arXiv subjects

B. Andrei Bernevig

Publications and source records attributed to B. Andrei Bernevig.

At least 19 recordsLinked to original sources

arXiv2026

2D Theoretically Twistable Material Database

The study of twisted two-dimensional (2D) materials, where twisting layers create moiré superlattices, has created opportunities for investigating topological phases and strongly correlated physics. The broader potential of a seemingly infinite set of twistable 2D materials remains largely unexplored. Here, we define ''theoretically twistable materials'' as single- or multi-layer structures that allow for the construction of simple continuum models of their moiré structures. Our high-throughput algorithm systematically searches for theoretically twistable semimetals and insulators based on the Topological 2D Materials Database (2D-TQCDB). By analyzing key electronic properties, we identify thousands of candidate materials, propose representative twistable materials, and provide examples of crystal growth and exfoliation for several of them. Our results provide a resource for future experimental and theoretical studies of moiré systems.

cond-mat.mtrl-sci↗

arXiv2026

Transport and Temperature: Exact spectrum and Drude weight for the one-dimensional infinite-$U$ Hubbard model

Understanding charge transport in strongly correlated systems remains a central challenge in condensed matter physics, while exact analytical results for finite-temperature transport remain rare. Here, we investigate charge transport in the one-dimensional Hubbard model in the infinite-interaction limit. We first construct the exact \emph{and explicit - i.e. beyond Bethe ansatz} energy spectrum and eigenstates. Building on these explicit eigenstates, we derive a closed-form analytical expression for the charge Drude weight at arbitrary temperatures in the hole-dilute limit with a fixed number of doped holes, as well as analytical expressions in the low- and high-temperature limits at fixed hole density. We further show that, at low temperatures, the leading correction to the charge Drude weight is linear in $T$ when the number of holes is fixed, whereas it is quadratic in $T$ when the hole density is fixed. This analytically controlled example highlights the importance of identifying the underlying thermodynamic trajectory when interpreting finite-size numerical studies of charge transport in more general models.

cond-mat.str-el↗

arXiv2026

Large scale theoretical investigation of the phase diagram of twisted bilayer MoTe$_2$ at fractional fillings: agreements and contradictions with current experiments

We present a comprehensive exact-diagonalization study of interaction-driven phases in twisted bilayer MoTe$_2$ across experimentally relevant twist angles ($2.13^\circ$--$4^\circ$) and hole fillings. Using continuum-model moiré bands, we compare the one-band-per-valley (1BPV) projection with a two-band-per-valley (2BPV) calculation that includes interaction-driven band mixing, and we benchmark both the widely used first-harmonic continuum model and a parameter-free DFT ``fitting-free'' model. At odd-denominator fillings, the 2BPV calculation reproduces the experimentally observed hierarchy of fractional Chern insulators (FCIs) around $θ\approx 3.7^\circ$, including robust incompressible states at $ν=-2/3$, $-3/5$, and $-4/7$ while correctly finding the absence of an FCI at $ν=-3/7$, and it favors a charge density wave ground state at $ν=-1/3$ over the FCI. At half filling $ν=-1/2$, the 1BPV calculation exhibits clear composite Fermi liquid (CFL) signatures, whereas the band mixing in 2BPV calculations destabilizes the CFL ground state. Finally, motivated by the Landau-level analogy at $θ\approx 2.13^\circ$, we test the proposed non-abelian Pfaffian state at $ν=-3/2$ in the fully-polarized spin sector but find no evidence for this state within the models and parameters studied. Our results establish a unified numerical benchmark for correlated and topological phases in twisted bilayer MoTe$_2$ and clarify where multi-band physics is essential for a quantitative comparison with experiments.

cond-mat.str-el↗

arXiv2026

Distinguishing Mott and strain-induced anisotropic semimetals in magic-angle twisted bilayer graphene using Landau level spectroscopy

