arXiv subjects

B. Andrei Bernevig

Publications and source records attributed to B. Andrei Bernevig.

At least 19 recordsLinked to original sources

arXiv2026

Pairing from repulsive interactions in twisted WSe2 from functional renormalization

Motivated by the observation of superconductivity in twisted bilayer WSe$_2$ over an extended range of displacement fields, reaching from the correlated insulator down to zero field, we analyze the correlated electron phases of this system at hole filling $ν= -1$ and twist angle $3.65^\circ$ using Hartree--Fock, random phase approximation, and functional renormalization group calculations. We derive a continuum model with gate-screened Coulomb interaction from first principles and compare its instabilities to those of a realistic three-orbital Wannier model with a Hubbard interaction and an artificial single-orbital Hubbard model. In both cases, we find a superconducting instability of mixed $d$-wave singlet and $p$-wave triplet character, arising adjacent to inter-valley-coherent spin-density-wave order in the phase diagram spanned by displacement field and interaction strength. Our additional analysis of the pairing mechanism points to inter-valley coherent spin fluctuations as the pairing glue. The extent of the pairing regime and the associated critical temperatures depend on the model input, and we trace differences to the interaction range entering the projected interaction. Within the continuum model, the gate-screened Coulomb interaction yields pairing down to zero displacement field, bringing theory into agreement with experiment.

cond-mat.str-el↗

arXiv2026

Ring states in topological materials

Ingap states in semiconductors are commonly characterized by hydrogenic models within the effective mass approximation. However, when impurities are strong, this description fails. The bound states are non-perturbative with energy pinned to a zero of the impurity-projected Green's function. We show that in the presence of Wannier obstructions, such zeros are irremovable. That is, no symmetric, gap-preserving deformation of the bulk can return the ingap state to the band continuum. We call these states ring states: their wavefunctions show a node at the impurity site, and their mixed band character is set by minimizing the level repulsion exerted by the bands above and below the gap. In Chern insulators, the band mixing endows occupied ring states with local circulating currents, remnant of a small edge mode surrounding the vacancies. Clusters of vacancies bind ring states that hybridize to form dispersive chiral edge modes, providing a real-space view of bulk-boundary correspondence.

cond-mat.mes-hall↗

arXiv2026

Two-dimensional Topological Quantum Chemistry and Catalog of Topological Materials

Two-dimensional topological materials host symmetry-protected, disorder-robust edge states cen- tral to quantum technologies. Yet, they remain scarce compared with their three-dimensional coun- terparts. We adapt the topological quantum chemistry formalism to layer groups, and study the band topology of 8,872 entries from the computational materials databases C2DB and MC2D. We find 4,073 topological or obstructed entries, including 905 topological insulators and 1,003 obstructed atomic insulators, greatly expanding the library of such materials in two dimensions. Detailed elec- tronic and topological properties of all materials are compiled into a a Topological 2D Materials Database (2D-TQCDB), and the edge states of selected new materials are studied in detail. Our methodology is implemented in new publicly available programs, designed to study the topology of any non-magnetic monolayer or multilayer material.

cond-mat.mes-hall↗

arXiv2026

Symmetric Mode Ansatz: Theory of Magnon Collective Modes in Chern Insulators

Moiré materials host integer and fractional Chern insulators (FCIs) where time-reversal is broken spontaneously by flat band ferromagnetism. In twisted MoTe2, unlike in quantum Hall, opposite spins carry opposite Chern numbers and realize Ising ferromagnetism with gapped magnon excitations. Clarifying the nature of these collective modes and the origin of the magnon gap is key to understanding the stability of the Chern magnets in these materials. To do so, we develop a generalized single-mode approximation, which we call the symmetric mode ansatz (SyMA), to describe the low-energy magnon spectrum. We find it to be in exceptional agreement with numerical calculations at integer filling, and qualitatively accurate across fractional fillings including FCIs. To explain the accuracy of the SyMA, we present two families of Hubbard models (including the Haldane model and continuum ideal bands) whose collective modes are analytically solvable and for which the SyMA is either exact or an accurate approximation. For a class of these models where SyMA is exact, we prove two-sided bounds on the zero-momentum magnon gap in terms of the Chern number, Berry curvature, and quantum metric, revealing that uniform quantum geometry is sufficient for stabilizing magnetism in Chern bands.

cond-mat.str-el↗

arXiv2026

Incoherent Spectral Weight Emerging from a Van Hove Singularity in a Kagome Metal

Waterfall-like spectral features observed by angle-resolved photoemission spectroscopy (ARPES) are commonly associated with strong electronic correlations or electron-boson coupling. Here, we investigate this connection in the kagome metal LuFe6Ge6, a structurally simple member of the FeGe-derived family, using polarization-dependent ARPES, density functional theory and dynamical mean-field theory. We observe a pronounced vertical spectral feature at the L point extending over several hundred meV in binding energy. Its orbital character is identified as predominantly Fe dyz, and its energy onset coincides with a van Hove singularity located approximately 0.3 eV below EF . Despite the waterfall-like spectral response, dynamical mean-field theory (DMFT) reveals only weak electronic correlations, while the calculated electronic structure closely reproduces the experimental bulk bands. We propose that the anomalous spectral weight may arise from inelastic scattering of the outgoing photoelectrons, potentially associated with the large density of states near the van Hove singularity. Our results suggest that waterfall-like features can emerge without strong electronic correlations and highlight the possible role of the underlying band structure and photoelectron energy-loss processes in their interpretation.

cond-mat.str-el↗

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↗