arXiv subjects

B. Andrei Bernevig

Publications and source records attributed to B. Andrei Bernevig.

At least 145 records · Page 8Linked to original sources

arXiv2021

Magnetic Topological Quantum Chemistry

For over 100 years, the group-theoretic characterization of crystalline solids has provided the foundational language for diverse problems in physics and chemistry. However, the group theory of crystals with commensurate magnetic order has remained incomplete for the past 70 years, due to the complicated symmetries of magnetic crystals. In this work, we complete the 100-year-old problem of crystalline group theory by deriving the small corepresentations, momentum stars, compatibility relations, and magnetic elementary band corepresentations of the 1,421 magnetic space groups (MSGs), which we have made freely accessible through tools on the Bilbao Crystallographic Server. We extend Topological Quantum Chemistry to the MSGs to form a complete, real-space theory of band topology in magnetic and nonmagnetic crystalline solids - Magnetic Topological Quantum Chemistry (MTQC). Using MTQC, we derive the complete set of symmetry-based indicators of electronic band topology, for which we identify symmetry-respecting bulk and anomalous surface and hinge states.

cond-mat.mes-hall↗

arXiv2021

Bulk and Edge Properties of Twisted Double-Bilayer Graphene

The emergence of controlled, two-dimensional moiré materials has uncovered a new platform for investigating topological physics. Twisted double bilayer graphene (TDBG) has been predicted to host a topologically non-trivial gapped phase with Chern number equal to two at charge neutrality, when half the flat bands are filled. However, it can be difficult to diagnose topological states using a single measurement because it is ideal to probe the bulk and edge properties at the same time. Here, we report a combination of chemical potential measurements, transport measurements, and theoretical calculations that show that twisted double bilayer graphene can host metallic edge transport while simultaneously being insulating in the bulk. A Landauer-Buttiker analysis of measurements on multi-terminal samples allows us to quantitatively assess edge state scattering. We interpret these results as signatures of the predicted topological phase at charge neutrality.

cond-mat.mes-hall↗

arXiv2021

Higher-Order Topological Superconductivity in Twisted Bilayer Graphene

We show that introducing spin-singlet or spin-triplet superconductivity into twisted bilayer graphene induces higher-order topological superconductivity. $C_{2z}T$-protected corner states of Majorana Kramers pairs appear at the boundary between domains with opposite signs of pairing, and zero modes materialize in Abrikosov vortices. The topology of the superconducting phase originates from the anomaly [1] -- the absence of a lattice support -- of the single-valley band structure of twisted bilayer graphene, which is protected by $C_{2z}T$ and the particle-hole symmetry $\cal P$. We prove that any pairing (spin-singlet or spin-triplet) term preserving valley-U(1), spin-SU(2), time-reversal, $C_{2z}T$, and $\cal P$ must drive the system into a higher-order topological superconductor phase. Here spin-SU(2) is the global spin-SU(2) for the singlet pairing and a combination of two SU(2)'s in the two valleys for the triplet pairing. Using a Dirac Hamiltonian, we demonstrate the existence of corner modes and confirm this with numerical calculations. These corner states are stable even if the approximate particle-hole symmetry $\cal P$ is weakly broken, which is true in experimental setups. Finally, we suggest an experiment to detect the topological superconductivity: by observing the fractional Josephson effect in a TBG-TSC Josephson system.

cond-mat.supr-con↗

arXiv2021

Topology invisible to eigenvalues in obstructed atomic insulators

We consider the extent to which symmetry eigenvalues reveal the topological character of bands. Specifically, we compare distinct atomic limit phases (band representations) that share the same irreducible representations (irreps) at all points in the Brillouin zone and, therefore, appear equivalent in a classification based on eigenvalues. We derive examples where such "irrep-equivalent" phases can be distinguished by a quantized Berry phase or generalization thereof. These examples constitute a generalization of the Su-Schrieffer-Heeger chain: neither phase is topological, in the sense that localized Wannier functions exist, yet there is a topological obstruction between them. We refer to two phases as "Berry obstructed atomic limits" if they have the same irreps, but differ by Berry phases. This is a distinct notion from eigenvalue obstructed atomic limits, which differ in their symmetry irreps at some point in the Brillouin zone. We compute exhaustive lists of elementary band representations that are irrep-equivalent, in all space groups, with and without time-reversal symmetry and spin-orbit coupling, and use group theory to derive a set of necessary conditions for irrep-equivalence. Finally, we conjecture, and in some cases prove, that irrep-equivalent elementary band representations that are not equivalent can be distinguished by a topological invariant.

