About

B. Andrei Bernevig is a professor of physics at Princeton University and a leading figure in the field of topological electronic states in solids. He is renowned for his initial theoretical proposal of the quantum spin Hall effect in HgTe quantum wells, a prediction that was soon followed by dramatic experimental confirmation. Bernevig has developed a comprehensive theoretical framework for topological insulators and authored a highly regarded book on the subject. His research has significantly advanced the understanding of topological superconductivity, particularly in metal chains on superconducting surfaces, and he has predicted two types of Weyl semimetal states in transition metal monophosphides and WTe2, stimulating extensive theoretical and experimental activity in the field. Bernevig earned his doctorate at Stanford University and completed a postdoctoral fellowship at the Princeton Center for Theoretical Physics. His outstanding contributions have been recognized with numerous prestigious awards, including the 2014 Sackler Prize, the 2016 New Horizons Prize, a 2017 Guggenheim Fellowship, and the 2019 James C. McGroddy Prize for New Materials from the American Physical Society.

Research topics

• Condensed matter physics
• Computer Science
• Physics
• Quantum mechanics
• Mathematics
• Geometry
• Chemistry
• Materials science
• Business
• Theoretical physics

Selected publications

• Universal Wilson Loop Bound of Quantum Geometry

  Physical Review Letters · 2025-08-19 · 4 citations

  articleSenior author

  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.

  PublisherDOI

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

  ArXiv.org · 2025-09-19

  preprintOpen accessSenior author

  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.

  PublisherOA PDFDOI

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

  ArXiv.org · 2025-10-14

  preprintOpen access

  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.

  PublisherOA PDFDOI

• Dilute Paramagnetism and Non-Trivial Topology in Quasicrystal Approximant Fe4Al13

  Crystals · 2025-05-21

  articleOpen access

  A very fundamental property of both weakly and strongly interacting materials is the nature of their magnetic response. In this work, we detail the growth of crystals of the quasicrystal approximant Fe4Al13 with an Al flux solvent method. We characterize our samples using electrical transport and heat capacity, yielding results consistent with a simple non-magnetic metal. However, magnetization measurements portray an extremely unusual response for a dilute paramagnet and do not exhibit the characteristic Curie behavior expected for a weakly interacting material at high temperature. Electronic structure calculations confirm metallic behavior but also indicate that each isolated band near the Fermi energy hosts non-trivial topologies, including strong, weak, and nodal components, with resultant topological surface states distinguishable from bulk states on the (001) surface. With half-filled flat bands apparent in the calculation, but an absence of long-range magnetic order, the unusual quasi-paramagnetic response suggests the dilute paramagnetic behavior in this quasicrystal approximant is surprising and may serve as a test of the fundamental assumptions that are taken for granted for the magnetic response of weakly interacting systems.

  PublisherOA PDFDOI

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

  ArXiv.org · 2025-07-08

  preprintOpen access

  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.

  PublisherOA PDFDOI

• Phonon spectra, quantum geometry, and the Goldstone theorem

  Physical review. B./Physical review. B · 2025-11-21 · 2 citations

  article

  Phonons are essential quasiparticles of all crystals and play a key role in fundamental properties such as thermal transport and superconductivity. 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 wave function. We then examine the role of quantum geometry in shaping the phonon spectrum of the material, and we find that removing the nontrivial quantum geometric contribution from the dynamical matrix causes the acoustic phonon modes to behave in a nonanalytic fashion.

