arXiv subjects

Yves H. Kwan

Publications and source records attributed to Yves H. Kwan.

At least 19 recordsLinked to original sources

arXiv2026

Strain-Tuned Incommensurate Kekulé Spiral Order in Twisted Bilayer Graphene: a Quantum Many-Body Study

The physics of twisted bilayer graphene away from the exactly solvable chiral limit and the quantum Monte Carlo sign-problem-free charge neutrality point is elusive due to the exponential increase in the computational complexity, which has rendered explanations of experimentally observed insulating and superconducting phases restricted largely to the perturbative level. Here we focus on the filling factor $ν=\pm2$ and address the question of the strain dependence of the interacting ground state by approximate quantum Monte Carlo (AQMC), state-of-the-art exact diagonalization (ED) and Hartree-Fock (HF) mean field, in order to investigate the strain-tuned transition from the Kramers intervalley coherent (KIVC) state to the incommensurate Kekulé spiral (IKS) state. While all three methods capture the KIVC order, only ED and HF detect the weaker IKS order that AQMC does not capture adequately. As the AQMC is still capable of capturing stronger orders like the KIVC, our combined protocol may open the door for further understanding of the rich phases of twisted bilayer graphene and other strongly-correlated systems.

cond-mat.str-el↗

arXiv2026

Quantized Transport through a Supermoiré Chern Mosaic

Magic-angle helical trilayer graphene---three graphene layers sequentially twisted in the same direction by $\sim1.8^\circ$---relaxes into a mosaic of domains that, at zero field, carry opposite valley-resolved Chern numbers, with boundaries hosting a network of gapless conducting modes. Charge transport through this network depends sensitively on how the modes connect and scatter, making well-quantized transport unlikely. Contrary to this expectation, we observe a field-induced Chern gap with Chern number $C=-6$ emanating from charge neutrality; in this gap, the Hall resistance is quantized to within $2\%$ of the expected value, $-h/6e^2$, at 4.6 K. We explain this behavior using both Hofstadter and orbital Zeeman calculations, which show that a moderate magnetic field drives a valley-selective topological transition. Above the transition, the total Chern number of the occupied states in each spin-valley flavor becomes identical across neighboring domains, and the domain-wall modes can become gapped. Though the central valence-band Chern numbers still differ between the two domain types, the observed quantized transport attests to a global gap.

cond-mat.mes-hall↗

arXiv2026

The "Moiré Capacitor Effect" and Stabilization of Fractional Chern Insulators in Rhombohedral Graphene Superlattices

While the necessity of a moiré potential for fractional Chern insulators (FCIs) in rhombohedral graphene-hBN superlattices, first predicted in Ref. 1, is now grounded in experiments, a theory of its origin and importance remains at large. We present a mechanism---the moiré capacitor effect---that enhances the moiré potential by electrostatically imprinting the valence charge density onto the conduction bands. We derive the analytical form of this term and reveal its crucial role in stabilizing a parent state with Chern number $C=1$ at filling $ν=1$. We propose a parent state theory which posits that stability of the Chern insulator and flatness of its hole excitations are necessary for obtaining FCIs upon doping. We then perform multi-band exact diagonalization calculations to confirm the emergence of FCIs at $ν= 2/3$ in the presence of the moiré capacitor effect. Our FCI state is stabilized by inter-band fluctuations, unlike in the moire-free case which collapses with band-mixing. We provide the first consistent theory for this state in aligned samples and explain its absence in unaligned ones.

cond-mat.str-el↗

arXiv2026

Fermiology and the Candidate Chiral Superconductor in Rhombohedral Tetralayer Graphene

Chiral superconductivity, in which the phase of the superconducting order parameter winds in momentum space, has long been sought for its close link to topological superconductivity. Recent work reported a superconductor in rhombohedral multilayer graphene emerging from a time-reversal symmetry broken normal state, suggesting that it could be a chiral superconductor. However, the possibility of chirality depends on the symmetry and structure of the normal-state Fermi surface, which have not been directly measured. Here we measure quantum oscillations in rhombohedral tetralayer graphene over a broad range of the phase diagram, including the superconducting region. At densities well above the onset of superconductivity, we reproduce previously-reported oscillations consistent with a spin- and valley-polarized quarter metal with a single simply-connected Fermi pocket. As the carrier density is reduced, we find a transition to a complex "multitone" state that persists through the superconducting region. This state's spectrum of quantum oscillations is incompatible with a simply-connected quarter metal. The next-simplest candidate normal states suggested by our microscopic modeling (fully-polarized annular, nematic, and three-pocket states) are inconsistent with our measurements, albeit difficult to rule out entirely. The normal state is thus seen to be richer than previously envisaged, reshaping the search for the superconducting mechanism and the possible chirality of the pairing channel.

