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B. Andrei Bernevig

Publications and source records attributed to B. Andrei Bernevig.

At least 217 records · Page 12Linked to original sources
arXiv2016

Imaging electronic states on topological semimetals using scanning tunneling microscopy

Following the intense studies on topological insulators, significant efforts have recently been devoted to the search for gapless topological systems. These materials not only broaden the topological classification of matter but also provide a condensed matter realization of various relativistic particles and phenomena previously discussed mainly in high energy physics. Weyl semimetals host massless, chiral, low-energy excitations in the bulk electronic band structure, whereas a symmetry protected pair of Weyl fermions gives rise to massless Dirac fermions. We employed scanning tunneling microscopy/spectroscopy to explore the behavior of electronic states both on the surface and in the bulk of topological semimetal phases. By mapping the quasiparticle interference and emerging Landau levels at high magnetic field in Dirac semimetals Cd$_3$As$_2$ and Na$_3$Bi, we observed extended Dirac-like bulk electronic bands. Quasiparticle interference imaged on Weyl semimetal TaAs demonstrated the predicted momentum dependent delocalization of Fermi arc surface states in the vicinity of the surface-projected Weyl nodes.

cond-mat.mtrl-sci↗
arXiv2016

MoTe2: A Type-II Weyl Topological Metal

Based on the ab initio calculations, we show that MoTe2, in its low-temperature orthorhombic structure characterized by an X-ray diffraction study at 100 K, realizes 4 type-II Weyl points between the N-th and N+1-th bands, where N is the total number of valence electrons per unit cell. Other WPs and nodal lines between different other bands also appear close to the Fermi level due to a complex topological band structure. We predict a series of strain-driven topological phase transitions in this compound, opening a wide range of possible experimental realizations of different topological semimetal phases. Crucially, with no strain, the number of observable surface Fermi arcs in this material is 2 - the smallest number of arcs consistent with time-reversal symmetry.

cond-mat.mtrl-sci↗
arXiv2016

No-Go Theorem for Boson Condensation in Topologically Ordered Quantum Liquids

Certain phase transitions between topological quantum field theories (TQFT) are driven by the condensation of bosonic anyons. However, as bosons in a TQFT are themselves nontrivial collective excitations, there can be topological obstructions that prevent them from condensing. Here we formulate such an obstruction in the form of a no-go theorem. We use it to show that no condensation is possible in SO(3)$_k$ TQFTs with odd $k$. We further show that a layered theory obtained by tensoring SO(3)$_k$ TQFT with itself any integer number of times does not admit condensation transitions either. This includes (as the case $k=3$) the noncondensability of any number of layers of the Fibonacci TQFT.

cond-mat.str-el↗
arXiv2016

Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals

In quantum field theory, we learn that fermions come in three varieties: Majorana, Weyl, and Dirac. Here we show that in solid state systems this classification is incomplete and find several additional types of crystal symmetry-protected free fermionic excitations . We exhaustively classify linear and quadratic 3-, 6- and 8- band crossings stabilized by space group symmetries in solid state systems with spin-orbit coupling and time-reversal symmetry. Several distinct types of fermions arise, differentiated by their degeneracies at and along high symmetry points, lines, and surfaces. Some notable consequences of these fermions are the presence of Fermi arcs in non-Weyl systems and the existence of Dirac lines. Ab-initio calculations identify a number of materials that realize these exotic fermions close to the Fermi level.

cond-mat.mes-hall↗
arXiv2016

Berry-phase description of Topological Crystalline Insulators

We study a class of translational-invariant insulators with discrete rotational symmetry. These insulators have no spin-orbit coupling, and in some cases have no time-reversal symmetry as well, i.e., the relevant symmetries are purely crystalline. Nevertheless, topological phases exist which are distinguished by their robust surface modes. Like many well-known topological phases, their band topology is unveiled by the crystalline analog of Berry phases, i.e., parallel transport across certain non-contractible loops in the Brillouin zone. We also identify certain topological phases without any robust surface modes -- they are uniquely distinguished by parallel transport along bent loops, whose shapes are determined by the symmetry group. Our findings have experimental implications in cold-atom systems, where the crystalline Berry phase has been directly measured.

