arXiv subjects

Jiabin Yu

Publications and source records attributed to Jiabin Yu.

At least 37 records · Page 2Linked to original sources

arXiv2025

Quantum Geometry in Quantum Materials

Quantum geometry, characterized by the quantum geometric tensor, is pivotal in diverse physical phenomena in quantum materials. In condensed matter systems, quantum geometry refers to the geoemtric properties of Bloch states in the Brillouin zone. This pedagogical review provides an accessible introduction to the concept of quantum geometry, emphasizing its extensive implications across multiple domains. Specifically, we discuss the role of quantum geometry in optical responses, Landau levels, and fractional Chern insulators, as well as its influence on superfluid weight, spin stiffness, exciton condensates, electron-phonon coupling, etc. By integrating these topics, we underscore the pervasive significance of quantum geometry in understanding emergent behaviors in quantum materials. Finally, we present an outlook on open questions and potential future directions, highlighting the need for continued exploration in this rapidly developing field.

cond-mat.mes-hall↗

arXiv2025

Heavy Fermions as an Efficient Representation of Atomistic Strain and Relaxation in Twisted Bilayer Graphene

Although the strongly interacting flat bands in twisted bilayer graphene (TBG) have been approached using the minimal Bistritzer-MacDonald (BM) Hamiltonian, there is mounting evidence that strain and lattice relaxation are essential in correctly determining the order of the correlated insulator groundstates. These effects can be incorporated in an enhanced continuum model by introducing additional terms computed from the relaxation profile. To develop an analytical and physical understanding of these effects, we include strain and relaxation in the topological heavy fermion (HF) model of TBG. We find that strain and relaxation are very well captured in first order perturbation theory by projection onto the fully symmetric HF Hilbert space, and remarkably do not alter the interacting terms in the periodic Anderson model. Their effects are fully incorporated in the single-particle HF Hamiltonian, and can be reproduced in a minimal model with only 4 symmetry-breaking terms. Our results demonstrate that the heavy fermion framework of TBG is an efficient and robust representation of the perturbations encountered in experiment.

cond-mat.mes-hall↗

arXiv2025

Kekulé Spiral Order from Strained Topological Heavy Fermions

The topological heavy fermion (THF) model of twisted bilayer graphene is a framework for treating its strongly interacting topological flat bands. In this work, we employ the THF model with heterostrain and particle-hole symmetry breaking corrections to study its symmetry-broken ground states. We find that the heterostrain correction motivates a specific parent-state wavefunction which dictates the presence or absence of an incommensurate Kekulé spiral (IKS) at each integer filling by invoking Dirac node braiding and annihilation as a mechanism to achieve low energy gapped states. We then show that one-shot Hartree-Fock faithfully replicates the numerical results of fully self-consistent states and motivates an analytical approximation for the IKS wavevector. We can also account for the particle-hole asymmetry in the correlated insulator gaps. In particular, the THF model predicts stronger correlated states on the electron side rather than hole side in agreement with magic angle experiments, despite the electron side being more dispersive in the single-particle band structure. This work demonstrates that we can analytically explain even the more subtle symmetry breaking order properties observed in experiments where heterostrain, relaxation, and interactions together determine the ground state.

cond-mat.str-el↗

arXiv2025

Probing the Quantized Berry Phases in 1H-NbSe$_2$ Using Scanning Tunneling Microscopy

Topologically trivial insulators are classified into two primary categories: unobstructed and obstructed atomic insulators. While both types can be described by exponentially localized Wannier orbitals, a defining feature of obstructed atomic insulators is that the centers of charge of these orbitals are positioned at empty sites within the unit cell, rather than on atoms. Despite extensive theoretical predictions, the unambiguous and quantitative experimental identification of an obstructed atomic phase has remained elusive. In this work, we present the first direct experimental evidence of such a phase in 1H-NbSe$_2$. We develop a novel method to extract the inter-orbital correlation functions from the local spectral function probed by scanning tunneling microscopy (STM), leveraging the orbital wave functions obtained from ab initio calculations. Applying this technique to STM images, we determine the inter-orbital correlation functions for the atomic band of 1H-NbSe$_2$ that crosses the Fermi level. Our results show that this band realizes an optimally compact obstructed atomic phase, providing the first unambiguous experimental identification of such a phase. Our approach of deconvolving the STM signal using ab initio orbital wave functions is broadly applicable to other material platforms, offering a powerful tool for exploring other electronic phases.

