arXiv subjects

B. A. Bernevig

Publications and source records attributed to B. A. Bernevig.

At least 19 recordsLinked to original sources

arXiv2024

Discovery of an Antiferromagnetic Topological Nodal-line Kondo Semimetal

The symbiosis of strong interactions, flat bands, topology and symmetry has led to the discovery of exotic phases of matter, including fractional Chern insulators, correlated moiré topological superconductors, and Dirac and Weyl semimetals. Correlated metals, such as those present in Kondo lattices, rely on the screening of local moments by a sea of non-magnetic conduction electrons. Here, we report on a unique topological Kondo lattice compound, CeCo2P2, where the Kondo effect - whose existence under the magnetic Co phase is protected by PT symmetry - coexists with antiferromagnetic order emerging from the flat bands associated with the Co atoms. Remarkably, this is the only known Kondo lattice compound where magnetic order occurs in non-heavy electrons, and puzzlingly, at a temperature significantly higher than that of the Kondo effect. Furthermore, at low temperatures, the emergence of the Kondo effect, in conjunction with a glide-mirror-z symmetry, results in a nodal line protected by bulk topology near the Fermi energy. These unusual properties, arising from the interplay between itinerant and correlated electrons from different constituent elements, lead to novel quantum phases beyond the celebrated topological Kondo insulators and Weyl Kondo semimetals. CeCo2P2 thus provides an ideal platform for investigating narrow bands, topology, magnetism, and the Kondo effect in strongly correlated electron systems.

cond-mat.str-el↗

arXiv2023

Superfluidity and Quantum Geometry in Twisted Multilayer Systems

Designer 2D materials where the constituent layers are not aligned may result in band structures with dispersionless, "flat" bands. Twisted bilayer graphene has been found to show correlated phases as well as superconductivity related to such flat bands. In parallel, theory work has discovered that superconductivity and superfluidity is determined by the quantum geometry and topology of the band structure. These recent key developments are merging to a flourishing research topic: understanding the possible connection and ramifications of quantum geometry on the induced superconductivity and superfluidity in moiré multilayer and other flat band systems. This article presents an introduction to how quantum geometry governs superfluidity in platforms including, and beyond, graphene. We explain how a new type of topology discovered in TBG could affect superconductivity, pinpoint the geometric contribution in its Beretzinskii-Kosterlitz-Thouless (BKT) critical temperature, and mention moiré materials beyond TBG. Ultracold gases are introduced as a complementary platform for quantum geometric effects and a comparison is made to moiré materials. An outlook sketches the prospects of twisted multilayer systems in providing the route to room temperature superconductivity.

cond-mat.supr-con↗

arXiv2023

Symmetric Kondo Lattice States in Doped Strained Twisted Bilayer Graphene

We use the topological heavy fermion (THF) model and its Kondo Lattice (KL) formulation to study the symmetric Kondo state in twisted bilayer graphene. Via a large-N approximation, we find a symmetric Kondo (SK) state in KL mode at fillings $ν=0,\pm 1,\pm 2$. In the SK state, all symmetries are preserved and the local moments are Kondo screened by the conduction electrons. At the mean-field level of the THF model at $ν=0,\pm 1, \pm 2, \pm 3$, we also find a similar symmetric state. We study the stability of the symmetric state by comparing its energy with the ordered states and find the ordered states to have lower energy. However, moving away from integer fillings by doping holes to the light bands, we find the energy difference is reduced, which suggests the loss of ordering and a tendency towards Kondo screening. In order to include many-body effects beyond the mean-field approximation, we perform dynamical mean-field theory (DMFT) calculations on the THF model. We find the spin susceptibility follows a Curie behavior at $ν=0, \pm 1,\pm 2$ down to $\sim 2\text{K}$ where the onset of screening of the local moment becomes visible. This hints to very low Kondo temperatures at these fillings, in agreement with the outcome of our mean-field calculations. At non-integer filling $ν=\pm 0.5,\pm 0.8,\pm 1.2$ DMFT shows deviations from a $1/T$-susceptibility at much higher temperatures, suggesting a more effective screening of local moments with doping. Finally, we study the effect of a $C_{3z}$-rotational-symmetry-breaking strain via mean-field approaches and find that a symmetric phase (that only breaks $C_{3z}$ symmetry) can be stabilized at sufficiently large strain at $ν=0,\pm 1, \pm 2$. Our results suggest that a symmetric Kondo phase is strongly suppressed at integer fillings, but could be stabilized either at non-integer fillings or by applying strain.