cond-mat.supr-con↗

arXiv2026

Engineering topological flat bands in $Γ$-valley moiré systems with Ising-type SOC: twisted 1T-ZrS$_2$ and 1T-SnSe$_2$

Twisted moiré superlattices hosting topological flat bands provide a platform to explore the interplay between topology and correlations. Here we investigate topological band structures in $Γ$-valley moiré systems based on 1T-ZrS$_2$ and 1T-SnSe$_2$. Using large-scale ab initio calculations and continuum modelling, we demonstrate that both materials exhibit an approximate spin-$U(1)$ symmetry and host isolated topological moiré valence bands, including quantum spin Hall and high spin Chern states. By constructing a hierarchy of $Γ$-valley moiré continuum models, we show that isolated moiré bands carry a trivial $C_3$ symmetry indicator when the low-energy physics is described by a single effective orbital and a single layer-hybridized branch, either bonding or antibonding. Topological bands therefore arise from inter-branch and/or inter-orbital coupling. Moreover, we determine interaction-driven phase diagrams using Hartree--Fock and exact diagonalization, finding various phases tunable by twist angle, interaction strength, and displacement field. We identify specific conditions under which fractional Chern insulators are favored. Together with previous work showing that the moiré conduction bands of 1T-ZrS$_2$ and 1T-SnSe$_2$ realize $M$-valley twisting and host quasi-one-dimensional physics, our results establish these systems as ideal platforms for strongly correlated moiré physics and provide a systematic framework for understanding topological band structures in $Γ$-valley moiré materials.

cond-mat.mtrl-sci↗

arXiv2026

Mesoscopic transport in a Chern mosaic

We analyze mesoscopic electronic transport in a Chern mosaic: a regular pattern of domains whose electronic bands carry differing local Chern numbers. An example platform where a Chern mosaic can arise is a moiré heterostructure, where variations in the local moiré parameters can produce such domains. We compute resistances at linear response for a variety of domain wall network geometries at zero temperature and magnetic field. Simple domain configurations can exhibit zero, integer, or fractional multiples of the quantum of resistance in both the longitudinal and transverse (Hall) responses. Our simple semi-classical analysis provides a useful computational method and comparative catalog for ongoing experiments in two-dimensional topological materials.

cond-mat.mes-hall↗

arXiv2026

Electrically controllable valence-conduction band reversals in helical trilayer graphene

In moiré graphene systems, electronic interactions lift spin and valley degeneracies, leading to symmetry-broken ground states. In helical trilayer graphene (HTG), we uncover a distinct interaction-driven mechanism in which the roles of sublattice-polarized valence and conduction bands are cyclically reversed. Using scanning nano-SQUID magnetometry, we detect a series of sharp magnetic signatures consistent with seesaw-like transitions, where occupied and unoccupied valence and conduction bands interchange repeatedly with doping, accompanied by a novel form of magnetic hysteresis. These transitions occur entirely within metallic regimes and leave only weak fingerprints in transport measurements. Self-consistent Hartree-Fock calculations reveal that interactions reorganize all eight low-energy flat bands, driving abrupt changes in orbital magnetization. Our results establish HTG as the first system where electronic interactions provide doping-controlled access to all three internal degrees of freedom - spin, valley, and sublattice - introducing a new class of correlated phase transitions.

cond-mat.mes-hall↗

arXiv2025

Mean-field Modelling of Moiré Materials: A User's Guide with Selected Applications to Twisted Bilayer Graphene

We review the theoretical modelling of moiré materials, focusing on various aspects of magic-angle twisted bilayer graphene (MA-TBG) viewed through the lens of Hartree-Fock mean-field theory. We first provide an elementary introduction to the continuum modelling of moiré bandstructures, and explain how interactions are incorporated to study correlated states. We then discuss how to implement mean-field simulations of ground state structure and collective excitations in this setting. With this background established, we rationalize the power of mean-field approximations in MA-TBG, by discussing the idealized "chiral-flat" strong-coupling limit, in which ground states at electron densities commensurate with the moiré superlattice are exactly captured by mean-field ansätze. We then illustrate the phenomenological shortcomings of this limit, leading us naturally into a discussion of the intermediate-coupling incommensurate Kekulé spiral (IKS) order and its origins in ever-present heterostrain. IKS and its placement within an expanded Hartree-Fock manifold form our first "case study". Our second case study involves time-dependence, and focuses on the collective modes of various broken-symmetry insulators in MA-TBG. As a third and final case study, we return to the strong-coupling picture, which can be stabilized by aligning MA-TBG to an hBN substrate. In this limit, we show how mean field theory can be adapted to the translationally non-invariant setting in order to quantitatively study the energetics of domain walls in orbital Chern insulating states. We close with a discussion of extensions and further applications. Used either as a standalone reference or alongside the accompanying open-source code, this review should enable readers with a basic knowledge of band theory and many-body physics to systematically build and analyze detailed models of generic moiré systems.