cond-mat.mes-hall↗

arXiv2025

Corner Charge Fluctuation as an Observable for Quantum Geometry and Entanglement in Two-dimensional Insulators

Measuring bipartite fluctuations of a conserved charge, such as the particle number, is a powerful approach to understanding quantum systems. When the measured region has sharp corners, the bipartite fluctuation receives an additional contribution known to exhibit a universal angle-dependence in 2D isotropic and uniform systems. Here we establish that, for generic lattice systems of interacting particles, the corner charge fluctuation is directly related to quantum geometry. We first provide a practical scheme to isolate the corner contribution on lattices, and analytically prove that its angle-dependence in the small-angle limit measures exclusively the integrated quantum metric. A model of a compact obstructed atomic insulator is introduced to illustrate this effect analytically, while numerical verification for various Chern insulator models further demonstrate the experimental relevance of the corner charge fluctuation in a finite-size quantum simulator as a probe of quantum geometry. Last but not least, for free fermions, we unveil an intimate connection between quantum geometry and quantum information through the lens of corner entanglement entropies.

cond-mat.mes-hall↗

arXiv2024

A New Moiré Platform Based on M-Point Twisting

We introduce a new class of moiré systems and materials based on monolayers with triangular lattices and low-energy states at the M points of the Brillouin zone. These M-point moiré materials are fundamentally distinct from those derived from $Γ$- or K-point monolayers, featuring three time-reversal-preserving valleys related by three-fold rotational symmetry. We propose twisted bilayers of experimentally exfoliable 1T-SnSe$_2$ and 1T-ZrS$_2$ as realizations of this new class. Using extensive ab initio simulations, we develop quantitative continuum models and analytically show that the corresponding M-point moiré Hamiltonians exhibit emergent momentum-space non-symmorphic symmetries and a kagome plane-wave lattice in momentum space. This represents the first experimentally viable realization of a projective representation of crystalline space groups in a non-magnetic system. With interactions, these materials represent six-flavor Hubbard simulators with Mott physics, as can be seen by their flat Wilson loops. Furthermore, the presence of a non-symmorphic momentum-space in-plane mirror symmetry makes some of the M-point moiré Hamiltonians quasi-one-dimensional in each valley, suggesting the possibility of realizing Luttinger liquid physics. We predict the twist angles at which a series of (conduction) flat bands appear, provide a faithful continuum Hamiltonian, analyze its topology and charge density and briefly discuss several aspects of the physics of this new platform.

cond-mat.str-el↗

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.

cond-mat.mes-hall↗

arXiv2024

Topological Heavy Fermion Principle For Flat (Narrow) Bands With Concentrated Quantum Geometry

We propose a general principle for the low-energy theory of narrow bands with concentrated Berry curvature and Fubini-Study metric in the form of a map to Anderson-"+" models composed of heavy fermions hybridizing and interacting with semi-metallic modes. This map resolves the obstruction preventing topological bands from being realized in a local Hamiltonian acting on the low-energy degrees of freedom. The concentrated quantum geometry is reproduced through band inversion with a dispersive semi-metal, leaving a nearly flat, trivial band which becomes the heavy fermion. This representation is natural when the narrow band is not energetically isolated on the scale of the interaction and an enlarged Hilbert space is inescapable, but also provides analytical insight into the projected-interaction limit. First exemplified in twisted bilayer graphene (TBG), we extend it to (1) the twisted checkerboard, which we find has a chiral symmetric stable anomaly that forbids a lattice realization at all energies, and (2) the Lieb lattice with gapless flat bands, where we show the heavy fermions can be obtained by minimizing a Euclidean instanton action to saturate its BPS bound. The heavy fermion approach is widely applicable and physically transparent: heavy electrons carry the strong correlations and dispersive electrons carry the topology. This simple picture unifies the dichotomous phenomena observed in TBG and points to connections between moiré and stoichiometric materials.

