arXiv subjects

B. Andrei Bernevig

Publications and source records attributed to B. Andrei Bernevig.

At least 37 records · Page 2Linked to original sources

arXiv2026

New Crystal Structures Hide in Plain Sight: A Stress Test for AI-Guided Materials Discovery

New types of crystal structures are discovered only rarely, and the artificial intelligence (AI) models now reshaping materials discovery have so far produced new chemical compositions within known structural families rather than genuinely new structures. We report GdNiSn4 and LuNiSn4, intermetallics that adopt a previously unreported structure type, found not by computation but by exploratory synthesis. Single-crystal diffraction shows that the structure is an intergrowth of two known structural units. We then use this system as a benchmark for two leading generative models, MatterGen and DiffCSP++. For DiffCSP++, the benchmark is performed in its crystallographically constrained setting, using the required space-group and Wyckoff-position inputs. Under our sampling budget, neither model recovers the experimentally reported monoclinic structure within the structural-matching tolerance. The generated structures are evaluated without further structural relaxation using the nonmagnetic analog LuNiSn4, where we rule out 4f magnetism as the cause. Because the new structure is built from familiar building blocks, it should be derivable. We argue that encoding chemical reasoning, such as the stacking of known motifs, is a concrete path toward AI that can discover structurally novel materials.

cond-mat.mtrl-sci↗

arXiv2026

Mixed-dimensional quantum Monte Carlo studies of M-point moiré materials

A new moiré-material platform has recently been proposed based on twisting two-dimensional triangular-lattice monolayers whose low-energy states lie at the three M points of the Brillouin zone. Continuum models derived from extensive ab initio simulations suggest that electrons in the conduction bands of one such M-point moiré material, twisted AA-stacked SnSe$_2$, realize a three-orbital Hubbard model with orbitally-selective, quasi-one-dimensional (quasi-1D) hopping, protected by a projective mirror symmetry. Here, we show that the resulting "mixed-dimensional" limit -- in which the hopping is exactly quasi-1D in each valley, while the valleys are coupled by interactions into a fully two-dimensional network -- can be sampled with Stochastic Series Expansion (SSE) quantum Monte Carlo (QMC) without a sign problem at any filling. We develop an efficient new SSE QMC algorithm that combines custom global updates with parallel tempering to overcome the equilibration challenges posed by the mixed-dimensional setting. We then use this algorithm to explore the phase diagram of M-point twisted AA-stacked SnSe$_2$. Over extended and realistic ranges of twist angles and interaction strengths, we find that at integer fillings the system supports correlated insulators whose nature and strength depend strongly on angle. At certain commensurate fractional fillings, we further find evidence for Wigner-Mott insulators. We analytically account for the main features observed numerically using a strong-coupling description. Finally, we discuss perturbations away from the mixed-dimensional limit and the possibility of applying our method to other realizations of mixed-dimensional Hubbard models.

cond-mat.str-el↗

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

Twisted Bilayer Graphene Lifetimes At Integer Fillings: An Analytic Result

Twisted bilayer graphene near integer fillings hosts correlated single-particle excitations whose dispersion and linewidth are increasingly accessible experimentally. We study these excitations using the topological heavy-fermion model, which captures both strong correlations and band topology of twisted bilayer graphene. In the decoupled limit, where both the single-particle fc hybridization and the Hund coupling between f and c electrons are absent, the model admits exact solutions in which free Dirac fermions coexist with interacting f electrons that form zero-width Hubbard bands. By treating the fc hybridization and Hund coupling perturbatively around this solvable limit, we obtain analytical results for the single-particle self-energy. From the resulting self-energy, we derive explicit expressions for both dispersion renormalization and scattering rates of both Hubbard-band excitations and low-energy Dirac modes, thereby establishing an analytical framework for understanding correlated excitations in twisted bilayer graphene. We analyze the scattering of the two kinds, Gamma3 and Gamma1,2, of Dirac electrons and find that they arise from different mechanisms. We also briefly investigate the effect of strain. Finally, we compare these analytical expressions with DMFT results for the same model.

cond-mat.str-el↗

arXiv2026

Interplay between many-body correlations, strain and lattice relaxation in twisted bilayer graphene

In twisted bilayer graphene, a unified understanding of the mechanisms governing temperature-dependent electronic spectra and thermodynamic properties remains controversial despite extensive theoretical efforts. Here, we present a comprehensive theoretical framework that quantitatively accounts for scanning tunneling spectroscopy, quantum twisting microscopy, and thermodynamic properties of magic angle twisted bilayer graphene. We demonstrate that the observed behavior arises from the interplay between electron correlations and external symmetry-breaking induced by strain and lattice relaxation. These effects act cooperatively to shape the emergent electronic behavior, leaving characteristic signatures across spectroscopy, compressibility and entropy.

