arXiv subjects

B. Andrei Bernevig

Publications and source records attributed to B. Andrei Bernevig.

At least 163 records · Page 9Linked to original sources

arXiv2020

Experimental characterization of fragile topology in an acoustic metamaterial

Symmetries crucially underlie the classification of topological phases of matter. Most materials, both natural as well as architectured, possess crystalline symmetries. Recent theoretical works unveiled that these crystalline symmetries can stabilize fragile Bloch bands that challenge our very notion of topology: while answering to the most basic definition of topology, one can trivialize these bands through the addition of trivial Bloch bands. Here, we fully characterize the symmetry properties of the response of an acoustic metamaterial to establish the fragile nature of the low-lying Bloch bands. Additionally, we present a spectral signature in the form of spectral flow under twisted boundary conditions.

cond-mat.mes-hall↗

arXiv2020

High-throughput calculations of magnetic topological materials

The discoveries of intrinsically magnetic topological materials, including semimetals with a large anomalous Hall effect and axion insulators, have directed fundamental research in solid-state materials. Topological quantum chemistry has enabled the understanding of and the search for paramagnetic topological materials. Using magnetic topological indices obtained from magnetic topological quantum chemistry (MTQC), here we perform a high-throughput search for magnetic topological materials based on first-principles calculations. We use as our starting point the Magnetic Materials Database on the Bilbao Crystallographic Server, which contains more than 549 magnetic compounds with magnetic structures deduced from neutron-scattering experiments, and identify 130 enforced semimetals (for which the band crossings are implied by symmetry eigenvalues), and topological insulators. For each compound, we perform complete electronic structure calculations, which include complete topological phase diagrams using different values of the Hubbard potential. Using a custom code to find the magnetic co-representations of all bands in all magnetic space groups, we generate data to be fed into the algorithm of MTQC to determine the topology of each magnetic material. Several of these materials display previously unknown topological phases, including symmetry-indicated magnetic semimetals, three-dimensional anomalous Hall insulators and higher-order magnetic semimetals. We analyse topological trends in the materials under varying interactions: 60 per cent of the 130 topological materials have topologies sensitive to interactions, and the others have stable topologies under varying interactions. We provide a materials database for future experimental studies and open-source code for diagnosing topologies of magnetic materials.

cond-mat.mtrl-sci↗

arXiv2020

Fractional Chiral Hinge Insulator

We propose and study a wave function describing an interacting three-dimensional fractional chiral hinge insulator (FCHI) constructed by Gutzwiller projection of two non-interacting second order topological insulators with chiral hinge modes at half filling. We use large-scale variational Monte Carlo computations to characterize the model states via the entanglement entropy and charge-spin-fluctuations. We show that the FCHI possesses fractional chiral hinge modes characterized by a central charge $c=1$ and Luttinger parameter $K=1/2$, like the edge modes of a Laughlin $1/2$ state. By changing the boundary conditions for the underlying fermions, we investigate the topological degeneracy of the FCHI. Within the range of the numerically accessible system sizes, we observe a non-trivial topological degeneracy. A more numerically pristine characterization of the bulk topology is provided by the topological entanglement entropy (TEE) correction to the area law. While our computations indicate a vanishing bulk TEE, we show that the gapped surfaces host a two-dimensional topological order with a TEE per surface compatible with half that of a Laughlin $1/2$ state, a value that cannot be obtained from topological quantum field theory.

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arXiv2020

Spin-Orbit-Induced Topological Flat Bands in Line and Split Graphs of Bipartite Lattices

Topological flat bands, such as the band in twisted bilayer graphene, are becoming a promising platform to study topics such as correlation physics, superconductivity, and transport. In this work, we introduce a generic approach to construct two-dimensional (2D) topological quasi-flat bands from line graphs and split graphs of bipartite lattices. A line graph or split graph of a bipartite lattice exhibits a set of flat bands and a set of dispersive bands. The flat band connects to the dispersive bands through a degenerate state at some momentum. We find that, with spin-orbit coupling (SOC), the flat band becomes quasi-flat and gapped from the dispersive bands. By studying a series of specific line graphs and split graphs of bipartite lattices, we find that (i) if the flat band (without SOC) has inversion or $C_2$ symmetry and is non-degenerate, then the resulting quasi-flat band must be topologically nontrivial, and (ii) if the flat band (without SOC) is degenerate, then there exists an SOC potential such that the resulting quasi-flat band is topologically nontrivial. This generic mechanism serves as a paradigm for finding topological quasi-flat bands in 2D crystalline materials and meta-materials.