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arXiv2021

Filling-Enforced Obstructed Atomic Insulators

Topological band theory has achieved great success in the high-throughput search for topological band structures both in paramagnetic and magnetic crystal materials. However, a significant proportion of materials are topologically trivial insulators at the Fermi level. In this paper, we show that, remarkably, for a subset of the topologically trivial insulators, knowing only their electron number and the Wyckoff positions of the atoms we can separate them into two groups: the obstructed atomic insulator (OAI) and the atomic insulator (AI). The interesting group, the OAI, have a center of charge not localized on the atoms. Using the theory of topological quantum chemistry, in this work we first derive the necessary and sufficient conditions for a topologically trivial insulator to be a filling enforced obstructed atomic insulator (feOAI) in the 1651 Shubnikov space groups. Remarkably, the filling enforced criteria enable the identification of obstructed atomic bands without knowing the representations of the band structures. Hence, no ab-initio calculations are needed for the filling enforced criteria, although they are needed to obtain the band gaps. With the help of the Topological Quantum Chemistry website, we have performed a high-throughput search for feOAIs and have found that 957 ICSD entries (638 unique materials) are paramagnetic feOAIs, among which 738 (475) materials have an indirect gap. The metallic obstructed surface states of feOAIs are also showcased by several material examples.

cond-mat.mtrl-sci↗

arXiv2021

General Construction and Topological Classification of All Magnetic and Non-Magnetic Flat Bands

Exotic phases of matter emerge from the interplay between strong electron interactions and non-trivial topology. Owing to their lack of dispersion at the single-particle level, systems harboring flat bands are excellent testbeds for strongly interacting physics, with twisted bilayer graphene serving as a prime example. On the other hand, existing theoretical models for obtaining flat bands in crystalline materials, such as the line-graph formalism, are often too restrictive for real-life material realizations. Here we present a generic technique for constructing perfectly flat bands from bipartite crystalline lattices. Our prescription encapsulates and generalizes the various flat band models in the literature, being applicable to systems with any orbital content, with or without spin-orbit coupling. Using Topological Quantum Chemistry, we build a complete topological classification in terms of symmetry eigenvalues of all the gapped and gapless flat bands, for all 1651 Magnetic Space Groups. In addition, we derive criteria for the existence of symmetry-protected band touching points between the flat and dispersive bands, and we identify the gapped flat bands as prime candidates for fragile topological phases. Finally, we show that the set of all (gapped and gapless) perfectly flat bands is finitely generated and construct the corresponding bases for all 1651 Shubnikov Space Groups.

cond-mat.mes-hall↗

arXiv2021

Open Momentum Space Method for Hofstadter Butterfly and the Quantized Lorentz Susceptibility

We develop a generic $\mathbf{k}\cdot \mathbf{p}$ open momentum space method for calculating the Hofstadter butterfly of both continuum (Moiré) models and tight-binding models, where the quasimomentum is directly substituted by the Landau level (LL) operators. By taking a LL cutoff (and a reciprocal lattice cutoff for continuum models), one obtains the Hofstadter butterfly with in-gap spectral flows. For continuum models such as the Moiré model for twisted bilayer graphene, our method gives a sparse Hamiltonian, making it much more efficient than existing methods. The spectral flows in the Hofstadter gaps can be understood as edge states on a momentum space boundary, from which one can determine the two integers ($t_ν,s_ν$) of a gap $ν$ satisfying the Diophantine equation. The spectral flows can also be removed to obtain a clear Hofstadter butterfly. While $t_ν$ is known as the Chern number, our theory identifies $s_ν$ as a dual Chern number for the momentum space, which corresponds to a quantized Lorentz susceptibility $γ_{xy}=eBs_ν$.