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

Nontrivial Quantum Geometry and the Strength of Electron-Phonon Coupling

The coupling of electrons to phonons (electron-phonon coupling) is crucial for the existence of various phases of matter, in particular superconductivity and density waves. Here, we devise a theory that incorporates the quantum geometry of the electron bands into the electron-phonon coupling, demonstrating the crucial contributions of the Fubini-Study metric or its orbital selective version to the dimensionless electron-phonon coupling constant. We apply the theory to two materials, graphene and MgB$_2$ where the geometric contributions account for approximately 50\% and 90\% of the total electron-phonon coupling constant, respectively. The quantum geometric contributions in the two systems are further bounded from below by topological contributions. Our results suggest that the nontrivial electron band geometry/topology might favor superconductivity with relatively high critical temperature.

cond-mat.supr-con↗

arXiv2024

Two-stage growth for highly ordered epitaxial C$_{60}$ films on Au(111)

As an organic semiconductor and a prototypical acceptor molecule in organic photovoltaics, C$_{60}$ has broad relevance to the world of organic thin film electronics. Although highly uniform C$_{60}$ thin films are necessary to conduct spectroscopic analysis of the electronic structure of these C$_{60}$-based materials, reported C$_{60}$ films show a relatively low degree of order beyond a monolayer. Here, we develop a generalizable two-stage growth technique that consistently produces single-domain C$_{60}$ films of controllable thicknesses, using Au(111) as an epitaxially well-matched substrate. We characterize the films using low-energy electron diffraction, low-energy electron microscopy, scanning tunneling microscopy, and angle-resolved photoemission spectroscopy (ARPES). We report highly oriented epitaxial film growth of C$_{60}$/Au(111) from 1 monolayer (ML) up to 20 ML films. The high-quality of the C$_{60}$ thin films enables the direct observation of the electronic dispersion of the HOMO and HOMO-1 bands via ARPES without need for small spot sizes. Our results indicate a path for the growth of organic films on metallic substrates with long-range ordering.

cond-mat.mtrl-sci↗

arXiv2023

Moiré Fractional Chern Insulators III: Hartree-Fock Phase Diagram, Magic Angle Regime for Chern Insulator States, the Role of the Moiré Potential and Goldstone Gaps in Rhombohedral Graphene Superlattices

We investigate in detail the $ν=+1$ displacement-field-tuned interacting phase diagram of $L=3,4,5,6,7$ layer rhombohedral graphene aligned to hBN (R$L$G/hBN). Our calculations account for the 3D nature of the Coulomb interaction, the inequivalent stacking orientations $ξ=0,1$, the effects of the filled valence bands, and the choice of `interaction scheme' for specifying the many-body Hamiltonian. We show that the latter has a dramatic impact on the Hartree-Fock phase boundaries and the properties of the phases, including for pentalayers (R5G/hBN) with large displacement field $D$ where recent experiments observed a Chern insulator at $ν=+1$ and fractional Chern insulators for $ν<1$. In this large $D$ regime, the low-energy conduction bands are polarized away from the aligned hBN layer, and are hence well-described by the folded bands of moiréless rhombohedral graphene at the non-interacting level. Despite this, the filled valence bands develop moiré-periodic charge density variations which can generate an effective moiré potential, thereby explicitly breaking the approximate continuous translation symmetry in the conduction bands, and leading to contrasting electronic topology in the ground state for the two stacking arrangements. Within time-dependent Hartree-Fock theory, we further characterize the strength of the moiré pinning potential in the Chern insulator phase by computing the low-energy $\mathbf{q}=0$ collective mode spectrum, where we identify competing gapped pseudophonon and valley magnon excitations. Our results emphasize the importance of careful examination of both the single-particle and interaction model for a proper understanding of the correlated phases in R$L$G/hBN.