cond-mat.str-el↗

arXiv2020

Colossal magnetoresistance in a nonsymmorphic antiferromagnetic insulator

Here we investigate antiferromagnetic Eu$_{5}$In$_{2}$Sb$_{6}$, a nonsymmorphic Zintl phase. Our electrical transport data show that Eu$_{5}$In$_{2}$Sb$_{6}$ is remarkably insulating and exhibits an exceptionally large negative magnetoresistance, which is consistent with the presence of magnetic polarons. From {\it ab initio} calculations, the paramagnetic state of Eu$_{5}$In$_{2}$Sb$_{6}$ is a topologically nontrivial semimetal within the generalized gradient approximation (GGA), whereas an insulating state with trivial topological indices is obtained using a modified Becke-Johnson potential. Notably, GGA+U calculations suggest that the antiferromagnetic phase of Eu$_{5}$In$_{2}$Sb$_{6}$ may host an axion insulating state. Our results provide important feedback for theories of topological classification and highlight the potential of realizing clean magnetic narrow-gap semiconductors in Zintl materials.

cond-mat.str-el↗

arXiv2020

`Unhinging' the surfaces of higher-order topological insulators and superconductors

We show that the chiral Dirac and Majorana hinge modes in three-dimensional higher-order topological insulators (HOTIs) and superconductors (HOTSCs) can be gapped while preserving the protecting $\mathsf{C}_{2n}\mathcal T$ symmetry upon the introduction of non-Abelian surface topological order. In both cases, the topological order on a single side surface breaks time reversal symmetry, but appears with its time-reversal conjugate on alternating sides in a $\mathsf{C}_{2n}\mathcal T$ preserving pattern. In the absence of the HOTI/HOTSC bulk, such a pattern necessarily involves gapless chiral modes on hinges between $\mathsf{C}_{2n}\mathcal T$-conjugate domains. However, using a combination of $K$-matrix and anyon condensation arguments, we show that on the boundary of a 3D HOTI/HOTSC these topological orders are fully gapped and hence `anomalous'. Our results suggest that new patterns of surface and hinge states can be engineered by selectively introducing topological order only on specific surfaces.

cond-mat.str-el↗

arXiv2019

Topological Lifshitz Transitions and Fermi Arc Manipulation in Weyl Semimetal NbAs

Surface Fermi arcs (SFAs), the unique open Fermi-surfaces (FSs) discovered recently in topological Weyl semimetals (TWSs), are unlike closed FSs in conventional materials and can give rise to many exotic phenomena, such as anomalous SFA-mediated quantum oscillations, chiral magnetic effects, three-dimensional quantum Hall effect, non-local voltage generation and anomalous electromagnetic wave transmission. Here, by using in-situ surface decoration, we demonstrate successful manipulation of the shape, size and even the connections of SFAs in a model TWS, NbAs, and observe their evolution that leads to an unusual topological Lifshitz transition not caused by the change of the carrier concentration. The phase transition teleports the SFAs between different parts of the surface Brillouin zone. Despite the dramatic surface evolution, the existence of SFAs is robust and each SFA remains tied to a pair of Weyl points of opposite chirality, as dictated by the bulk topology.