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arXiv2020

Large Classes of Quantum Scarred Hamiltonians from Matrix Product States

Motivated by the existence of exact many-body quantum scars in the AKLT chain, we explore the connection between Matrix Product State (MPS) wavefunctions and many-body quantum scarred Hamiltonians. We provide a method to systematically search for and construct parent Hamiltonians with towers of exact eigenstates composed of quasiparticles on top of an MPS wavefunction. These exact eigenstates have low entanglement in spite of being in the middle of the spectrum, thus violating the strong Eigenstate Thermalization Hypothesis (ETH). Using our approach, we recover the AKLT chain starting from the MPS of its ground state, and we derive the most general nearest-neighbor Hamiltonian that shares the AKLT quasiparticle tower of exact eigenstates. We further apply this formalism to other simple MPS wavefunctions, and derive new families of Hamiltonians that exhibit AKLT-like quantum scars. As a consequence, we also construct a scar-preserving deformation that connects the AKLT chain to the integrable spin-1 pure biquadratic model. Finally, we also derive other families of Hamiltonians that exhibit new types of exact quantum scars, including a $U(1)$-invariant perturbed Potts model.

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arXiv2020

Symmetry broken Chern insulators and magic series of Rashba-like Landau level crossings in magic angle bilayer graphene

Flat-bands in magic angle twisted bilayer graphene (MATBG) have recently emerged as a rich platform to explore strong correlations, superconductivity and mag-netism. However, the phases of MATBG in magnetic field, and what they reveal about the zero-field phase diagram remain relatively unchartered. Here we use magneto-transport and Hall measurements to reveal a rich sequence of wedge-like regions of quantized Hall conductance with Chern numbers C = +(-)1, +(-)2, +(-)3, +(-)4 which nucleate from integer fillings of the moire unit cell v = +(-)3, +(-)2, +(-)1, 0 correspondingly. We interpret these phases as spin and valley polarized Chern insulators, equivalent to quantum Hall ferro-magnets. The exact sequence and correspondence of Chern numbers and filling factors suggest that these states are driven directly by electronic interactions which specifically break time-reversal symmetry in the system. We further study quantum magneto-oscillation in the yet unexplored higher energy dispersive bands with a Rashba-like dis-persion. Analysis of Landau level crossings enables a parameter-free comparison to a newly derived magic series of level crossings in magnetic field and provides constraints on the parameters w0 and w1 of the Bistritzer-MacDonald MATBG Hamiltonian. Over-all, our data provides direct insights into the complex nature of symmetry breaking in MATBG and allows for quantitative tests of the proposed microscopic scenarios for its electronic phases.

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arXiv2020

Crystalline symmetry-protected non-trivial topology in prototype compound BaAl$_4$

The BaAl$_4$ prototype crystal structure is the most populous of all structure types, and is the building block for a diverse set of sub-structures including the famous ThCr$_2$Si$_2$ family that hosts high-temperature superconductivity and numerous magnetic and strongly correlated electron systems. The MA$_4$ family of materials (M=Sr, Ba, Eu; A=Al, Ga, In) themselves present an intriguing set of ground states including charge and spin orders, but have largely been considered as uninteresting metals. Using electronic structure calculations, symmetry analysis and topological quantum chemistry techniques, we predict the exemplary compound BaAl$_4$ to harbor a three-dimensional Dirac spectrum with non-trivial topology and possible nodal lines crossing the Brillouin zone, wherein one pair of semi-Dirac points with linear dispersion along the $k_z$ direction and quadratic dispersion along the $k_x/k_y$ direction resides on the rotational axis with $C_{4v}$ point group symmetry. Electrical transport measurements reveal the presence of an extremely large, unsaturating positive magnetoresistance in BaAl$_4$ despite an uncompensated band structure, and quantum oscillations and angle-resolved photoemission spectroscopy measurements confirm the predicted multiband semimetal structure with pockets of Dirac holes and a Van Hove singularity (VHS) remarkably consistent with the theoretical prediction. We thus present BaAl$_4$ as a new topological semimetal, casting its prototype status into a new role as building block for a vast array of new topological materials.

