\'e landscape composed of inequivalent local topological domains with distinct electronic structures and unequal spatial areas. By electrostatic tuning, we identify a trilayer-hybridized regime where interactions and real-space reconstruction combine to generate a plethora of magnetic and topological states absent in the twisted bilayers. At moir\'e filling factor $\nu$ = -1, we observe a ferromagnetic insulating state that is robust against magnetic field and accompanied by a non-quantized anomalous Hall response ~-4 kOhms. This behaviour is consistent with a time-reversal-symmetry-breaking supermoir\'e Chern mosaic, in which the Hall response arises from the non-cancelling contributions of local domains with opposite Chern character arranged by the relaxed structure. Under strong magnetic fields, a symmetry-broken Chern insulating state (C = 1) emerges near $\nu$ = -2/3, displaying a much larger positive Hall response together with strongly enhanced longitudinal resistance, suggestive of field-reconstructed topological minibands and domain-boundary scattering. These results establish relaxed supermoir\'e semiconductor trilayers as a platform for spatially organized magnetism and topology beyond the bilayer limit.

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arXiv2026

Simultaneous nanoscale imaging of local conductivity and chemical potential in a quantum Hall isospin ferromagnet

Quantum Hall isospin ferromagnetism in multilayer graphene offers a versatile playground for exploring flat band correlated physics, driven by the intricate coupling of spin, valley, orbital, and layer degrees of freedom. However, a nanoscale probe capable of simultaneously mapping local conductivity and chemical potential in these exotic phases has yet to be realized. Here, we introduce scanning conductivity and chemical potential microscopy (SCCM), a technique integrating scanning microwave impedance microscopy and Kelvin probe force microscopy. We demonstrate SCCM by probing the quantum Hall states and many-body Landau level energy spectrum in bilayer graphene. Applied to marginally twisted double bilayer graphene, SCCM then reveals a cascade of quantum Hall isospin ferromagnetic states with unexpected re-emergence behaviors. Significantly, experimental many-body Landau level energy spectrum further uncovers the intricate connections of these complex phenomena to inter-subband Landau level crossings and Landau level single-particle wavefunctions. These insights enable the construction of a comprehensive quantum Hall phase diagram. Our results demonstrate SCCM's capability in decoding complex quantum phenomena, establishing it as a versatile nanoscale probe for electron correlation and topology.

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arXiv2026

Observation of a Reconstructed Chern Insulator in Twisted Bilayer MoTe2

Twisted bilayer MoTe2 is a prototypical moire material in which long-wavelength superlattices amplify electron correlations, enabling a wealth of emergent quantum phases. To date, experimental efforts have focused primarily on small twist angles (typically smaller than 4deg ), whereas the larger-angle regime-where moire bands become more dispersive and correlations are reduced-has remained largely unexplored. Here we chart the topological phase space of tMoTe2 at a relatively large twist angle of approximately 4.54deg, accessing a moderately correlated regime with enhanced bandwidth. In contrast to small-angle devices that predominantly host fractional quantum anomalous Hall or spin Hall responses, we uncover multiple Chern-insulating states with C = 1 at moire fillings v = -1, -0.53 and -1/2. Strikingly, at v = -2/3 a magnetic field induces a fractional Chern insulator accompanied by an insulator-metal transition. Our results broaden the topological phase diagram of tMoTe2 and establish large-angle moire superlattices as a versatile platform for engineering robust topological states beyond the strong-correlation limit.

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arXiv2026

EEG-SeeGraph: Interpreting functional connectivity disruptions in dementias via sparse-explanatory dynamic EEG-graph learning

Robust and interpretable dementia diagnosis from noisy, non-stationary electroencephalography (EEG) is clinically essential yet remains challenging. To this end, we propose SeeGraph, a Sparse-Explanatory dynamic EEG-graph network that models time-evolving functional connectivity and employs a node-guided sparse edge mask to reveal the connections that drive diagnostic decisions, while remaining robust to noise and cross-site variability. SeeGraph comprises four components: (1) a dual-trajectory temporal encoder that models dynamic EEG with two streams, where node signals capture regional oscillations and edge signals capture interregional coupling; (2) a topology-aware positional encoder that derives graph-spectral Laplacian coordinates from the fused connectivity and augments node embeddings; (3) a node-guided sparse explanatory edge mask that gates the connectivity into a compact subgraph; and (4) a gated graph predictor that operates on the sparsified graph. The framework is trained using cross-entropy loss together with a sparsity regularizer on the mask, yielding noise-robust and interpretable diagnoses. The effectiveness of SeeGraph is validated on public and in-house EEG cohorts, including patients with neurodegenerative dementias and healthy controls, under both raw and noise-perturbed conditions. Its sparse, node-guided explanations highlight disease-relevant connections and align with established clinical findings on functional connectivity alterations, thereby offering transparent cues for neurological evaluation.

