arXiv subjects

Jennifer Cano

Publications and source records attributed to Jennifer Cano.

At least 91 records · Page 5Linked to original sources

arXiv2021

Staggered Pseudo Magnetic Field in Twisted Transition Metal Dichalcogenides: Physical Origin and Experimental Consequences

Strong magnetic fields profoundly affect the quantum physics of charged particles, as seen for example by the integer and fractionally quantized Hall effects, and the fractal `Hofstadter butterfly' spectrum of electrons in the presence of a periodic potential and a magnetic field. Intrinsic physics can lead to effects equivalent to those produced by an externally applied magnetic field. Examples include the `staggered flux' phases emerging in some theories of quantum spin liquids and the Chern insulator behavior of twisted bilayer graphene when valley symmetry is broken. In this paper we show that when two layers of the transition metal dichalcogenide material WSe2 are stacked at a small relative twist angle to form a Moire bilayer, the resulting low energy physics can be understood in terms of electrons moving in a strong and tunable staggered flux. We predict experimental consequences including sign reversals of the Hall coefficient on application of an interlayer potential and spin currents appearing at sample edges and interfaces.

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arXiv2021

Hartree-Fock study of the moiré Hubbard model for twisted bilayer transition metal dichalcogenides

Twisted bilayer transition metal dichalcogenides have emerged as important model systems for the investigation of correlated electron physics because their interaction strength, carrier concentration, band structure, and inversion symmetry breaking are controllable by device fabrication, twist angle, and most importantly, gate voltage, which can be varied in situ. The low energy physics of some of these materials has been shown to be described by a "moiré Hubbard model" generalized from the usual Hubbard model by the addition of strong, tunable spin orbit coupling and inversion symmetry breaking. In this work, we use a Hartree-Fock approximation to reach a comprehensive understanding of the moiré Hubbard model on the mean field level. We determine the magnetic and metal-insulator phase diagrams, and assess the effects of spin orbit coupling, inversion symmetry breaking, and the tunable van Hove singularity. We also consider the spin and orbital effects of applied magnetic fields. This work provides guidance for experiments and sets the stage for beyond mean-field calculations.

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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

Band Engineering of Dirac Semimetals using Charge Density Waves

New developments in the field of topological matter are often driven by materials discovery, including novel topological insulators, Dirac semimetals and Weyl semimetals. In the last few years, large efforts have been performed to classify all known inorganic materials with respect to their topology. Unfortunately, a large number of topological materials suffer from non-ideal band structures. For example, topological bands are frequently convoluted with trivial ones, and band structure features of interest can appear far below the Fermi level. This leaves just a handful of materials that are intensively studied. Finding strategies to design new topological materials is a solution. Here we introduce a new mechanism that is based on charge density waves and non-symmorphic symmetry to design an idealized Dirac semimetal. We then show experimentally that the antiferromagnetic compound GdSb$_{0.46}$Te$_{1.48}$ is a nearly ideal Dirac semimetal based on the proposed mechanism, meaning that most interfering bands at the Fermi level are suppressed. Its highly unusual transport behavior points to a thus far unknown regime, in which Dirac carriers with Fermi energy very close to the node seem to gradually localize in the presence of lattice and magnetic disorder.

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arXiv2021

Chiral Approximation to Twisted Bilayer Graphene: Exact Intra-Valley Inversion Symmetry, Nodal Structure and Implications for Higher Magic Angles

This paper presents a mathematical and numerical analysis of the flatband wavefunctions occurring in the chiral model of twisted bilayer graphene at the "magic" twist angles. We show that the chiral model possesses an exact intra-valley inversion symmetry. Writing the flatband wavefunction as a product of a lowest Landau level quantum Hall state and a spinor, we show that the components of the spinor are anti-quantum Hall wavefunctions related by the inversion symmetry operation introduced here. We then show numerically that as one moves from the lowest to higher magic angles, the spinor components of the wavefunction exhibit an increasing number of zeros, resembling the changes in the quantum Hall wavefunction as the Landau level index is increased. The wavefunction zeros are characterized by a chirality, with zeros of the same chirality clustering near the center of the moire unit cell, while opposite chirality zeros are pushed to the boundaries of the unit cell. The enhanced phase winding at higher magic angles suggests an increased circulating current. Physical implications for scanning tunneling spectroscopy, orbital magnetization and interaction effects are discussed.