cond-mat.mtrl-sci↗

arXiv2019

The (High Quality) Topological Materials In The World

"Topological Quantum Chemistry (TQC) links the chemical and symmetry structure of a given material with its topological properties. This field tabulates the data of the 10398 real-space atomic limits of materials, and solves the compatibility relations of electronic bands in momentum space. A material that is not an atomic limit or whose bands do not satisfy the compatibility relations, is a topological insulator/semimetal. We use TQC to find the topological stoichiometric non-magnetic, "high-quality'' materials in the world. We develop several code additions to VASP which can compute all characters of all symmetries at all high-symmetry points in the Brillouin Zone (BZ). Using TQC we then develop codes to check which materials in ICSD are topological. Out of 26938 stoichiometric materials in our filtered ICSD database, we find 2861 topological insulators (TI) and 2936 topological semimetals (2505 and 2560 non-f electron, respectively). Our method is uniquely capable to show that none of the TI's found exhibit fragile topology. We partition the topological materials in different physical classes. For the majority of the 5797 "high-quality'' topological material, we compute: the topological class (equivalence classes of TQC elementary band representations -- equivalent to the topological index), the symmetry(ies) that protects the topological class, the representations at high symmetry points and the direct gap (for insulators), and the topological index. For topological semimetals we then compute whether the system becomes a topological insulator (whose index/class we compute) upon breaking symmetries -- useful for experiments. 2152 more TI's are obtained in this way. For almost all 5065 non-f-electron topological materials, we provide the electronic band structures, allowing the identification of quantitative properties (gaps, velocities). Remarkably, our exhaustive results show that a large proportion ( ~ 24% !) of all materials in nature are topological (confirmed by calculations of "low-quality'' materials). We confirm the topology of several new materials by Wilson loop calculations. We added an open-source code and end-user button on the Bilbao Crystallographic Server (BCS) which checks the topology of any material. We comment on the chemistry of each compound and sample part of the "low-quality'' ICSD data to find more materials."

cond-mat.mtrl-sci↗

arXiv2018

A gap-protected zero-Hall effect state in the quantum limit of the nonsymmorphic metal KHgSb

A recurring theme in topological matter is the protection of unusual electronic states by symmetry, for example, protection of the surface states in Z2 topological insulators by time reversal symmetry [1-3]. Recently interest has turned to unusual surface states in the large class of nonsymmorphic materials [4-11]. In particular KHgSb is predicted to exhibit double quantum spin Hall (QSH) states [10]. Here we report observation of a novel feature of the Hall conductivity in KHgSb in strong magnetic field B. In the quantum limit, the Hall conductivity is observed to fall exponentially to zero, but the diagonal conductivity is finite. A large gap protects this unusual zero-Hall state. We propose that, in this limit, the chemical potential drops into the bulk gap, intersecting equal numbers of right and left-moving QSH surface modes to produce the zero-Hall state.

cond-mat.str-el↗

arXiv2018

Band Connectivity for Topological Quantum Chemistry: Band Structures As A Graph Theory Problem

The conventional theory of solids is well suited to describing band structures locally near isolated points in momentum space, but struggles to capture the full, global picture necessary for understanding topological phenomena. In part of a recent paper [B. Bradlyn et al., Nature 547, 298 (2017)], we have introduced the way to overcome this difficulty by formulating the problem of sewing together many disconnected local "k-dot-p" band structures across the Brillouin zone in terms of graph theory. In the current manuscript we give the details of our full theoretical construction. We show that crystal symmetries strongly constrain the allowed connectivities of energy bands, and we employ graph-theoretic techniques such as graph connectivity to enumerate all the solutions to these constraints. The tools of graph theory allow us to identify disconnected groups of bands in these solutions, and so identify topologically distinct insulating phases.

cond-mat.mes-hall↗

arXiv2017

The chiral anomaly factory: Creating Weyl fermions with a magnetic field

Weyl fermions can be created in materials with both time reversal and inversion symmetry by applying a magnetic field, as evidenced by recent measurements of anomalous negative magnetoresistance. Here, we do a thorough analysis of the Weyl points in these materials: by enforcing crystal symmetries, we classify the location and monopole charges of Weyl points created by fields aligned with high-symmetry axes. The analysis applies generally to materials with band inversion in the $T_d$, $D_{4h}$ and $D_{6h}$ point groups. For the $T_d$ point group, we find that Weyl nodes persist for all directions of the magnetic field. Further, we compute the anomalous magnetoresistance of field-created Weyl fermions in the semiclassical regime. We find that the magnetoresistance can scale non-quadratically with magnetic field, in contrast to materials with intrinsic Weyl nodes. Our results are relevant to future experiments in the semi-classical regime.