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arXiv2026

Abelian and non-Abelian fractionalized states in twisted MoTe$_2$: A generalized Landau-level theory

Fractional Chern insulators are lattice analogs of fractional quantum Hall states that realize fractionalized quasiparticles without an external magnetic field. A key strategy to understand and design these phases is to map Chern bands onto Landau levels (LLs). Here, we introduce a universal framework that variationally decomposes Bloch bands into generalized LLs, providing a controlled and quantitative characterization of their effective LL nature. Applying this approach to twisted bilayer MoTe$_2$ modeled by first-principles-derived moir\'e Hamiltonians, we find that the first moir\'e valence band is dominated by the generalized zeroth LL across a broad range of twist angles, facilitating the formation of Abelian fractional Chern insulators in the Jain sequences. The second moir\'e band, renormalized via Hartree-Fock calculations at hole filling $\nu_h = 2$, is dominated by the generalized first LL at twist angles $\theta = 2.45^\circ$ and $2.13^\circ$. At $\theta = 2.45^\circ$, we find numerical evidence for a non-Abelian Moore--Read (MR) state at $\nu_h = 5/2$, with consistent signatures in both the energy spectrum and the particle entanglement spectrum. Interpolation studies further demonstrate an adiabatic connection between this state and the MR state in the conventional first LL. In contrast, at $\theta = 2.13^\circ$, a charge-density-wave state prevails in the competition with the MR state due to the larger bandwidth. Our variational mapping provides a theoretical framework for exploring exotic fractionalized phases, including non-Abelian states, in realistic systems.

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arXiv2025

Quantum Phases in Twisted Homobilayer Transition Metal Dichalcogenides

Twisted homobilayer transition metal dichalcogenides - specifically twisted bilayer MoTe$_2$ and twisted bilayer WSe$_2$ - have recently emerged as a versatile platform for strongly correlated and topological phases of matter. These two-dimensional systems host tunable flat Chern bands in which Coulomb interactions can dominate over kinetic energy, giving rise to a variety of interaction-driven phenomena. A series of groundbreaking experiments have revealed a rich landscape of quantum phases, including integer and fractional quantum anomalous Hall states, quantum spin Hall states, anomalous Hall metals, zero-field composite Fermi liquids, and unconventional superconductors, along with more conventional topologically trivial correlated states including antiferromagnets. This review surveys recent experimental discoveries and theoretical progress in understanding these phases, with a focus on the key underlying mechanisms - band topology, electron interactions, symmetry breaking, and charge fractionalization. We emphasize the unique physics of twisted TMD homobilayers in comparison to other related systems, discuss open questions, and outline promising directions for future research.

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arXiv2025

Signature of gate tunable superconducting network in twisted bilayer graphene

Twisted van der Waals materials provide a tunable platform for investigating two-dimensional superconductivity and quantum phases. Using spectra-imaging scanning tunneling microscopy, we study the superconducting states in twisted bilayer graphene and track their evolution from insulating phases. Gate-dependent spectroscopic measurements reveal two distinct regimes: under-doped ({\nu} = -2.3) and optimally doped ({\nu} = -2.6). In the under-doped regime, partial superconductivity arises, forming a network interspersed with non-gapped regions. At optimal doping, the entire unit cell demonstrates superconductivity, with gap size modulation showing an anti-correlation with the local density of states. This gate-dependent transition from an insulating phase to a modulated superconductor uncovers an unexpected spatial hierarchy in pairing behavior and offers direct microscopic insights to constrain theories of superconductivity in moir\'e systems.

cond-mat.supr-con↗

arXiv2025

Characterization of fractional Chern insulator quasiparticles in twisted homobilayer MoTe$_2$