cond-mat.str-el↗

arXiv2025

Higher Chern bands in helical homotrilayer transition metal dichalcogenides

We propose helically twisted homotrilayer transition metal dichalcogenides as a platform for realizing correlated topological phases of matter with higher and tunable Chern numbers. We show that a clear separation of scales emerges for small twist angles, allowing us to derive a low-energy continuum model that captures the physics within moiré-scale domains. We identify regimes of twist angle and displacement field for which the highest-lying hole band is isolated from other bands and is topological with $K$-valley Chern number $C=-2$. We demonstrate that varying the displacement field can induce a transition from $C=-2$ to $C=-1$, as well as from a topologically trivial band to a $C=-1$ band. We derive an effective tight-binding description for a high-symmetry stacking domain which is valid for a wide range of twist angles, and we show that the $C=-2$ band can remain stable at filling fraction $ν=-1$ in the presence of interactions in Hartree-Fock calculations.

cond-mat.mes-hall↗

arXiv2025

Does Moire Matter? Critical Moire Dependence with Quantum Fluctuations in Graphene Based Integer and Fractional Chern Insulators

Rhombohedral multilayer graphene has emerged as a powerful platform for investigating flat-band-driven correlated phenomena, yet most aspects remain not understood. In this work, we systematically study the moire-dependent band topology in rhombohedral hexalayer graphene. For the first time we demonstrate that the moire twist angle plays a crucial role in the formation of the moire Chern insulators in rhombohedral hexalayer graphene/hexagonal boron nitride (RHG/hBN) moire superlattices. In the moire-distant regime at filling factor v = 1, only systems with a twist angle θ < 1.1° exhibit an integer moire Chern insulator, while the fractional Chern insulator at v = 2/3 requires smaller twist angle to be stabilized. Our theoretical modelling, which includes quantum fluctuations and exact diagonalization results, suggests that mean-field theory, which has been widely adopted, does not explain the twist-angle dependence of the v = 1 phase diagram, and that correlation effects are crucial. Moreover, we realize two distinct stacking configurations ( /Xi=0 and /Xi=1) between graphene and hBN, and find that both cases can yield a Chern insulator at v = 1. Our experimental work upends the current mean-field paradigm, illuminates how quantum fluctuations and moiré effects shape the RHG/hBN phase diagram, and paves the way for future understanding and engineering of topological correlated states in rhombohedral graphene moire systems.

cond-mat.mes-hall↗

arXiv2025

Berry Trashcan With Short Range Attraction:Exact $p_x+i p_y$ Superconductivity in Rhombohedral Graphene

We show the presence of analytic $p_x + i p_y$ superconducting ground states in the Berry Trashcan -- a minimal model of rhombohedral graphene valid for $n \ge 4$ layers -- under short-range attractive interactions. We demonstrate that the model, whose dispersion consists of a flat bottom surrounded by steep walls of prohibitive kinetic energy, serves as a building block to understand superconductivity in the moiré-free limit. We find that the ground-state chirality has a ``ferromagnetic'' coupling to that of the uniform Berry curvature of the model, and compare the analytically obtained binding energies, excitation spectra and off-diagonal long-range order (ODLRO) with numerical exact diagonalization results. We show that the analytic structure of this model is that of a restricted spectrum generating algebra (RSGA), initially developed for quantum scars, and build a variety of other exact (but contrived) models with exact chiral superconductivity based on a method developed in Ref.[1]. However, under short range attraction, we show that the Berry Trashcan is the optimal and only realistic point in the class of GMP-like algebras to host a chiral superconductor state. A toy model in 1D and its related physics is also investigated. Our results reveal that chiral superconductivity is natural under attractive interactions in the Berry trashcan model of rhombohedral graphene in displacement field, although we make no claim about the origin of the attraction.

cond-mat.supr-con↗

arXiv2025

Putting a new spin on the incommensurate Kekulé spiral: from spin-valley locking and collective modes to fermiology and implications for superconductivity