cond-mat.mtrl-sci↗

arXiv2020

Observation of backscattering induced by magnetism in a topological edge state

The boundary modes of topological insulators are protected by the symmetries of the non-trivial bulk electronic states. Unless these symmetries are broken, they can give rise to novel phenomena, such as the quantum spin Hall effect in one-dimensional (1D) topological edge states, where quasiparticle backscattering is suppressed by time-reversal symmetry (TRS). Here, we investigate the properties of the 1D topological edge state of bismuth in the absence of TRS, where backscattering is predicted to occur. Using spectroscopic imaging and spin-polarized measurements with a scanning tunneling microscope, we compared quasiparticle interference (QPI) occurring in the edge state of a pristine bismuth bilayer with that occurring in the edge state of a bilayer, which is terminated by ferromagnetic iron clusters that break TRS. Our experiments on the decorated bilayer edge reveal an additional QPI branch, which can be associated with spin-flip scattering across the Brioullin zone center between time-reversal band partners. The observed QPI characteristics exactly match with theoretical expectations for a topological edge state, having one Kramer's pair of bands. Together, our results provide further evidence for the non-trivial nature of bismuth, and, in particular, demonstrate backscattering inside a helical topological edge state induced by broken TRS through local magnetism.

cond-mat.mes-hall↗

arXiv2020

Strongly Correlated Chern Insulators in Magic-Angle Twisted Bilayer Graphene

Interactions among electrons and the topology of their energy bands can create novel quantum phases of matter. Most topological electronic phases appear in systems with weak electron-electron interactions. The instances where topological phases emerge only as a result of strong interactions are rare, and mostly limited to those realized in the presence of intense magnetic fields. The discovery of flat electronic bands with topological character in magic-angle twisted bilayer graphene (MATBG) has created a unique opportunity to search for new strongly correlated topological phases. Here we introduce a novel local spectroscopic technique using a scanning tunneling microscope (STM) to detect a sequence of topological insulators in MATBG with Chern numbers C = $\pm$ 1, $\pm$ 2, $\pm$ 3, which form near $ν$ = $\pm$ 3, $\pm$ 2, $\pm$ 1 electrons per moiré unit cell respectively, and are stabilized by the application of modest magnetic fields. One of the phases detected here (C = +1) has been previously observed when the sublattice symmetry of MATBG was intentionally broken by hexagonal boron nitride (hBN) substrates, with interactions playing a secondary role. We demonstrate that strong electron-electron interactions alone can produce not only the previously observed phase, but also new and unexpected Chern insulating phases in MATBG. The full sequence of phases we observed can be understood by postulating that strong correlations favor breaking time-reversal symmetry to form Chern insulators that are stabilized by weak magnetic fields. Our findings illustrate that many-body correlations can create topological phases in moiré systems beyond those anticipated from weakly interacting models.

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arXiv2020

Six-fold Excitations in Electrides

Due to the lack of full rotational symmetry in condensed matter physics, solids exhibit new excitations beyond Dirac and Weyl fermions, of which the six-fold excitations have attracted considerable interest owing to the presence of the maximum degeneracy in bosonic systems. Here, we propose that a single linear dispersive six-fold excitation can be found in the electride Li$_{12}$Mg$_3$Si$_4$ and its derivatives. The six-fold excitation is formed by the floating bands of elementary band representation -- $A@12a$ -- originating from the excess electrons centered at the vacancies (${\it i.e.}$, the $12a$ Wyckoff sites). There exists a unique topological bulk-surface-edge correspondence for the spinless six-fold excitation, resulting in trivial surface 'Fermi arcs' but nontrivial hinge arcs. All energetically-gapped $k_z$-slices belong to a two-dimensional (2D) higher-order topological insulating phase, which is protected by a combined symmetry ${\mathcal T}{\widetilde S_{4z}}$ and characterized by a quantized fractional corner charge $Q_{corner}=\frac{3|e|}{4}$. Consequently, the hinge arcs are obtained in the hinge spectra of the $\widetilde S_{4z}$-symmetric rod structure. The state with a single six-fold excitation, stabilized by both nonsymmorphic crystalline symmetries and time-reversal symmetry, is located at the phase boundary and can be driven into various topologically distinct phases by explicit breaking of symmetries, making these electrides promising platforms for the systematic studies of different topological phases.