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arXiv2021

Tunable chiral symmetry breaking in symmetric Weyl materials

Asymmetric Weyl semimetals, which possess an inherently chiral structure, have different energies and dispersion relations for left- and right-handed fermions. They exhibit certain effects not found in symmetric Weyl semimetals, such as the quantized circular photogalvanic effect and the helical magnetic effect. In this work, we derive the conditions required for breaking chiral symmetry by applying an external field in symmetric Weyl semimetals. We explicitly demonstrate that in certain materials with the $T_d$ point group, magnetic fields along low symmetry directions break the symmetry between left- and right-handed fermions; the symmetry breaking can be tuned by changing the direction and magnitude of the magnetic field. In some cases, we find an imbalance between the number of type I left- and right-handed Weyl cones (which is compensated by the number of type II cones of each chirality.)

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arXiv2021

Filling anomaly for general 2D and 3D $C_4$ symmetric lattices

In this manuscript, we derive symmetry indicator formulas for the filling anomaly on 2D square lattices with and without time reversal, inversion symmetry, or their product, in the presence of spin-orbit coupling. We go beyond previous work by considering lattices with atoms occupying multiple Wyckoff positions. We also provide an algorithm using the Smith normal form that systematizes the derivation. The formulas determine the corner charge in 2D atomic or fragile topological insulators, as well as in 3D insulators and semimetals by studying their 2D slices. We apply our results to a 3D tight-binding model on a body-centered tetragonal lattice, whose projection into the 2D plane has two atoms in the unit cell. Our symmetry indicators correctly describe the higher-order hinge states and Fermi arcs in cases where the existing indicators do not apply.

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arXiv2020

A moiré superlattice on the surface of a topological insulator

Twisting van der Waals heterostructures to induce correlated many-body states provides a novel tuning mechanism in solid-state physics. In this work, we theoretically investigate the fate of the surface Dirac cone of a three-dimensional topological insulator subject to a superlattice potential. Using a combination of diagrammatic perturbation theory, lattice model simulations, and ab initio calculations we elucidate the unique aspects of twisting a single Dirac cone with an induced moiré potential and the role of the bulk topology on the reconstructed surface band structure. We report a dramatic renormalization of the surface Dirac cone velocity as well as demonstrate a topological obstruction to the formation of isolated minibands. Due to the topological nature of the bulk, surface band gaps cannot open; instead, additional satellite Dirac cones emerge, which can be highly anisotropic and made quite flat. We discuss the implications of our findings for future experiments.

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arXiv2020

Higher-order topological insulators in antiperovskites

We predict that a family of antiperovskite materials realize a higher order topological insulator phase, characterized by a previously introduced $\mathbb{Z}_4$ index. A tight binding model and a $k\cdot p$ model are used to capture the physics of the bulk, surface and hinge states of these materials. A phase diagram of the higher order and weak topological invariants is obtained for the tight binding model. The mirror Chern number is also discussed. In order to reveal the gapless hinge states in the presence of mirror Chern surface states, several ways of opening the surface gap are proposed and confirmed by calculation, including cleaving the crystal to reveal a low-symmetry surface, building a heterostructure, and applying strain. Upon opening the surface gap, we are able to study the hinge states by computing the momentum space band structure and real space distribution of mid-gap states.

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arXiv2020

Band Representations and Topological Quantum Chemistry

In this article, we provide a pedagogical review of the theory of topological quantum chemistry and topological crystalline insulators. We begin with an overview of the properties of crystal symmetry groups in position and momentum space. Next, we introduce the concept of a band representation, which quantifies the symmetry of topologically trivial band structures. By combining band representations with symmetry constraints on the connectivity of bands in momentum space, we show how topologically nontrivial bands can be catalogued and classified. We present several examples of new topological phases discovered using this paradigm, and conclude with an outlook towards future developments.