We provide a detailed study of Abelian quasiparticles of valley polarized fractional Chern insulators (FCIs) residing in the top valence band of twisted bilayer MoTe$_2$ (tMoTe$_2$) at hole filling $\nu_h=2/3$. We construct a tight-binding model of delocalized quasiparticles to capture the energy dispersion of a single quasiparticle. We then localize quasiparticles by short-range delta impurity potentials. Unlike the fractional quantum Hall (FQH) counterpart in the lowest Landau level (LLL), the density profile around the localized FCI quasiparticle in tMoTe$_2$ depends on the location of the impurity potential and loses the continuous rotation invariance. The FCI quasiparticle localized at moir\'e lattice center closely follows the anyon Wannier state of the tight-binding model of the mobile quasiparticle. Despite of the difference in density profiles, we find that the excess charge around the impurity potential for the $\nu_h=2/3$ FCIs in tMoTe$_2$ is still similar to that of the $\nu=2/3$ FQH state in the LLL if an effective magnetic length on the moir\'e lattice is chosen as the length unit, which allows a rough estimation of the spatial extent of the FCI quasiparticle. Far away from the impurity potential, this excess charge has the tendency to reach $e/3$, as expected for the Laughlin quasiparticle. The braiding phase of two FCI quasiparticles in tMoTe$_2$ also agrees with the theoretical prediction of fractional statistics. We characterize the interaction between two FCI quasiparticles and find a crossover from repulsive to attractive interaction as gate-to-sample distances decreases. Based on the nearly ideal quantum geometry of the top valence band of tMoTe$_2$, we propose a trial wave function for localized FCI quasiparticles, which reproduces the key feature of the density profile around a quasiparticle.

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arXiv2025

Deep Learning Sheds Light on Integer and Fractional Topological Insulators

Electronic topological phases of matter, characterized by robust boundary states derived from topologically nontrivial bulk states, are pivotal for next-generation electronic devices. However, understanding their complex quantum phases, especially at larger scales and fractional fillings with strong electron correlations, has long posed a formidable computational challenge. Here, we employ a deep learning framework to express the many-body wavefunction of topological states in twisted ${\rm MoTe_2}$ systems, where diverse topological states are observed. Leveraging neural networks, we demonstrate the ability to identify and characterize topological phases, including the integer and fractional Chern insulators as well as the $Z_2$ topological insulators. Our deep learning approach significantly outperforms traditional methods, not only in computational efficiency but also in accuracy, enabling us to study larger systems and differentiate between competing phases such as fractional Chern insulators and charge density waves. Our predictions align closely with experimental observations, highlighting the potential of deep learning techniques to explore the rich landscape of topological and strongly correlated phenomena.

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arXiv2025

Electrical switching of Chern insulators in moire rhombohedral heptalayer graphene

In orbital Chern insulators, the chemical potential acts as a tuning knob to reverse chirality in dissipationless edge currents, enabling electric-field control of magnetic order-key for future quantum electronics. Despite the rise of orbital Chern insulators, electrically switchable quantum anomalous Hall effect (QAHE) remains rare, necessitating further investigation. Here, we demonstrate electric-field-induced reversal of orbital Chern insulators in a moire superlattice composed of rhombohedral heptalayer graphene (r-7LG) aligned with hexagonal boron nitride. At one electron per moire unit cell, two emerging Chern insulating phases - one pointing away from and the other toward graphene's charge neutrality point in the phase diagram of carrier density (n) versus magnetic field (B) - exhibit energetic competition modulated by both n and B. This switchable QAHE chirality in r-7LG demonstrates a layer-number dependent response: similar phenomena in moire r-6LG require much higher magnetic fields and are absent in thinner rhombohedral graphene. Our findings establish moire-engineered rhombohedral graphene as a promising platform for exploring topological quantum materials with electrically controllable chiral edge modes and magnetic order.

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arXiv2025

Topological magnons and domain walls in twisted bilayer MoTe$_2$

We theoretically investigate the magnetic excitations in the quantum anomalous Hall insulator phase of twisted bilayer MoTe$_2$ at a hole filling factor of $\nu=1$, focusing on magnon and domain wall excitations. Using a generalized interacting Kane-Mele model, we obtain the quantum anomalous Hall insualtor ground state with spin polarization. The magnon spectrum is then computed via the Bethe-Salpeter equation, revealing two low-energy topological magnon bands with opposite Chern numbers. To further explore the magnon topology, we construct a tight-binding model for the magnon bands, which is analogous to the Haldane model. We also calculate the energy cost of domain walls that separate regions with opposite Chern numbers and bind chiral edge states. Finally, we propose an effective spin model that describes both magnon and domain wall excitations, incorporating Heisenberg spin interactions and Dzyaloshinskii-Moriya interactions. The coupling constants in this model are determined from the numerical results for magnons and domain walls. This model accounts for the Ising anisotropy of the system, captures the magnon topology, and allows for the estimation of the magnetic ordering temperature. Our findings provide a comprehensive analysis of magnetic excitations in twisted MoTe$_2$ and offer new insights into collective excitations in moir\'e systems.