cond-mat.mes-hall↗

arXiv2021

Delocalization Transition of Disordered Axion Insulator

The axion insulator is a higher-order topological insulator protected by inversion symmetry. We show that under quenched disorder respecting inversion symmetry {\it on average}, the topology of the axion insulator stays robust, and an intermediate metallic phase in which states are delocalized is unavoidable at the transition from an axion insulator to a trivial insulator. We derive this conclusion from general arguments, from classical percolation theory, and from the numerical study of a 3D quantum network model simulating a disordered axion insulator through a layer construction. We find the localization length critical exponent near the delocalization transition to be $ν=1.42\pm 0.12$. We further show that this delocalization transition is stable even to weak breaking of the average inversion symmetry, up to a critical strength. We also quantitatively map our quantum network model to an effective Hamiltonian and we find its low energy k$\cdot$p expansion.

cond-mat.mes-hall↗

arXiv2021

Cascades between light and heavy fermions in the normal state of magic angle twisted bilayer graphene

We present a framework for understanding the recently observed cascade transitions and the Landau level degeneracies at every integer filling of twisted bilayer graphene. The Coulomb interaction projected onto narrow bands causes the charged excitations at an integer filling to disperse, forming new bands. If the excitation moves the filling away from the charge neutrality point, then it has a band minimum at the moire Brillouin zone center with a small mass that compares well with the experiment; if towards the charge neutrality point, then it has a much larger mass and a higher degeneracy. At a non-zero density away from an integer filling the excitations interact. The system on the small mass side has a large bandwidth and forms a Fermi liquid. On the large mass side the bandwidth is narrow, the compressibility is negative and the Fermi liquid is likely unstable. This explains the observed sawtooth features in compressibility, the Landau fans pointing away from charge neutrality as well as their degeneracies. By providing a description of the charge itineracy in the normal state this framework sets the stage for superconductivity at lower temperatures.

cond-mat.str-el↗

arXiv2021

TSTG I: Single-Particle and Many-Body Hamiltonians and Hidden Non-local Symmetries of Trilayer Moiré Systems with and without Displacement Field

We derive the Hamiltonian for trilayer moiré systems with the Coulomb interaction projected onto the bands near the charge neutrality point. Motivated by the latest experimental results, we focus on the twisted symmetric trilayer graphene (TSTG) with a mirror-symmetry with respect to the middle layer. We provide a full symmetry analysis of the non-interacting Hamiltonian with a perpendicular displacement field coupling the band structure made otherwise of the twisted bilayer graphene (TBG) and the high velocity Dirac fermions, and we identify a hidden non-local symmetry of the problem. In the presence of this displacement field, we construct an approximate single-particle model, akin to the tripod model for TBG, capturing the essence of non-interacting TSTG. We also derive more quantitative perturbation schemes for the low-energy physics of TSTG with displacement field, obtaining the corresponding eigenstates. This allows us to obtain the Coulomb interaction Hamiltonian projected in the active band TSTG wavefunctions and derive the full many-body Hamiltonian of the system. We also provide an efficient parameterization of the interacting Hamiltonian. Finally, we show that the discrete symmetries at the single-particle level promote the $\mathrm{U} \left( 2 \right) \times \mathrm{U} \left( 2 \right)$ spin-valley symmetry to enlarged symmetry groups of the interacting problem under different limits. The interacting part of the Hamiltonian exhibits a large $\mathrm{U} \left( 4 \right) \times \mathrm{U} \left( 4 \right) \times \mathrm{U} \left( 4 \right) \times \mathrm{U} \left( 4 \right)$ symmetry in the chiral limit. Moreover, by identifying a new symmetry which we dub spatial many-body charge conjugation, we show that the physics of TSTG is symmetric around charge neutrality.

cond-mat.str-el↗

arXiv2021

An $O(N)$ $Ab~initio$ Calculation Scheme for Large-Scale Moiré Structures

We present a two-step method specifically tailored for band structure calculation of the small-angle moiré-pattern materials which contain tens of thousands of atoms in a unit cell. In the first step, the self-consistent field calculation for ground state is performed with $O(N)$ Krylov subspace method implemented in OpenMX. Secondly, the crystal momentum dependent Bloch Hamiltonian and overlap matrix are constructed from the results obtained in the first step and only a small number of eigenvalues near the Fermi energy are solved with shift-invert and Lanczos techniques. By systematically tuning two key parameters, the cutoff radius for electron hopping interaction and the dimension of Krylov subspace, we obtained the band structures for both rigid and corrugated twisted bilayer graphene structures at the first magic angle ($θ=1.08^\circ$) and other three larger ones with satisfied accuracy on affordable costs. The band structures are in good agreement with those from tight binding models, continuum models, plane-wave pseudo-potential based $ab~initio$ calculations, and the experimental observations. This efficient two-step method is to play a crucial role in other twisted two-dimensional materials, where the band structures are much more complex than graphene and the effective model is hard to be constructed.