cond-mat.str-el↗

arXiv2023

Moiré Fractional Chern Insulators II: First-principles Calculations and Continuum Models of Rhombohedral Graphene Superlattices

The experimental discovery of fractional Chern insulators (FCIs) in rhombohedral pentalayer graphene twisted on hexagonal boron nitride (hBN) has preceded theoretical prediction. Supported by large-scale first principles relaxation calculations at the experimental twist angle of $0.77^\circ$, we obtain an accurate continuum model of $n=3,4,5,6,7$ layer rhombohedral graphene-hBN moiré systems. Focusing on the pentalayer case, we analytically explain the robust $|C|=0,5$ Chern numbers seen in the low-energy single-particle bands and their flattening with displacement field, making use of a minimal two-flavor continuum Hamiltonian derived from the full model. We then predict nonzero valley Chern numbers at the $ν= -4,0$ insulators observed in experiment. Our analysis makes clear the importance of displacement field and the moiré potential in producing localized "heavy fermion" charge density in the top valence band, in addition to the nearly free conduction band. Lastly, we study doubly aligned devices as additional platforms for moiré FCIs with higher Chern number bands.

cond-mat.mes-hall↗

arXiv2023

Moiré Fractional Chern Insulators I: First-principles calculations and Continuum Models of Twisted Bilayer MoTe$_2$

Recent experiments observed fractional Chern insulators (FCI) in twisted bilayer MoTe$_2$ at zero magnetic field, yet even the single-particle model of this material is controversial, leading to unreliable predictions of the experimental phase diagram as discussed in [Yu et al., 2023]. In this light, we revisit the single-particle model of twisted bilayer MoTe$_2$. Utilizing large-scale density functional theory, we calculate the band structure of twisted AA-stacked bilayer MoTe$_2$ at various twist angles relevant to experiment. We find that a band inversion occurs near $4.41^\circ$ between the second and third bands. Our ab initio band structure is in qualitative agreement with [Wang et al., 2023], but shows important differences in the remote bands and in the $Γ$ valley. We incorporate two higher harmonic terms into the continuum model to capture the highest 3 valence bands per valley. We confirm that the two highest valence bands per valley have opposite Chern numbers with $|C|=1$ for small angles, and also use our model to predict a variety of Chern states in the remote bands accessible by displacement field. Finally, we perform DFT calculations and build models for the AB stacking configuration. Our work serves as a foundation for accurate determination of the correlated phases in twisted bilayer MoTe$_2$.

cond-mat.mes-hall↗

arXiv2023

Fractional Chern Insulators vs. Non-Magnetic States in Twisted Bilayer MoTe$_2$

Fractionally filled Chern bands with strong interactions may give rise to fractional Chern insulator (FCI) states, the zero-field analogue of the fractional quantum Hall effect. Recent experiments have demonstrated the existence of FCIs in twisted bilayer MoTe$_2$ without external magnetic fields -- most robust at $ν=-2/3$ -- as well as Chern insulators (CIs) at $ν=-1$. Although the appearance of both of these states is theoretically natural in an interacting topological system, experiments repeatedly observe nonmagnetic states (lacking FCIs) at $ν=-1/3$ and $-4/3$, a puzzling result which has not been fully theoretically explained. In this work, we perform Hartree-Fock and exact diagonalization calculations to test whether the standard MoTe$_2$ moiré model with the (greatly varying) parameter values available in the literature can reproduce the non-magnetic states at $ν=-1/3$ and $-4/3$ in unison with the FCI at $ν=-2/3$ and CI state at $ν= -1$. We focus on the experimentally relevant twist angles and, crucially, include remote bands. We find that the parameters proposed in [Wang et al. (2023)] can nearly capture the experimental phenomena at $ν=-1/3,-2/3,-1,-4/3$ simultaneously, though the predicted ground states at $ν=-1/3$ are still mostly fully-spin-polarized and a larger dielectric constant $ε>10$ than is typical of hexagonal boron nitride (h-BN) substrate $ε\sim 6$ is required. Our results show the importance of remote bands in identifying the competing magnetic orders and lay the groundwork for further study of the realistic phase diagram.