We revisit the global phase diagram of magic-angle twisted bilayer and [symmetric] trilayer graphene (MA-TBG/TSTG) in light of recent scanning tunneling microscopy (STM) measurements on these materials. These experiments both confirmed the importance of strain in stabilizing the predicted incommensurate Kekulé spiral (IKS) order near filling $|ν|=2$ of the weakly dispersive central bands in both systems, and suggested a key role for electron-phonon couplings and short-range Coulomb interactions in selecting between various competing orders at low strain in MA-TBG. Here, we show that such interactions $\textit{also}$ play a crucial role in selecting the spin structure of the strain-stabilized IKS state. This in turn influences the visibility of the IKS order in STM in a manner that allows us to infer their relative importance. We use this insight in conjunction with various other pieces of experimental data to build a more complete picture of the phase diagram, focusing on the spectrum of low-lying collective modes and the nature of the doped Fermi surfaces. We explore the broad phenomenological implications of these results for superconductivity.

cond-mat.str-el↗

arXiv2025

Unconventional Orbital Magnetism in Graphene-based Fractional Chern Insulators

Orbital magnetism in graphene originates from correlation-driven spontaneous valley symmetry breaking1-7. It can lead to various anomalous transport phenomena such as integer and fractional quantum anomalous Hall effects8-11. In general, the in-plane magnetic field B|| primarily couples to the spin degrees of freedom in graphene and has long been presumed to have a negligible effect on orbital magnetism due to the ultra-weak spin-orbit coupling12-18. In this work, we report multiple unconventional orbital magnetic phenomena that are highly sensitive to the B|| field in graphene/hBN superlattices hosting both integer and fractional Chern insulators (FCIs). We observed chirality-switching behaviors of the Chern insulator at moiré filling factor ν = 1 under a finite B_par, demonstrating that both the C = +-1 states are permissible ground states at zero perpendicular magnetic field B_per. For the FCI at ν = 2/3, we observed topological phase transitions between two states characterized by Hall resistivity \r{ho}xy = +-3h/2e2 under both B_per and B_par fields. In-plane B|| field can effectively suppress the FCI state at zero B_per field and enhance the FCI state with the opposite chirality, as resolved in Landau fan diagrams. Moreover, we observed rich phase transitions at 1 < ν < 2, accompanied by intervalley coherence and anomalous Hall effects (AHE) that can be triggered by sweeping either B_per or B_par. Our work has unveiled new properties of orbital magnetism, providing a new knob for engineering various AHE in graphene.

cond-mat.mes-hall↗

arXiv2025

"Berry Trashcan" Model of Interacting Electrons in Rhombohedral Graphene

We present a model for interacting electrons in a continuum band structure that resembles a ``trashcan'', with a flat bottom of radius $k_b$ beyond which the dispersion increases rapidly with velocity $v$. The form factors of the Bloch wavefunctions can be well-approximated by the Girvin-MacDonald-Platzman algebra, which encodes the uniform Berry curvature. We demonstrate how this model captures the salient features of the low-energy Hamiltonian for electron-doped pristine $n$-layer rhombohedral graphene (R$n$G) for appropriate values of the displacement field, and provide corresponding expressions for $k_b$. In the regime where the Fermi wavevector is close to $k_b$, we analytically solve the Hartree-Fock equations for a gapped Wigner crystal in several limits of the model. We introduce a new method, the sliver-patch approximation, which extends the previous few-patch approaches and is crucial in both differentiating even vs odd Chern numbers of the ground state and gapping the Hartree-Fock solution. A key parameter is the Berry flux $φ_{\text{BZ}}$ enclosed by the (flat) bottom of the band. We analytically show that there is a ferromagnetic coupling between the signs of $φ_{\text{BZ}}$ and the Chern number $C$ of the putative Wigner crystal. We also study the competition between the $C=0$ and $1$ solutions as a function of the interaction potential for parameters relevant to R$n$G. By exhaustive comparison to numerical Hartree-Fock calculations, we demonstrate how the analytic results capture qualitative trends of the phase diagram, as well as quantitative details such as the enhancement of the effective velocity. Our analysis paves the way for an analytic and numerical examination of the stability and competition beyond mean-field theory of the Wigner crystals in this model.

cond-mat.str-el↗

arXiv2024

Fractional Chern mosaic in supermoiré graphene

We propose the realization of a fractional Chern mosaic: a state characterized by a spatially varying topological order. This state is enabled by a separation of length scales that emerges when three graphene sheets are sequentially rotated by a small twist angle. The resulting structure features not only conventional moiré lattices, but also a much larger supermoiré lattice. We demonstrate that a fractional Chern mosaic arises when electron correlations induce fractionalization locally on the moiré scale, while the pattern of fractionalization varies at the supermoiré scale.