cond-mat.str-el↗

arXiv2026

Machine Learning-Guided Discovery of Kagome Superconductors YRu3B2 and LuRu3B2

We report the experimental discovery of bulk superconductivity in two kagome lattice compounds, YRu$_3$B$_2$ and LuRu$_3$B$_2$, which were predicted through machine learning-accelerated high-throughput screening combined with first principles calculations. These materials crystallize in the hexagonal CeCo$_3$B$_2$-type structure with planar kagome networks formed by Ru atoms. We observe superconducting critical temperatures of $T_{c} = 0.81$~K for YRu$_3$B$_2$ and $T_{c} = 0.95$~K for LuRu$_3$B$_2$, confirmed through magnetization and specific heat measurements. Both compounds exhibit nearly 100\% superconducting volume fractions, demonstrating bulk superconductivity. Compared with LaRu$_3$Si$_2$, YRu$_3$B$_2$ and LuRu$_3$B$_2$ show a more dispersive Ru local $d_{x^2-y^2}$ quasi-flat band (and thus a reduced DOS at $E_F$) together with an overall hardening of the phonon spectrum, both of which lower the electron-phonon coupling (EPC) constant $λ$. Meanwhile, the dominant real-space EPC between Ru local $d_{x^2-y^2}$ states and the low-frequency Ru in-plane local $x$ branch remains nearly unchanged, indicating that the reduction of $λ$ originates from the $d_{x^2-y^2}$ DOS reduction and the overall phonon hardening. Superfluid weight calculations show that conventional contributions dominate over quantum geometric effects due to the dispersive nature of bands near the Fermi level. This work demonstrates the effectiveness of integrating machine learning screening, first principles theory, and experimental synthesis for accelerating the discovery of new superconducting materials.

cond-mat.supr-con↗

arXiv2026

Ideal Topological Flat Bands in Two-dimensional Moiré Heterostructures with Type-II Band Alignment

Topological flat bands play an essential role in inducing exotic interacting physics, ranging from fractional Chern insulators to superconductivity, in moiré materials. In this work, we propose a design principle for realizing topological flat bands with "ideal quantum geometry", namely the trace of Fubini-Study metric equals to the Berry curvature, in a class of two-dimensional moiré heterostructures with type-II band alignment. We first introduce a moiré Chern-band model to describe this system and show that topological flat bands can be realized in this model when the moiré superlattice potential is stronger than the type-II atomic band gap of the heterostructure. Next, we map this model into a topological heavy fermion model that consists of a localized orbital for "f-electron" and a conducting band for "c-electron". We find that both the flatness and quantum geometry of the flat band in the topological heavy fermion model depend on the energy gap between c-electron and f-electron bands at $Γ$ which is experimentally controllable via external gate voltages. This tunability will allow us to realize an ideal topological flat band with zero band-width and ideal quantum geometry. Our design strategy of topological flat bands is insensitive of twist angle. We also discuss possible material candidates for moiré heterostructures with type-II band alignment.

cond-mat.mes-hall↗

arXiv2026

Topological Protection by Local Support Symmetry and Destructive Interference

Conventionally, symmetry-protected topological phases and band crossings are protected by global symmetries acting on the entire system. Here, we show that symmetries preserved only on a partial region of a system, termed local support symmetries, can protect topological features of the full system, even in the presence of symmetry-breaking couplings. We establish a unified framework by deriving explicit conditions for such protection in both insulating and metallic phases and show that destructive interference of Bloch wave functions plays a key role. Using representative tight-binding models, we demonstrate band crossings and topological bands protected by local support crystalline and time-reversal symmetries, and further present a realistic material realization in a fluorinated biphenylene network, where a band crossing is protected by a local support C$_2$ symmetry.

cond-mat.str-el↗

arXiv2025

Phonon spectra, quantum geometry, and the Goldstone theorem

Phonons are essential quasi-particles of all crystals and play a key role in fundamental properties such as thermal transport and superconductivity. In particular, acoustic phonons can be interpreted as Goldstone modes that emerge due to the spontaneous breaking of translational symmetry. In this article, we investigate the quantum geometric contribution to the phonon spectrum in the absence of Holstein phonons. Using graphene as a case study, we decompose the dynamical matrix into distinct terms that exhibit different dependencies on the electron energy and wavefunction. We then examine the role of quantum geometry in shaping the material's phonon spectrum, and we find that removing the nontrivial quantum geometric contribution from the dynamical matrix causes the acoustic phonon modes to behave in a non-analytic fashion.