  PublisherDOI

• Moiré materials based on M-point twisting

  Nature · 2025-07-09 · 8 citations

  preprintOpen accessSenior author

  Abstract When two monolayer materials are stacked with a relative twist, an effective moiré translation symmetry emerges, leading to fundamentally different properties in the resulting heterostructure. As such, moiré materials have recently provided highly tunable platforms for exploring strongly correlated systems 1,2 . However, previous studies have focused almost exclusively on monolayers with triangular lattices and low-energy states near the Γ (refs. 3,4 ) or K (refs. 5–9 ) points of the Brillouin zone (BZ). Here we introduce a new class of moiré systems based on monolayers with triangular lattices but low-energy states at the M points of the BZ. These M-point moiré materials feature three time-reversal-preserving valleys related by threefold rotational symmetry. We propose twisted bilayers of exfoliable 1T-SnSe 2 and 1T-ZrS 2 as realizations of this new class. Using extensive ab initio simulations, we identify twist angles that yield flat conduction bands, provide accurate continuum models, analyse their topology and charge density and explore the platform’s rich physics. Notably, the M-point moiré Hamiltonians exhibit emergent momentum-space non-symmorphic symmetries and a kagome plane-wave lattice structure. This represents, to our knowledge, the first experimentally viable realization of projective representations of crystalline space groups in a non-magnetic system. With interactions, these systems act as six-flavour Hubbard simulators with Mott physics. Moreover, the presence of a momentum-space non-symmorphic in-plane mirror symmetry renders some of the M-point moiré Hamiltonians quasi-one-dimensional in each valley, suggesting the possibility of realizing Luttinger-liquid physics.

  PublisherOA PDFDOI

• Stable Real-Space Invariants and Topology Beyond Symmetry Indicators

  ArXiv.org · 2025-05-14

  preprintOpen access

  We show that certain band gaps, which appear topologically trivial from the perspective of symmetry indicators (SIs), must instead be topological, as guaranteed by real-space information that follows from Topological Quantum Chemistry (TQC). To address this, we introduce stable real-space invariants (SRSIs) that generalize the previously discovered local and composite real-space invariants to global topological invariants of a given set of bands. These are linear combinations of Wannier state multiplicities at Wyckoff positions and take the form of $\mathbb{Z}$- and $\mathbb{Z}_n$-valued quantities ($n=2,4$). We enumerate all $\mathbb{Z}$SRSIs and $\mathbb{Z}_n$SRSIs in all non-magnetic space groups (SGs) with and without spin-orbit coupling. SRSIs fully diagnose the stable equivalence of atomic insulators, ensuring that two atomic insulators with matching SRSIs are adiabatically deformable to one another in the presence of auxiliary trivial bands. For both atomic and topological bands, $\mathbb{Z}$SRSIs are determined by the momentum-space symmetry data and thus determine the SIs. $\mathbb{Z}_n$SRSIs provide additional information about trivial band structures not captured by momentum-space data. While split elementary band representations (EBRs), where the bands forming an EBR split into disconnected parts, must induce band topology, there are 211 cases across 51 SGs where the momentum-space data of an EBR decomposes linearly with positive integer coefficients into those of other EBRs. We demonstrate that $\mathbb{Z}_n$SRSIs successfully identify the band topology in the majority of these split EBR cases, diagnosing all but 8 cases in 5 SGs. Our results solidify the conceptual framework of TQC as containing, but going beyond, SIs and momentum-space symmetry data.

  PublisherOA PDFDOI

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

  ArXiv.org · 2025-10-17

  preprintOpen access

  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.

  PublisherOA PDFDOI

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

  ArXiv.org · 2025-09-23

  preprintOpen access

  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.

  PublisherOA PDFDOI

Recent grants

• CAREER: Emergent Phenomena in New Quantum Materials

  NSF · $450k · 2010–2016

• EAGER: Topological Semimetals, Insulators and Supersymmetry

  NSF · $300k · 2016–2020

Frequent coauthors

• Nicolas Regnault

  Columbia University

  666 shared

• Maia G. Vergniory

  Donostia International Physics Center

  254 shared

• Zhijun Wang

  218 shared

• Claudia Felser

  123 shared

• Luis Elcoro

  University of the Basque Country

  123 shared

• Zhida Song

  Xinjiang University

  122 shared

• Barry Bradlyn

  University of Illinois Urbana-Champaign

  99 shared

• Jennifer Cano

  97 shared

Labs

• The Bernevig GroupPI

Education

• Post Doc Fellow, Physics

  Princeton University

  2009

• PhD, Physics

  Stanford University

  2006

• MMath, Mathematics

  Stanford University

  2001

• B.S., Physics

  Stanford University

  2001

Awards & honors

• EuroPhysics Prize from the European Physical Society (2023)
• APS James C. McGroddy Prize for New Materials (2019)
• Guggenheim Fellowship (2017)
• Fellow of the American Physical Society (2022)
• EPS Europhysics Prize