Recent quantum twisting microscopy experiments [1] have provided unprecedented momentum- and energy-resolved imaging of magic-angle twisted bilayer graphene, revealing a stark dichotomy between the heavy and light electronic characters of its narrow bands. In this work, we provide a sharp distinguishing criterion between the two most likely candidate states that exhibit spectroscopic features consistent with the experimental results. Focusing on charge neutrality, these states are 1) the 'Mott semimetal', governed by strong dynamical correlations, and 2) the 'strain-induced anisotropic semimetal', characterized by weak Hartree-Fock effects. We demonstrate that an out-of- plane magnetic field serves as a sharp discriminating probe based on the expected Landau level gap size hierarchy. We find that the strain-induced anisotropic semimetal has a robust gap hierarchy where the Chern C gaps, Δ_C , decrease in order Δ_{\pm 4} > Δ_{\pm 8} > Δ_{\pm 12}. In contrast, for the Mott semimetal, Δ_{\pm 4} remains the largest gap, while the relative magnitude of the C = \pm 8, \pm 12 gaps depends sensitively on the applied magnetic field. We test the robustness of these results against strain orientation and lattice relaxation finding consistency between the gap hierarchy of the strained semimetal and previous incompressibility measurements at finite magnetic field [2].

cond-mat.str-el↗

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

Resonant Far-Infrared Spectroscopy of Flat-Band Fermions in Magic Angle Graphene

Moiré engineering in twisted two-dimensional (2D) materials radically alters low-energy bands, interactions and topological quantum states. Despite extensive studies, optical spectroscopy of interacting moiré bands in the characteristic far-infrared (FIR) regime has remained largely unexplored due to extreme experimental challenges. Using a newly developed millikelvin FIR platform, we report the observation of the long-sought-after characteristic FIR resonances of flat-band electrons in magic-angle twisted bilayer graphene (MATBG). We observe highly tunable spectroscopic signatures of interacting light and heavy fermions that constitute the flat bands in MATBG. Using the topological heavy-fermion model (THF), we show that itinerant topological electrons act as an "antenna" that couples strongly to the optical field, with resonant frequencies renormalized by the hybridization with localized heavy electrons. We establish optical selection rules of MATBG which uncovers the key symmetry governing light-heavy fermion hybridization. At charge neutrality, we observe pronounced resonances at energies below the on-site Coulomb energy, implying the emergence of new many-body modes. Our experiments and modeling provide a fundamental understanding of light-matter interactions in MATBG and enable resonant optical spectroscopy of moiré bands down to millikelvin temperatures.

cond-mat.mes-hall↗

arXiv2026

Momentum Structure of Superconductivity and Sublattice Effects from Quasiparticle Interference in CsV$_3$Sb$_5$

Quantum interference encoded in the sublattice texture of kagome Bloch wavefunctions has been widely invoked as a route to correlated states, including chiral charge order, unconventional superconductivity, and their possible intertwining in pair-density-wave (PDW) states. Using sub-Kelvin scanning tunneling microscopy, we conducted spectroscopic mapping of the kagome material CsV$_3$Sb$_5$ with high energy resolution and dense energy sampling through the superconducting gap. Quasiparticle interference (QPI) analysis, aided by ab initio and symmetry calculations, reveals an isotropic superconducting gap on the Fermi surfaces derived from V $M_z$-even ($M_z^+$) $d$ orbitals, thereby constraining possible gap symmetries and limiting any gap anisotropy to the remaining V $M_z$-odd ($M_z^-$) and Sb $p_z$ bands. Meanwhile, the CDW-peak-selected d$I$/d$V$ spectra closely track the spatially averaged density of states and show no distinct enhancement restricted to subgap energies, which do not support an additional PDW modulation within our sensitivity. Finally, the selective absence of specific QPI scattering vectors points to a spectroscopic sensitivity to sublattice character on the Fermi surface. Together, these results provide a clearer experimental picture of the low-energy electronic structure relevant to kagome superconductivity in CsV$_3$Sb$_5$.