cond-mat.str-el↗

arXiv2024

Moiré Fractional Chern Insulators IV: Fluctuation-Driven Collapse of FCIs in Multi-Band Exact Diagonalization Calculations on Rhombohedral Graphene

The fractional Chern insulators (FCIs) observed in pentalayer rhombohedral graphene/hexagonal boron nitride superlattices have a unique origin contrary to theoretical expectations: their non-interacting band structure is gapless, unlike standard FCIs and the Landau level. Hartree-Fock (HF) calculations at filling $ν=1$ yield a gapped ground state with Chern number 1 through band mixing, identifying a possible parent state. However, many-body calculations restricted to the occupied HF band predispose the system towards FCIs and are essentially uncontrolled. In this work, we use unbiased multi-band exact diagonalization (ED) to allow fluctuations into the gapless bands for two normal-ordering schemes. In the "charge neutrality" scheme, the weak moiré potential leads to theoretical proposals based on Wigner crystal-like states. However, we find that FCIs seen in 1-band ED calculations are destroyed by band mixing, becoming gapless as fluctuations are included. In the "average" scheme, the Coulomb interaction with the periodic valence charge background sets up a stronger moiré potential. On small systems, FCIs at $ν=1/3$ are destroyed in multi-band calculations, while those at $ν=2/3$ are initially strengthened. However we do not converge to a stable FCI at $ν=2/3$ even on the largest accessible systems. These findings question prior results obtained within projection to a single HF band. They suggest that current models do not support FCIs with correlation length small enough to be converged in accessible, unbiased ED calculations, or do not support FCIs at all.

cond-mat.str-el↗

arXiv2024

When Could Abelian Fractional Topological Insulators Exist in Twisted MoTe$_2$ (and Other Systems)

Using comprehensive exact diagonalization calculations on $θ\approx 3.7 ^{\circ}$ twisted bilayer MoTe$_2$ ($t$MoTe$_2$), as well as idealized Landau level models also relevant for lower $θ$, we extract general principles for engineering fractional topological insulators (FTIs) in realistic situations. First, in a Landau level setup at $ν=1/3+1/3$, we investigate what features of the interaction destroy an FTI. For both pseudopotential interactions and realistic screened Coulomb interactions, we find that sufficient suppression of the short-range repulsion is needed for stabilizing an FTI. We then study $θ\approx 3.7 ^{\circ}$ $t$MoTe$_2$ with realistic band-mixing and anisotropic non-local dielectric screening. Our finite-size calculations only find an FTI phase at $ν=-4/3$ in the presence of a significant additional short-range attraction $g$ that acts to counter the Coulomb repulsion at short distances. We discuss how further finite-size drifts, dielectric engineering, Landau level character, and band-mixing effects may reduce the required value of $g$ closer towards the experimentally relevant conditions of $t$MoTe$_2$. Projective calculations into the $n=1$ Landau level, which resembles the second valence band of $θ\simeq 2.1^\circ$ $t$MoTe$_2$, do not yield FTIs for any $g$, suggesting that FTIs at low-angle $t$MoTe$_2$ for $ν=-8/3$ and $-10/3$ may be unlikely. While our study highlights the challenges, at least for the fillings considered, to obtaining an FTI with transport plateaus, even in large-angle $t$MoTe$_2$ where fractional Chern insulators are experimentally established, we also provide potential sample-engineering routes to improve the stability of FTI phases.

cond-mat.str-el↗

arXiv2024

Textured Exciton Insulators

We introduce and study new interacting topological states that arise in time-reversal symmetric bands with an underlying obstruction to forming localized states. If the $U(1)$ valley symmetry linked to independent charge conservation in each time-reversal sector is spontaneously broken, the corresponding `excitonic' order parameter is forced to form a topologically non-trivial texture across the Brillouin zone. We show that the resulting phase, which we dub a textured exciton insulator, cannot be given a local-moment description due to a form of delicate topology. Using toy models of bands with Chern or Euler obstructions to localization we construct explicit examples of the Chern or Euler texture insulators (CTIs or ETIs) they support, and demonstrate that these are generically competitive ground states at intermediate coupling. We construct field theories that capture the response properties of these new states. Finally, we identify the incommensurate Kekulé spiral phase observed in magic-angle bi- and trilayer graphene as a concrete realization of an ETI.

cond-mat.str-el↗