cond-mat.mes-hall↗

arXiv2021

A Charge-Density-Wave Topological Semimetal

Topological physics and strong electron-electron correlations in quantum materials are typically studied independently. However, there have been rapid recent developments in quantum materials in which topological phase transitions emerge when the single-particle band structure is modified by strong interactions. We here demonstrate that the room-temperature phase of (TaSe$_4$)$_2$I is a Weyl semimetal with 24 pairs of Weyl nodes. Owing to its quasi-1D structure, (TaSe$_4$)$_2$I hosts an established CDW instability just below room temperature. Using X-ray diffraction, angle-resolved photoemission spectroscopy, and first-principles calculations, we find that the CDW in (TaSe$_4$)$_2$I couples the bulk Weyl points and opens a band gap. The correlation-driven topological phase transition in (TaSe$_4$)$_2$I provides a route towards observing condensed-matter realizations of axion electrodynamics in the gapped regime, topological chiral response effects in the semimetallic phase, and represents an avenue for exploring the interplay of correlations and topology in a solid-state material.

cond-mat.mtrl-sci↗

arXiv2020

Competing zero-field Chern insulators in Superconducting Twisted Bilayer Graphene

The discovery of magic angle twisted bilayer graphene (MATBG) has unveiled a rich variety of superconducting, magnetic and topologically nontrivial phases. The existence of all these phases in one material, and their tunability, has opened new pathways for the creation of unusual gate tunable junctions. However, the required conditions for their creation - gate induced transitions between phases in zero magnetic field - have so far not been achieved. Here, we report on the first experimental demonstration of a device that is both a zero-field Chern insulator and a superconductor. The Chern insulator occurs near moire cell filling factor v = +1 in a hBN non-aligned MATBG device and manifests itself via an anomalous Hall effect. The insulator has Chern number C = +-1 and a relatively high Curie temperature of Tc = 4.5 K. Gate tuning away from this state exposes strong superconducting phases with critical temperatures of up to Tc = 3.5 K. In a perpendicular magnetic field above B > 0.5 T we observe a transition of the /C/= +1 Chern insulator from Chern number C = +-1 to C = 3, characterized by a quantized Hall plateau with Ryx = h/3e2. These observations show that interaction-induced symmetry breaking in MATBG leads to zero-field ground states that include almost degenerate and closely competing Chern insulators, and that states with larger Chern numbers couple most strongly to the B-field. By providing the first demonstration of a system that allows gate-induced transitions between magnetic and superconducting phases, our observations mark a major milestone in the creation of a new generation of quantum electronics.

cond-mat.mes-hall↗

arXiv2020

Multiple Flat Bands and Topological Hofstadter Butterfly in Twisted Bilayer Graphene Close to the Second Magic Angle

Moiré superlattices in two-dimensional (2D) van der Waals (vdW) heterostructures provide 20 an efficient way to engineer electron band properties. The recent discovery of exotic quantum phases and their interplay in twisted bilayer graphene (tBLG) has built this moiré system one of the most renowned condensed matter platforms (1-10). So far the studies of tBLG has been mostly focused on the lowest two flat moiré bands at the first magic angle θm1 ~ 1.1°, leaving high-order moiré bands and magic angles largely unexplored. Here we report 25 an observation of multiple well-isolated flat moiré bands in tBLG close to the second magic angle θm2 ~ 0.5°, which cannot be explained without considering electron-election interactions. With high magnetic field magneto-transport measurements, we further reveal a qualitatively new, energetically unbound Hofstadter butterfly spectrum in which continuously extended quantized Landau level gaps cross all trivial band-gaps. The 30 connected Hofstadter butterfly strongly evidences the topologically nontrivial textures of the multiple moiré bands. Overall, our work provides a new perspective for understanding the quantum phases in tBLG and the fractal Hofstadter spectra of multiple topological bands.