cond-mat.mtrl-sci↗

arXiv2020

Detection of Topological Materials with Machine Learning

Databases compiled using ab-initio and symmetry-based calculations now contain tens of thousands of topological insulators and topological semimetals. This makes the application of modern machine learning methods to topological materials possible. Using gradient boosted trees, we show how to construct a machine learning model which can predict the topology of a given existent material with an accuracy of 90%. Such predictions are orders of magnitude faster than actual ab-initio calculations. Through extensive testing of different models we determine which properties help detect topological materials. We identify the sources of our model's errors and we discuss approaches to overcome them.

cond-mat.mtrl-sci↗

arXiv2020

Eta-Pairing in Hubbard Models: From Spectrum Generating Algebras to Quantum Many-Body Scars

We revisit the $η$-pairing states in Hubbard models and explore their connections to quantum many-body scars to discover a universal scars mechanism. $η$-pairing occurs due to an algebraic structure known as a Spectrum Generating Algebra (SGA), giving rise to equally spaced towers of eigenstates in the spectrum. We generalize the original $η$-pairing construction and show that several Hubbard-like models on arbitrary graphs exhibit SGAs, including ones with disorder and spin-orbit coupling. We further define a Restricted Spectrum Generating Algebra (RSGA) and give examples of perturbations to the Hubbard-like models that preserve an equally spaced tower of the original model as eigenstates. The states of the surviving tower exhibit a sub-thermal entanglement entropy, and we analytically obtain parameter regimes for which they lie in the bulk of the spectrum, showing that they are exact quantum many-body scars. The RSGA framework also explains the equally spaced towers of eigenstates in several well-known models of quantum scars, including the AKLT model.

cond-mat.str-el↗

arXiv2020

Fragile Phases As Affine Monoids: Classification and Material Examples

Topological phases in electronic structures contain a new type of topology, called fragile, which can arise, for example, when an Elementary Band Representation (Atomic Limit Band) splits into a particular set of bands. We obtain, for the first time, a complete classification of the fragile topological phases which can be diagnosed by symmetry eigenvalues, to find an incredibly rich structure which far surpasses that of stable/strong topological states. We find and enumerate all hundreds of thousands of different fragile topological phases diagnosed by symmetry eigenvalues (available at http://www.cryst.ehu.es/html/doc/FragileRoots.pdf), and link the mathematical structure of these phases to that of Affine Monoids in mathematics. Furthermore, we predict and calculate, for the first time, (hundred of realistic) materials where fragile topological bands appear, and show-case the very best ones.

cond-mat.mes-hall↗

arXiv2020

The Landau Level of Fragile Topology

We study the Hofstadter butterfly and Landau levels of the twisted bilayer graphene (TBG). We show that the nontrivial fragile topology of the lowest two bands near the charge neutral point makes their Hofstadter butterfly generically connected with higher bands, closing the gap between the first and second conduction (valence) bands at a certain magnetic flux per unit cell. We also develop a momentum space method for calculating the TBG Hofstadter butterfly, from which we identify three phases where the Hofstadter butterflies of the lowest two bands and the higher bands are connected in different ways. We show this leads to a crossing between the $ν=4$ Landau fan from the charge neutral point and the zero field band gap at one flux per Moiré unit cell, which corresponds to a magnetic field $25θ^2$T (twist angle $θ$ in degrees). This provides an experimentally testable feature of the fragile topology. In general, we expect it to be a generic feature that the Hofstadter butterfly of topological bands are connected with the Hofstadter spectra of other bands. We further show the TBG band theory with Zeeman splitting being the most sizable splitting could result in Landau fans at the charge neutral point and half fillings near the magic angle, and we predict their variations under an in-plane magnetic field.