cond-mat.supr-con↗

arXiv2026

Extended s-wave superconductivity in M-point twisted bilayer SnSe2

We investigate the emergence of electronic order and unconventional superconductivity in M-valley moiré materials. Starting from a first-principles Wannier model of AB-stacked twisted SnSe2, we tackle the (gate-screened) long-ranged Coulomb interaction with functional renormalization group simulations resolving the momentum structure and energy scales of the leading Fermi surface instabilities. Upon doping an antiferromagnetic stripe state at half-filling ($ν=3$ electrons per moiré unit cell) of the moiré flat bands, magnetic order gives way to unconventional superconductivity mediated by valley-selective spin fluctuations: Large hole doping ($ν\approx1$) leads to weak-coupling superconductors with various pairing symmetries, while slight electron- and hole-doping ($ν\approx2,4$) stabilizes a spin-singlet, extended s-wave state that benefits from scattering between virtual particle and hole states that are detuned from the Fermi level. These findings establish M-point moiré materials as a quantum simulation platform with phenomenological parallels to the class of iron pnictide superconductors.

cond-mat.supr-con↗

arXiv2026

Organizing Principles for Moiré Quantum Matter

Moiré flat bands in van der Waals bilayers are usually discussed through a small set of mechanisms associated with the $Γ$ and $K$ valleys of hexagonal crystals, and more recently with $M$-valleys systems. Here we show that this view is incomplete. The momentum-space location and effective local orbital character of the monolayer's band edge, in conjunction with the moiré symmetry and the symmetry representations of the resulting bands, provide a general set of organizing variables for the emergent low-energy moiré Hamiltonian. Applying fully relaxed first-principles calculations, band unfolding and symmetry-representation analysis to more than 600 commensurate twisted bilayers spanning all 2D lattice classes, we identify several routes to moiré quantum matter beyond the conventional single-orbital paradigm. The resulting flat bands realize trigonal, honeycomb, square, checkerboard and kagome-like Hubbard models with single-orbital, multi-orbital and multi-site Hilbert spaces; spin-orbit-coupled multi-orbital flat bands exhibit symmetry-indicated topology beyond the conventional $K$-valley setting; and nonsymmorphic moiré symmetries enforce semimetallic flat-band connectivity. Analogous quasi-one-dimensional flat-band structures are found in $M$-valley hexagonal systems and $X$-valley square or rectangular systems resulting from emergent momentum-space nonsymmorphic symmetries. Separately, coupled multi-valley manifolds with kagome-like connectivity are identified in several systems whose parent band edges lie at non-high-symmetry points. These results establish a valley-orbital-symmetry framework for connecting parent-material electronic structure to emergent moiré Hamiltonians relevant to correlated, topological and symmetry-enforced moiré phases.

cond-mat.mtrl-sci↗

arXiv2026

Quantum geometry and critical temperature enhancement in MgB$_2$ superconductivity

MgB$_2$, a phonon-mediated superconductor with record-high critical temperature $T_c\simeq 39$ K, is revisited to obtain a comprehensive theory of electrons, phonons, and their coupling with minimal ab initio input. We construct compact analytic models for the electronic structure, phonons, and electron-phonon coupling (EPC) of MgB$_2$. We show that strong in-plane B $sp^2$ bonding realizes an obstructed band structure whose natural description is a bond-centered kagome lattice, yielding small quasi-2D $σ$-band Fermi-surface cylinders and pronounced quantum-geometric effects. The phonon spectrum is found to closely track that of a graphene-like boron layer, but the heavy intercalated Mg atoms dominate the three acoustic branches and rigidly lift the boron modes into the optical sector, while the in-plane B-B bond-stretching mode exhibits a pronounced softening along $Γ$-A. By symmetry, this $Γ$-point bond-stretching mode is the only $Γ$ phonon that can couple to the $σ$ Fermi surface, explaining its dominant contribution to the EPC. Upon electron doping toward the doubly degenerate band edge of the $σ$ sheets, we find that a reduced density of states competes with enhanced EPC matrix elements. At light electron doping, ab initio calculations show that the EPC enhancement dominates, leading to an increase in $T_c$ (within the clean doping limit without disorder effects). Using the Gaussian approximation for the EPC tensor, we further show that this enhancement is overwhelmingly quantum geometric in origin, arising from a geometric EPC contribution of the small $σ$ Fermi surface peaked at $Γ$. Overall, our results provide a transparent, symmetry-based account of superconductivity in MgB$_2$ and suggest that quantum-geometric effects can be essential for shaping doping trends in phonon-mediated superconductors.