cond-mat.mes-hall↗

arXiv2025

Integer characteristic polynomial factorization and Hilbert space fragmentation

Models with Hilbert space fragmentation are characterized by (exponentially) many dynamically disconnected subspaces, not associated with conventional symmetries but captured by nontrivial Krylov subspaces. These subspaces usually exhibit a whole range of thermalization properties, from chaotic to integrable, to quantum many-body scars. However, so far, they have not been properly defined, nor can they be easily found, given a Hamiltonian. In this work, we consider Hamiltonians that have integer representations, a common feature of many (most) celebrated models in condensed matter. We show the equivalence of the integer characteristic polynomial factorization and the existence of Krylov subspaces generated from integer vectors. Considering the pair-hopping model, we illustrate how the factorization property can be used as a method to unveil Hilbert space fragmentation. We discuss the generalization over other rings of integers, for example those based on the cyclotomic field which are relevant when working in a given ($\ne 0, π$) momentum sector.

cond-mat.stat-mech↗

arXiv2025

Projected and Solvable Topological Heavy Fermion Model of Twisted Bilayer Graphene

We investigate the topological heavy-fermion (THF) model of magic-angle twisted bilayer graphene (MATBG) in the projected limit, where only the flat bands are present in the low-energy spectrum. Such limit has been previously analyzed in momentum-space Bistritzer-MacDonald-type continuum models, but not in a real-space formalism. In this regime, the Hubbard interaction ($U_1$) of the $f$-electrons is larger than the bandwidth ($2M$) of the flat bands but smaller than the gap ($γ$) between the flat and remote bands. In the THF model, concentrated charge (in real space) and concentrated Berry curvature (in momentum space) are respectively realized by exponentially localized $f$-orbitals and itinerant Dirac $c$-electrons. Local moments naturally arise from $f$-orbitals. Hybridizing the $f$-electrons with $c$-electrons produces power-law tails of the flat-band Wannier functions, raising the question of relevance of the local moment picture in the projected $U_1\ll γ$ limit. Nonetheless, we find that the local moments remain stable as long as $U_1 \gg Δ(ω)$ for $|ω|\lesssim U_1$, where $Δ(ω)\sim γ^2 N(ω)$ is the hybridization function seen by each $f$-site, and $N(ω)$ is the density of states of the Dirac $c$-bands. Notably, the comparison between $U_1$ and $γ$ is irrelevant to the local moment formation if $N(ω)$ is unknown. Within the framework of THF, we also derive the correlated self-energy of the flat bands using the Hubbard-I approximation and estimate the coupling strength between the local moments. Finally, we comment that, in the regime of extremely concentrated Berry curvature, the single-particle gap between flat bands and remote bands vanishes and the interaction is always larger than the gap.

cond-mat.str-el↗

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

Chern-Selective multi-valley Flat Bands in Twisted Mono-Bilayer and Mono-Trilayer MoTe$_2$

The interplay between moiré flat bands originating from different valleys can give rise to a variety of exotic quantum phases. In this work, we investigate the electronic properties of twisted mono-bilayer (A-AB) and mono-trilayer (A-ABA) MoTe$_2$ using first-principles calculations and continuum models. Unlike previous studies on twisted bilayer systems, in which low-energy flat bands originate solely from the $K/K'$ valleys, in A-AB and A-ABA twisted MoTe$_2$ (\tmt) the moiré bands at low energies arise from both the $Γ$ and $K/K'$ valleys, with spin Chern numbers $C_s=0$ (for $Γ$) and $C_{\uparrow/\downarrow}=\pm1$ (for $K/K'$), respectively. We show that the multi-valley moiré flat bands are governed by interlayer-hybridization effects, and that different stacking configurations and thicknesses tune the relative energy alignment between the $Γ$ and $K$ valley moiré flat bands. By constructing valley-resolved continuum models and performing Wannierization for the low-energy moiré bands, we further uncover that the Berry curvature and quantum metric distributions can be effectively tuned by the layer number and stacking configuration. Unlike other moiré systems, where only one kind of valley influenced the low energy physics, the simultaneous appearance of two distinct types of valleys, with different symmetries, establish A-AB and A-ABA \tmt\ as ideal platforms for studying layer-controlled multi-valley physics.

cond-mat.mtrl-sci↗

arXiv2025

Obtaining the Spectral Function of Moiré Graphene Heavy-Fermions Using Iterative Perturbation Theory