cond-mat.mes-hall↗

arXiv2016

The chiral anomaly and thermopower of Weyl fermions in the half-Heusler GdPtBi

The Dirac and Weyl semimetals are unusual materials in which the nodes of the bulk states are protected against gap formation by crystalline symmetry. The chiral anomaly~\cite{Adler,Bell}, predicted to occur in both systems, was recently observed as a negative longitudinal magnetoresistance (LMR) in Na$_3$Bi and in TaAs. An important issue is whether Weyl physics appears in a broader class of materials. We report evidence for the chiral anomaly in the half-Heusler GdPtBi. In zero field, GdPtBi is a zero-gap semiconductor with quadratic bands. In a magnetic field, the Zeeman energy leads to Weyl nodes. We have observed a large negative LMR with the field-steering properties specific to the chiral anomaly. The chiral anomaly also induces strong suppression of the thermopower. We report a detailed study of the thermoelectric response function $α_{xx}$ of Weyl fermions. The scheme of creating Weyl nodes from quadratic bands suggests that the chiral anomaly may be observable in a broad class of semimetals.

cond-mat.str-el↗

arXiv2016

Experimental Discovery of the First Nonsymmorphic Topological Insulator KHgSb

Topological insulators (TIs) host novel states of quantum matter, distinguished from trivial insulators by the presence of nontrivial conducting boundary states connecting the valence and conduction bulk bands. Up to date, all the TIs discovered experimentally rely on the presence of either time reversal or symmorphic mirror symmetry to protect massless Dirac-like boundary states. Very recently, it has been theoretically proposed that several materials are a new type of TIs protected by nonsymmorphic symmetry, where glide-mirror can protect novel exotic surface fermions with hourglass-shaped dispersion. However, an experimental confirmation of such new nonsymmorphic TI (NSTI) is still missing. Using angle-resolved photoemission spectroscopy, we reveal that such hourglass topology exists on the (010) surface of crystalline KHgSb while the (001) surface has no boundary state, which is fully consistent with first-principles calculations. We thus experimentally demonstrate that KHgSb is a NSTI hosting hourglass fermions. By expanding the classification of topological insulators, this discovery opens a new direction in the research of nonsymmorphic topological properties of materials.

cond-mat.mtrl-sci↗

arXiv2015

Correlation Lengths and Topological Entanglement Entropies of Unitary and Non-Unitary Fractional Quantum Hall Wavefunctions

Using the newly developed Matrix Product State (MPS) formalism for non-abelian Fractional Quantum Hall (FQH) states, we address the question of whether a FQH trial wave function written as a correlation function in a non-unitary Conformal Field Theory (CFT) can describe the bulk of a gapped FQH phase. We show that the non-unitary Gaffnian state exhibits clear signatures of a pathological behavior. As a benchmark we compute the correlation length of Moore-Read state and find it to be finite in the thermodynamic limit. By contrast, the Gaffnian state has infinite correlation length in (at least) the non-Abelian sector, and is therefore gapless. We also compute the topological entanglement entropy of several non-abelian states with and without quasiholes. For the first time in FQH the results are in excellent agreement in all topological sectors with the CFT prediction for unitary states. For the non-unitary Gaffnian state in finite size systems, the topological entanglement entropy seems to behave like that of the Composite Fermion Jain state at equal filling.

cond-mat.str-el↗

arXiv2014

One-dimensional Topological Edge States of Bismuth Bilayers

The hallmark of a time-reversal symmetry protected topologically insulating state of matter in two-dimensions (2D) is the existence of chiral edge modes propagating along the perimeter of the system. To date, evidence for such electronic modes has come from experiments on semiconducting heterostructures in the topological phase which showed approximately quantized values of the overall conductance as well as edge-dominated current flow. However, there have not been any spectroscopic measurements to demonstrate the one-dimensional (1D) nature of the edge modes. Among the first systems predicted to be a 2D topological insulator are bilayers of bismuth (Bi) and there have been recent experimental indications of possible topological boundary states at their edges. However, the experiments on such bilayers suffered from irregular structure of their edges or the coupling of the edge states to substrate's bulk states. Here we report scanning tunneling microscopy (STM) experiments which show that a subset of the predicted Bi-bilayers' edge states are decoupled from states of Bi substrate and provide direct spectroscopic evidence of their 1D nature. Moreover, by visualizing the quantum interference of edge mode quasi-particles in confined geometries, we demonstrate their remarkable coherent propagation along the edge with scattering properties that are consistent with strong suppression of backscattering as predicted for the propagating topological edge states.