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arXiv2020

A systematic study of stacked square nets: from Dirac fermions to material realizations

Non-symmorphic symmetries protect Dirac line nodes in square net materials. This phenomenon has been most prominently observed in ZrSiS. Here, we systematically study the symmetry-protected nodal fermions that result from different ways of embedding the square net into a larger unit cell. Surprisingly, we find that a nonsymmorphic space group is not a necessary condition for a filling enforced semimetal: symmorphic space groups can also host nodal fermions that are enforced by band folding and electron count, that is, a combination of a particular structural motif combined with electron filling. We apply the results of this symmetry analysis to define an algorithm, which we utilize to find square net materials with nodal fermions in specific symmorphic space groups. We highlight one result of this search, the compound ThGeSe, which has not been discussed before in the context of nodal fermions. Finally, we discuss how band folding can impose constraints on band connectivity beyond the connectivity of single elementary band representations.

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arXiv2020

The role of delocalized chemical bonding in square-net-based topological semimetals

Principles that predict reactions or properties of materials define the discipline of chemistry. In this work we derive chemical rules, based on atomic distances and chemical bond character, which predict topological materials in compounds that feature the structural motif of a square-net. Using these rules we identify over 300 potential new topological materials. We show that simple chemical heuristics can be a powerful tool to characterize topological matter. In contrast to previous database-driven materials categorization our approach allows us to identify candidates that are alloys, solid-solutions, or compounds with statistical vacancies. While previous material searches relied on density functional theory, our approach is not limited by this method and could also be used to discover magnetic and statistically-disordered topological semimetals.

cond-mat.mtrl-sci↗

arXiv2020

Observation of high-temperature quantum anomalous Hall regime in intrinsic MnBi$_2$Te$_4$/Bi$_2$Te$_3$ superlattice

The quantum anomalous Hall effect is a fundamental transport response of a topologically non-trivial system in zero magnetic field. Its physical origin relies on the intrinsically inverted electronic band structure and ferromagnetism, and its most consequential manifestation is the dissipation-free flow of chiral charge currents at the edges that can potentially transform future quantum electronics. Here we report a previously unknown Berry-curvature-driven anomalous Hall regime ('Q-window') at above-Kelvin temperatures in the magnetic topological bulk crystals where through growth Mn ions self-organize into a period-ordered MnBi$_2$Te$_4$/Bi$_2$Te$_3$ superlattice. Robust ferromagnetism of the MnBi$_2$Te$_4$ monolayers opens a large surface gap, and anomalous Hall conductance reaches an $e^2/h$ quantization plateau when the Fermi level is tuned into this gap within a Q-window in which the anomalous Hall conductance from the bulk is to a high precision zero. The quantization in this new regime is not obstructed by the bulk conduction channels and thus should be present in a broad family of topological magnets.

cond-mat.mtrl-sci↗

arXiv2019

Partial lattice defects in higher order topological insulators

Nonzero weak topological indices are thought to be a necessary condition to bind a single helical mode to lattice dislocations. In this work we show that higher-order topological insulators (HOTIs) can, in fact, host a single helical mode along screw or edge dislocations (including step edges) in the absence of weak topological indices. When this occurs, the helical mode is necessarily bound to a dislocation characterized by a fractional Burgers vector, macroscopically detected by the existence of a stacking fault. The robustness of a helical mode on a partial defect is demonstrated by an adiabatic transformation that restores translation symmetry in the stacking fault. We present two examples of HOTIs, one intrinsic and one extrinsic, that show helical modes at partial dislocations. Since partial defects and stacking faults are commonplace in bulk crystals, the existence of such helical modes can measurably affect the expected conductivity in these materials.