cond-mat.mes-hall↗

arXiv2023

Magic-Angle Twisted Symmetric Trilayer Graphene as Topological Heavy Fermion Problem

Recently, Ref. [1] reformulated magic-angle twisted bilayer graphene (MATBG) as a topological heavy fermion problem, and used this reformulation to provide a deeper understanding for the correlated phases at integer fillings. In this work, we generalize this heavy-fermion paradigm to magic-angle twisted symmetric trilayer graphene (MATSTG), and propose a low-energy $f-c-d$ model that reformulates MATSTG as heavy localized $f$ modes coupled to itinerant topological semimetalic $c$ modes and itinerant Dirac $d$ modes. Our $f-c-d$ model well reproduces the single-particle band structure of MATSTG at low energies for displacement field $\mathcal{E}\in[0,300]$meV. By performing Hartree-Fock calculations with the $f-c-d$ model for $ν=0,-1,-2$ electrons per Moiré unit cell, we reproduce all the correlated ground states obtain from the previous numerical Hartree-Fock calculations with the Bistritzer-MacDonald-type (BM-type) model, and we find additional new correlated ground states at high displacement field. Based on the numerical results, we propose a simple rule for the ground states at high displacement fields by using the $f-c-d$ model, and provide analytical derivation for the rule at charge neutrality. We also provide analytical symmetry arguments for the (nearly-)degenerate energies of the high-$\mathcal{E}$ ground states at all the integer fillings of interest, and make experimental predictions of which charge-neutral states are stabilized in magnetic fields. Our $f-c-d$ model provides a new perspective for understanding the correlated phenomena in MATSTG, suggesting that the heavy fermion paradigm of Ref. [1] should be the generic underpinning of correlated physics in multilayer moire graphene structures.

cond-mat.mes-hall↗

arXiv2023

Pb$_9$Cu(PO4)$_6$(OH)$_2$: Phonon bands, Localized Flat Band Magnetism, Models, and Chemical Analysis

In a series of recent reports, doped lead apatite (LK-99) has been proposed as a candidate ambient temperature and pressure superconductor. However, from both an experimental and theoretical perspective, these claims are largely unsubstantiated. To this end, our synthesis and subsequent analysis of an LK-99 sample reveals a multiphase material that does not exhibit high-temperature superconductivity. We study the structure of this phase with single-crystal X-ray diffraction (SXRD) and find a structure consistent with doped $\text{Pb}_{10}(\text{PO}_4)_6(\text{OH})_2$. However, the material is transparent which rules out a superconducting nature. From ab initio defect formation energy calculations, we find that the material likely hosts $\text{OH}^-$ anions, rather than divalent $\text{O}^{2-}$ anions, within the hexagonal channels and that Cu substitution is highly thermodynamically disfavored. Phonon spectra on the equilibrium structures reveal numerous unstable phonon modes. Together, these calculations suggest it is doubtful that Cu enters the structure in meaningful concentrations, despite initial attempts to model LK-99 in this way. However for the sake of completeness, we perform ab initio calculations of the topology, quantum geometry, and Wannier function localization in the Cu-dominated flat bands of four separate doped structures. In all cases, we find they are atomically localized by irreps, Wilson loops, and the Fubini-Study metric. It is unlikely that such bands can support strong superfluidity, and instead are susceptible to ferromagnetism (or out-of-plane antiferromagnetism) at low temperatures, which we find in ab initio studies. In sum, $\text{Pb}_{9}\text{Cu}(\text{PO}_4)_6(\text{OH})_2$ could more likely be a magnet, rather than an ambient temperature and pressure superconductor.

cond-mat.supr-con↗