cond-mat.mes-hall↗

arXiv2020

Cascade of electronic transitions in magic-angle twisted bilayer graphene

Magic-angle twisted bilayer graphene (MATBG) exhibits a rich variety of electronic states, including correlated insulators, superconductors, and topological phases. Understanding the microscopic mechanisms responsible for these phases requires determining the interplay between electron-electron interactions and quantum degeneracy due to spin and valley degrees of freedom. Signatures of strong electron-electron correlations have been observed at partial fillings of the flat electronic bands in recent spectroscopic measurements. Transport experiments have shown changes in the Landau level degeneracy at fillings corresponding to an integer number of electrons per moiré unit cell. However, the interplay between interaction effects and the degeneracy of the system is currently unclear. Using high-resolution scanning tunneling microscopy (STM), we observed a cascade of transitions in the spectroscopic properties of MATBG as a function of electron filling. We find distinct changes in the chemical potential and a rearrangement of the low-energy excitations at each integer filling of the moiré flat bands. These spectroscopic features are a direct consequence of Coulomb interactions, which split the degenerate flat bands into Hubbard sub-bands. We find these interactions, the strength of which we can extract experimentally, to be surprisingly sensitive to the presence of a perpendicular magnetic field, which strongly modifies the spectroscopic transitions. The cascade of transitions we report here characterizes the correlated high-temperature parent phase from which various insulating and superconducting ground-state phases emerge at low temperatures in MATBG.

cond-mat.mes-hall↗

arXiv2020

Application of the induction procedure and the Smith Decomposition in the calculation and topological classification of electronic band structures in the 230 space groups

The electronic properties in a solid depend on the specific form of the wave-functions that represent the electronic states in the Brillouin zone. Since the discovery of topological insulators, much attention has been paid to the restrictions that the symmetry imposes on the electronic band structures. In this work we apply two different approaches to characterize all types of bands in a solid by the analysis of the symmetry eigenvalues: the induction procedure and the Smith Decomposition method. The symmetry eigenvalues or irreps of any electronic band in a given space group can be expressed as the superposition of the eigenvalues of a relatively small number of building units (the \emph{basic} bands). These basic bands in all the space groups are obtained following a group-subgroup chain starting from P1. Once the whole set of basic bands are known in a space group, all other types of bands (trivial, strong topological or fragile topological) can be easily derived. In particular, we confirm previous calculations of the fragile root bands in all the space groups. Furthermore, we define an automorphism group of equivalences of the electronic bands which allows to define minimum subsets of, for instance, independent basic or fragile root bands.

cond-mat.mes-hall↗

arXiv2019

Higher-Order Topology in Bismuth

The mathematical field of topology has become a framework to describe the low-energy electronic structure of crystalline solids. A typical feature of a bulk insulating three-dimensional topological crystal are conducting two-dimensional surface states. This constitutes the topological bulk-boundary correspondence. Here, we establish that the electronic structure of bismuth, an element consistently described as bulk topologically trivial, is in fact topological and follows a generalized bulk-boundary correspondence of higher-order: not the surfaces of the crystal, but its hinges host topologically protected conducting modes. These hinge modes are protected against localization by time-reversal symmetry locally, and globally by the three-fold rotational symmetry and inversion symmetry of the bismuth crystal. We support our claim theoretically and experimentally. Our theoretical analysis is based on symmetry arguments, topological indices, first-principle calculations, and the recently introduced framework of topological quantum chemistry. We provide supporting evidence from two complementary experimental techniques. With scanning-tunneling spectroscopy, we probe the unique signatures of the rotational symmetry of the one-dimensional states located at step edges of the crystal surface. With Josephson interferometry, we demonstrate their universal topological contribution to the electronic transport. Our work establishes bismuth as a higher-order topological insulator.

cond-mat.mtrl-sci↗

arXiv2019

Fermionic tensor networks for higher order topological insulators from charge pumping

We apply the charge pumping argument to fermionic tensor network representations of d-dimensional topological insulators (TIs) to obtain tensor network states for (d+1)-dimensional TIs. We exemplify the method by constructing a two-dimensional projected entangled pair states (PEPS)for a Chern insulator starting from a matrix product state (MPS) in d=1 describing pumping in the Su-Schrieffer-Heeger (SSH) model. In extending the argument to second-order TIs, we build a three-dimensional TNS for a chiral hinge TI from a PEPS in d=2 for the obstructed atomic insulator (OAI) of the quadrupole model. The (d+1)-dimensional TNSs obtained in this way have a constant bond dimension inherited from the d-dimensional TNSs in all but one spatial direction, making them candidates for numerical applications. From the d-dimensional models, we identify gapped next-nearest neighbour Hamiltonians interpolating between the trivial and OAI phases of the fully dimerized SSH and quadrupole models, whose ground states are given by an MPS and a PEPS with a constant bond dimension equal to 2, respectively.

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