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arXiv2019

Multifold nodal points in magnetic materials

We describe the symmetry protected nodal points that can exist in magnetic space groups and show that only 3-, 6-, and 8-fold degeneracies are possible (in addition to the 2- and 4-fold degeneracies that have already been studied.) The 3- and 6-fold degeneracies are derived from "spin-1" Weyl fermions. The 8-fold degeneracies come in different flavors. In particular, we distinguish between 8-fold fermions that realize non-chiral "Rarita-Schwinger fermions" and those that can be described as four degenerate Weyl fermions. We list the (magnetic and non-magnetic) space groups where these exotic fermions can be found. We further show that in several cases, a magnetic translation symmetry pins the Hamiltonian of the multifold fermion to an idealized exactly solvable point that is not achievable in non-magnetic crystals without fine-tuning. Finally, we present known compounds that may host these fermions and methods for systematically finding more candidate materials.

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arXiv2019

Modular Arithmetic with Nodal Lines: Drumhead Surface States in ZrSiTe

We study the electronic structure of the nodal line semimetal ZrSiTe both experimentally and theoretically. We find two different surface states in ZrSiTe - topological drumhead surface states and trivial floating band surface states. Using the spectra of Wilson loops, we show that a non-trivial Berry phase that exists in a confined region within the Brillouin Zone gives rise to the topological drumhead-type surface states. The $\mathbb{Z}_2$ structure of the Berry phase induces a $\mathbb{Z}_2$ 'modular arithmetic' of the surface states, allowing surface states deriving from different nodal lines to hybridize and gap out, which can be probed by a set of Wilson loops. Our findings are confirmed by \textit{ab-initio} calculations and angle-resolved photoemission experiments, which are in excellent agreement with each other and the topological analysis. This is the first complete characterization of topological surface states in the family of square-net based nodal line semimetals and thus fundamentally increases the understanding of the topological nature of this growing class of topological semimetals.

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arXiv2019

Disconnected Elementary Band Representations, Fragile Topology, and Wilson Loops as Topological Indices: An Example on the Triangular Lattice

In this work, we examine the topological phases that can arise in triangular lattices with disconnected elementary band representations. We show that, although these phases may be "fragile" with respect to the addition of extra bands, their topological properties are manifest in certain nontrivial holonomies (Wilson loops) in the space of nontrivial bands. We introduce an eigenvalue index for fragile topology, and we show how a nontrivial value of this index manifests as the winding of a hexagonal Wilson loop; this remains true even in the absence of time-reversal or sixfold rotational symmetry. Additionally, when time-reversal and twofold rotational symmetry are present, we show directly that there is a protected nontrivial winding in more conventional Wilson loops. Crucially, we emphasize that these Wilson loops cannot change without closing a gap to the nontrivial bands. By studying the entanglement spectrum for the fragile bands, we comment on the relationship between fragile topology and the "obstructed atomic limit" of B. Bradlyn et al., Nature 547, 298--305 (2017). We conclude with some perspectives on topological matter beyond the K-theory classification.

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arXiv2018

Symmetry-Protected Topological Interfaces and Entanglement Sequences

Gapped interfaces (and boundaries) of two-dimensional (2D) Abelian topological phases are shown to support a remarkably rich sequence of 1D symmetry-protected topological (SPT) states. We show that such interfaces can provide a physical interpretation for the corrections to the topological entanglement entropy of a 2D state with Abelian topological order found in Ref.~\onlinecite{cano-2015}. The topological entanglement entropy decomposes as $γ= γ_a + γ_s$, where $γ_a > 0$ only depends on universal topological properties of the 2D state, while a correction $γ_s > 0$ signals the emergence of the 1D SPT state that is produced by interactions along the entanglement cut and provides a direct measure of the stabilizing symmetry of the resulting SPT state. A correspondence is established between the possible values of $γ_s$ associated with a given interface - which is named Boundary Topological Entanglement Sequence - and classes of 1D SPT states. We show that symmetry-preserving domain walls along such 1D interfaces (or boundaries) generally host localized parafermion-like excitations that are stable to local symmetry-preserving perturbations.

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