cond-mat.mes-hall↗

arXiv2020

Fragile topology in line-graph lattices with two, three, or four gapped flat bands

The geometric properties of a lattice can have profound consequences on its band spectrum. For example, symmetry constraints and geometric frustration can give rise to topologicially nontrivial and dispersionless bands, respectively. Line-graph lattices are a perfect example of both of these features: their lowest energy bands are perfectly flat, and here we develop a formalism to connect some of their geometric properties with the presence or absence of fragile topology in their flat bands. This theoretical work will enable experimental studies of fragile topology in several types of line-graph lattices, most naturally suited to superconducting circuits.

cond-mat.mes-hall↗

arXiv2020

Hofstadter Topology: Non-crystalline Topological Materials at High Flux

The Hofstadter problem is the lattice analog of the quantum Hall effect and is the paradigmatic example of topology induced by an applied magnetic field. Conventionally, the Hofstadter problem involves adding $\sim 10^4$ T magnetic fields to a trivial band structure. In this work, we show that when a magnetic field is added to an initially topological band structure, a wealth of remarkable possible phases emerges. Remarkably, we find topological phases which cannot be realized in any crystalline insulators. We prove that threading magnetic flux through a Hamiltonian with nonzero Chern number enforces a phase transition at fixed filling and that a 2D Hamiltonian with nontrivial Kane-Mele invariant produces a 3D TI or 3D weak TI phase in periodic flux. We then study fragile topology protected by the product of two-fold rotation and time-reversal and show that there exists a 3D higher order TI phase where corner modes are pumped by flux. We show that a model of twisted bilayer graphene realizes this phase. Our results rely primarily on the magnetic translation group which exists at rational values of the flux. The advent of Moiré lattices also renders our work relevant experimentally. In Moiré lattices, it is possible for fields of order $1-30$ T to reach one flux per plaquette and allow access to our proposed Hofstadter topological phase.

cond-mat.mes-hall↗

arXiv2020

Quantum Many-body Scars in a Landau Level on a Thin Torus

We study a kinetically constrained pair hopping model that arises within a Landau level in the quantum Hall effect. At filling $ν= 1/3$, the model exactly maps onto the so-called "PXP model", a constrained model for the Rydberg atom chain that is numerically known to exhibit ETH-violating states in the middle of the spectrum or quantum many-body scars. Indeed, particular charge density wave configurations exhibit the same revivals seen in the PXP model. We generalize the mapping to fillings factors $ν= p/(2p+1)$, and show that the model is equivalent to non-integrable spin-chains within particular constrained Krylov Hilbert spaces. These lead to new examples of quantum many-body scars which manifest as revivals and slow thermalization of particular charge density wave states. Finally, we investigate the stability of the quantum scars under certain Hamiltonian perturbations motivated by the fractional quantum Hall physics.

cond-mat.str-el↗

arXiv2020

Fragile topology and flat-band superconductivity in the strong-coupling regime

In flat bands, superconductivity can lead to surprising transport effects. The superfluid "mobility", in the form of the superfluid weight $D_s$, does not draw from the curvature of the band but has a purely band-geometric origin. In a mean-field description, a non-zero Chern number or fragile topology sets a lower bound for $D_s$, which, via the Berezinskii-Kosterlitz-Thouless mechanism, might explain the relatively high superconducting transition temperature measured in magic-angle twisted bilayer graphene (MATBG). For fragile topology, relevant for the bilayer system, the fate of this bound for finite temperature and beyond the mean-field approximation remained, however, unclear. Here, we use numerically exact Monte Carlo simulations to study an attractive Hubbard model in flat bands with topological properties akin to those of MATBG. We find a superconducting phase transition with a critical temperature that scales linearly with the interaction strength. We then investigate the robustness of the superconducting state to the addition of trivial bands that may or may not trivialize the fragile topology. Our results substantiate the validity of the topological bound beyond the mean-field regime and further stress the importance of fragile topology for flat-band superconductivity.

cond-mat.supr-con↗