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arXiv2025

Surface-dependent Majorana vortex phases in topological crystalline insulators

The topological crystalline insulator SnTe exhibits two types of surface Dirac cones: one located at non-time-reversal-invariant momenta on the (001) and (110) surfaces, and the other at time-reversal-invariant momenta on the (111) surface. Motivated by the recent experimental evidence of Majorana vortex end modes (MVEMs) and their hybridization on the (001) surface [Nature 633, 71 (2024)], we present a comprehensive investigation of Majorana vortex phases in SnTe, including topological classification, surface-state Hamiltonians analysis, and lattice model calculations. By utilizing rotational and magnetic mirror symmetries, we present two equivalent methods to reveal the topology of Majorana phases on different surfaces. We find that the MVEMs on the (001) and (110) surfaces are protected by both magnetic group and rotational symmetries. In contrast, the MVEMs on the (111) surface are protected by magnetic group or particle-hole symmetry. Due to the different properties of Dirac fermions in the $\bar{\Gamma}$ and $\bar{M}$ valleys on the (111) surfaces, including Fermi velocities and energy levels, we find that abundant vortex phase transitions can occur for the [111]-direction vortex. As the chemical potential increases, the number of robust MVEMs can change from $0\rightarrow 1\rightarrow 2$. These vortex transitions are characterized by both $Z$ winding number and $Z_2$ pfaffian topological invariants.

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arXiv2025

Visualization of intervalley coherent phase in PtSe2/HOPG heterojunction

Intervalley coherent (IVC) phase in graphene systems arises from the coherent superposition of wave functions of opposite valleys, whose direct microscopic visualization provides pivotal insight into the emergent physics but remains elusive. Here, we successfully visualize the IVC phase in a heterostructure of monolayer PtSe2 on highly oriented pyrolytic graphite. Using spectroscopic imaging scanning tunneling microscopy, we observe a Root3 by Root3 modulation pattern superimposed on the higher-order moire superlattice of the heterostructure, which correlates with a small gap opening around the Fermi level and displays an anti-phase real-space conductance distribution of the two gap edges. Such modulation pattern and small-gap vanish on the heterostructure of monolayer PtSe2 on bilayer-graphene-covered SiC substrate, due to the increased carrier density in the bilayer graphene. We provide a theoretical mechanism that the Root3 by Root3 modulation pattern originates from the IVC phase of few-layer graphene, which is magnified by the higher-order moire superlattice. Our work achieves visualization of the IVC phase, and develops an avenue for its generation and amplification via a moir\'e interface.

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arXiv2024

Quantized Landau-level crossing checkerboard in large-angle twisted graphene

When charge transport occurs under conditions like topological protection or ballistic motion, the conductance of low-dimensional systems often exhibits quantized values in units of $e^{2}/h$, where $e$ and $h$ are the elementary charge and Planck's constant. Such quantization has been pivotal in quantum metrology and computing. Here, we demonstrate a novel quantized quantity: the ratio of the displacement field to the magnetic field, $D/B$, in large-twist-angle bilayer graphene. In the high magnetic field limit, Landau level crossings between the top and bottom layers manifest equal-sized checkerboard patterns throughout the $D/B$-$\nu$ space. It stems from a peculiar electric-field-driven interlayer charge transfer at one elementary charge per flux quantum, leading to quantized intervals of critical displacement fields, (i.e., $\delta D$ = $\frac{e}{2\pi l_{B}^{2}}$, where $l_B$ is the magnetic length). Our findings suggest that interlayer charge transfer in the quantum Hall regime can yield intriguing physical phenomena, which has been overlooked in the past.

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arXiv2024

Family of third-order topological insulators from Su-Schrieffer-Heeger stacking

We construct a family of chiral symmetry-protected third-order topological insulators by stacking Su-Schrieffer-Heeger (SSH) chains and provide a unified topological characterization by a series of Bott indices. Our approach is informed by the analytical solution of corner states for the model Hamiltonians written as a summation of the extended SSH model along three orthogonal directions. By utilizing the generalized Pauli matrices, an enumeration of the constructed model Hamiltonians generates ten distinct models, including the well-studied three-dimensional Benalcazar-Bernevig-Hughes model. By performing a boundary projection analysis for the ten models, we find that certain surfaces and hinges of the systems can exhibit, respectively, nontrivial second-order and first-order topology in the phase of the third-order topological insulators. Furthermore, we analyze the phase diagram for one of the predicted models and reveal a rich set of topological phases, including the third-order topological insulators, second-order weak topological insulators, and second-order nodal semimetals.

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