The spectral functions of twisted bilayer graphene (TBG) in the absence of strain have recently been investigated in both the symmetric and symmetry-broken phases using dynamical mean-field theory (DMFT). The theoretically predicted Mott-Hubbard bands and gapless semimetallic state at half-filling have since been confirmed experimentally. Here, we develop several second-order perturbation theory approaches to the topological heavy-fermion (THF) model of TBG and twisted symmetric trilayer graphene (TSTG). In the symmetric phase, we adapt, implement, and benchmark an iterative perturbation theory (IPT) impurity solver within DMFT, enabling computationally efficient yet accurate spectral function calculations. We present momentum- and energy-resolved spectra over a broad range of temperatures and fillings for both symmetric and symmetry-broken states. In addition, we derive analytic expressions for the spectral function within the ``Hubbard-I'' approximation of the THF model and, as expected, find that while it provides a tractable description of Mott physics, it does not capture the low-energy Kondo peak or the finite lifetime broadening of the bands. Our methodology can be extended to include strain, lattice relaxation, and parameter variations, thereby allowing systematic predictions of TBG and TSTG spectral properties across a wide range of physical regimes. Because our perturbative approaches are far less computationally intensive than DMFT with numerically exact impurity solvers, they can be used to efficiently benchmark and scan extensive phase diagrams of the THF parameters, paving the way for full DMFT analyses of the TBG spectral function in the presence of strain and relaxation.

cond-mat.str-el↗

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

Universal Wilson Loop Bound of Quantum Geometry

We define the absolute Wilson loop winding and prove that it bounds the (integrated) quantum metric from below. This Wilson loop lower bound naturally reproduces the known Chern and Euler bounds of the integrated quantum metric and provides an explicit lower bound of the integrated quantum metric due to the time-reversal protected $Z_2$ index, answering a hitherto open question. In general, the Wilson loop lower bound can be applied to any other topological invariants characterized by Wilson loop winding, such as the particle-hole $Z_2$ index. As physical consequences of the $Z_2$ bound, we show that the time-reversal $Z_2$ index bounds superfluid weight and optical conductivity from below and bounds the direct gap of a band insulator from above.

cond-mat.mes-hall↗

arXiv2025

Emergent Interacting Phases in the Strong Coupling Limit of Twisted M-Valley Moiré Systems: Application to SnSe${}_2$

We construct an interacting Wannier model for both AA-stacked and AB-stacked twisted SnSe2, revealing a rich landscape of correlated quantum phases. For the AA-stacked case, the system is effectively described by a three-orbital triangular lattice model, where each orbital corresponds to a valley and exhibits an approximate one-dimensional hopping structure due to a new momentum-space non-symmorphic symmetry. By exploring the interacting phase diagram using a combination of theoretical methods, including Hartree-Fock mean-field theory and exact solutions of the spin model in certain limits, we identify several exotic quantum phases. These include a dimerized phase with finite residual entropy, valence bond solids, and quantum paramagnetism. In the AB-stacked case, the system realizes an interacting kagome lattice model, where the Wannier orbitals associated with the three valleys form three sublattices. In the strong coupling regime, we use cluster mean-field methods to demonstrate the emergence of a classical spin liquid phase due to the frustrated lattice structure. The high tunability of the moiré system, which allows control over both the filling and interaction strength (via twist angle), renders twisted SnSe2 a versatile platform for realizing a wide range of exotic correlated quantum phases.

cond-mat.str-el↗

arXiv2025

Revealing electron-electron interactions in graphene at room temperature with the quantum twisting microscope

The Quantum Twisting Microscope (QTM) is a groundbreaking instrument that enables energy- and momentum-resolved measurements of quantum phases via tunneling spectroscopy across twistable van der Waals heterostructures. In this work, we significantly enhance the QTMs resolution and extend its measurement capabilities to higher energies and twist angles by incorporating hexagonal boron nitride (hBN) as a tunneling dielectric. This advancement unveils previously inaccessible signatures of the dispersion in the tunneling between two monolayer graphene (MLG) sheets, features consistent with a logarithmic correction to the linear Dirac dispersion arising from electron-electron (e-e) interactions with a fine-structure constant of alpha = 0.32. Remarkably, we find that this effect, for the first time, can be resolved even at room temperature, where these corrections are extremely faint. Our results underscore the exceptional resolution of the QTM, which, through interferometric interlayer tunneling, can amplify even subtle modifications to the electronic band structure of two-dimensional materials. Our findings reveal that strong e-e interactions persist even in symmetric, nonordered graphene states and emphasize the QTMs unique ability to probe spectral functions and their excitations of strongly correlated ground states across a broad range of twisted and untwisted systems.

cond-mat.mes-hall↗