cond-mat.mes-hall↗

arXiv2013

Fractional Quantum Hall Matrix Product States For Interacting Conformal Field Theories

Using truncated conformal field theory (CFT), we present the formalism necessary to obtain exact matrix product state (MPS) representations for any fractional quantum hall model state which can be written as an expectation value of primary fields in some conformal field theory. The auxiliary bond space is the Hilbert space of the descendants of primary fields and matrix elements can be calculated using well-known CFT commutation relations. We obtain a site-independent MPS representation on the thin annulus and cylinder, while a site-dependent representation is possible on the disk and sphere geometries. We discuss the complications that arise due to the presence of null vectors in the theory's Hilbert space, and present an array of procedures which optimize the numerical calculation of matrix elements. By truncating the Hilbert space of the CFT, we then build an approximate MPS representation for Laughlin, Moore-Read, Read-Rezayi, Gaffnian, minimal $M(3,r+2)$ models, and a series of superconformal minimal models. We show how to obtain, in the MPS representation, the Orbital, Particle, and Real Space entanglement spectrum in both the finite and infinite systems.

cond-mat.str-el↗

arXiv2013

Majorana fermions in chains of magnetic atoms on a superconductor

We propose an easy-to-build easy-to-detect scheme for realizing Majorana fermions at the ends of a chain of magnetic atoms on the surface of a superconductor. Model calculations show that such chains can be easily tuned between trivial and topological ground state. In the latter, spatial resolved spectroscopy can be used to probe the Majorana fermion end states. Decoupled Majorana bound states can form even in short magnetic chains consisting of only tens of atoms. We propose scanning tunneling microscopy as the ideal technique to fabricate such systems and probe their topological properties.

cond-mat.supr-con↗

arXiv2013

Matrix Product States for Trial Quantum Hall States

We obtain an exact matrix-product-state (MPS) representation of a large series of fractional quantum Hall (FQH) states in various geometries of genus 0. The states in question include all paired k=2 Jack polynomials, such as the Moore-Read and Gaffnian states, as well as the Read-Rezayi k=3 state. We also outline the procedures through which the MPS of other model FQH states can be obtained, provided their wavefunction can be written as a correlator in a 1+1 conformal field theory (CFT). The auxiliary Hilbert space of the MPS, which gives the counting of the entanglement spectrum, is then simply the Hilbert space of the underlying CFT. This formalism enlightens the link between entanglement spectrum and edge modes. Properties of model wavefunctions such as the thin-torus root partitions and squeezing are recast in the MPS form, and numerical benchmarks for the accuracy of the new MPS prescription in various geometries are provided.

cond-mat.str-el↗

arXiv2013

D-Algebra Structure of Topological Insulators

In the quantum Hall effect, the density operators at different wave-vectors generally do not commute and give rise to the Girvin MacDonald Plazmann (GMP) algebra with important consequences such as ground-state center of mass degeneracy at fractional filling fraction, and W_{1 + \infty} symmetry of the filled Landau levels. We show that the natural generalization of the GMP algebra to higher dimensional topological insulators involves the concept of a D-algebra formed by using the fully anti-symmetric tensor in D-dimensions. For insulators in even dimensional space, the D-algebra is isotropic and closes for the case of constant non-Abelian F(k) ^ F(k) ... ^ F(k) connection (D-Berry curvature), and its structure factors are proportional to the D/2-Chern number. In odd dimensions, the algebra is not isotropic, contains the weak topological insulator index (layers of the topological insulator in one less dimension) and does not contain the Chern-Simons θform (F ^ A - 2/3 A ^ A ^ A in 3 dimensions). The Chern-Simons form appears in a certain combination of the parallel transport and simple translation operator which is not an algebra. The possible relation to D-dimensional volume preserving diffeomorphisms and parallel transport of extended objects is also discussed.

cond-mat.str-el↗