cond-mat.supr-con↗

arXiv2026

Stable Real-Space Invariants and Topology Beyond Symmetry Indicators

We introduce stable real-space invariants (SRSIs), topological invariants defined from adiabatic deformations between Wannier states, generalizing previously discovered local and composite real-space invariants. SRSIs are $\mathbb{Z}$- and $\mathbb{Z}_n$-valued ($n=2,4$) linear combinations of Wannier state multiplicities characterizing the stable equivalence of atomic insulators. We enumerate all SRSIs in nonmagnetic space groups with and without spin-orbit coupling. $\mathbb{Z}$SRSIs are in one-to-one correspondence with momentum-space symmetry data and thus determine symmetry indicators of topology (SIs). $\mathbb{Z}_n$SRSIs capture real-space information beyond momentum-space symmetry data and SIs. Applying SRSIs to split elementary band representations (EBRs) whose symmetry data decomposes into positive sums of other EBR symmetry data, we diagnose the topology of all 211 cases across 51 space groups except for 8 exceptions in 5 space groups. Our results solidify Topological Quantum Chemistry beyond SIs and momentum-space symmetry data. Finally, we use SRSIs to diagnose an obstructed atomic insulator in a realistic material.

cond-mat.mes-hall↗

arXiv2026

Magnon-Mediated Superconductivity in a 2D Itinerant Ferromagnet with Weak Easy-plane Magnetic Anisotropy

Motivated by recent observations of superconductivity in a quarter-metal state of spin- and valley- polarized graphene multilayers, we investigate pairing within a ferromagnetic phase of a single-valley model of itinerant two-dimensional (2D) electrons with Hubbard-type interaction and no artificial high-energy cutoff. In 2D, the Stoner transition is first-order into a fully-polarized state wherein the only gapless collective excitations are transverse magnons. We find that in a spin-SU(2) symmetric model, this magnon-mediated pairing interaction between equal-spin fermions vanishes at $T=0$. We show that a small easy-plane magnetic anisotropy $Ω_0 \ll E_F$, where $E_F$ is the Fermi energy, breaks the SU(2) symmetry and generates an attractive interaction for equal-spin $p-$wave pairing. We explicitly derive the corresponding coupling constant $λ_p$ as the scaling function of both the relative strength of the easy-plane anisotropy, $Ω_0/E_F$, and the proximity to the ferromagnetic transition. While $λ_p$ is parametrically small in $Ω_0/E_F$ deep inside the ferromagnetic phase, it becomes enhanced near the ferromagnetic transition, reaching order unity regardless of how small $Ω_0/E_F$ is. This mechanism yields a sizable $T_c$, peaked near the onset of ferromagnetism.

cond-mat.supr-con↗

arXiv2026

Ferromagnetism vs. Antiferromagnetism in Narrow-Band Systems: Competition Between Quantum Geometry and Band Dispersion

Magnetism in narrow-band systems arises from the interplay between electronic correlations, quantum geometry, and band dispersion. In particular, both ferro and anti-ferro magnets are known to occur as ground states of (different) models featuring narrow bands. This poses the question of which is favored and under what conditions. In this work, we present a unified theoretical framework to investigate spin physics within narrow bands. By deriving an effective spin model, we show that the non-atomic wavefunction of the narrow bands generally favors ferromagnetic ordering, while band dispersion promotes antiferromagnetic correlations. We find that the competition between these effects gives rise to a tunable magnetic phase and rich spin phenomena. Our approach offers a systematic way to study the magnetic properties of narrow-band systems, integrating the roles of wave function, band structure, and correlation effects.

cond-mat.str-el↗

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↗