cond-mat.other↗
arXiv2016

Hourglass Fermions

Spatial symmetries in crystals are distinguished by whether they preserve the spatial origin. We show how this basic geometric property gives rise to a new topology in band insulators. We study spatial symmetries that translate the origin by a fraction of the lattice period, and find that these nonsymmorphic symmetries protect a novel surface fermion whose dispersion is shaped like an hourglass; surface bands connect one hourglass to the next in an unbreakable zigzag pattern. These exotic fermions are materialized in the large-gap insulators: KHgX (X=As,Sb,Bi), which we propose as the first material class whose topology relies on nonsymmorphic symmetries. Beside the hourglass fermion, another surface of KHgX manifests a 3D generalization of the quantum spin Hall effect, which has only been observed in 2D crystals. To describe the bulk topology of nonsymmorphic crystals, we propose a non-Abelian generalization of the geometric theory of polarization. Our nontrivial topology originates from an inversion of the rotational quantum numbers, which we propose as a fruitful criterion in the search for topological materials.

cond-mat.mes-hall↗
arXiv2016

Topological Insulators from Group Cohomology

We classify insulators by generalized symmetries that combine space-time transformations with quasimomentum translations. Our group-cohomological classification generalizes the nonsymmorphic space groups, which extend point groups by real-space translations, i.e., nonsymmorphic symmetries unavoidably translate the spatial origin by a fraction of the lattice period. Here, we further extend nonsymmorphic groups by reciprocal translations, thus placing real and quasimomentum space on equal footing. We propose that group cohomology provides a symmetry-based classification of quasimomentum manifolds, which in turn determines the band topology. In this sense, cohomology underlies band topology. Our claim is exemplified by the first theory of time-reversal-invariant insulators with nonsymmorphic spatial symmetries. These insulators may be described as 'piecewise topological', in the sense that subtopologies describe the different high-symmetry submanifolds of the Brillouin zone, and the various subtopologies must be pieced together to form a globally consistent topology. The subtopologies that we discovered include: a glide-symmetric analog of the quantum spin Hall effect, an hourglass-flow topology (exemplified by our recently-proposed KHgSb material class), and quantized non-Abelian polarizations. Our cohomological classification results in an atypical bulk-boundary correspondence for our topological insulators.

cond-mat.mes-hall↗
arXiv2016

Modular Anomalies in (2+1) and (3+1)-D Edge Theories

The classification of topological phases of matter in the presence of interactions is an area of intense interest. One possible means of classification is via studying the partition function under modular transforms, as the presence of an anomalous phase arising in the edge theory of a D-dimensional system under modular transformation, or modular anomaly, signals the presence of a (D+1)-D non-trivial bulk. In this work, we discuss the modular transformations of conformal field theories along a (2+1)-D and a (3+1)-D edge. Using both analytical and numerical methods, we show that chiral complex free fermions in (2+1)-D and (3+1)-D are modular invariant. However, we show in (3+1)-D that when the edge theory is coupled to a background U(1) gauge field this results in the presence of a modular anomaly that is the manifestation of a quantum Hall effect in a (4+1)-D bulk. Using the modular anomaly, we find that the edge theory of (4+1)-D insulator with spacetime inversion symmetry(P*T) and fermion number parity symmetry for each spin becomes modular invariant when 8 copies of the edges exist.

cond-mat.str-el↗
arXiv2016

Quasiparticle interference of the Fermi arcs and surface-bulk connectivity of a Weyl semimetal

Weyl semimetals host topologically protected surface states, with arced Fermi surface contours that are predicted to propagate through the bulk when their momentum matches that of the surface projections of the bulk's Weyl nodes. We use spectroscopic mapping with a scanning tunneling microscope to visualize quasi-particle scattering and interference at the surface of the Weyl semimetal TaAs. Our measurements reveal 10 different scattering wave vectors, which can be understood and precisely reproduced with a theory that takes into account the shape, spin texture, and momentum-dependent propagation of the Fermi arc surface states into the bulk. Our findings provide evidence that Weyl nodes act as sinks for electron transport on the surface of these materials.

cond-mat.mes-hall↗
arXiv2016

Universal signatures of Fermi arcs in quasiparticle interference on the surface of Weyl semimetals

Weyl semimetals constitute a newly discovered class of three-dimensional topological materials with linear touchings of valence and conduction bands in the bulk. The most striking property of topological origin in these materials, so far unequivocally observed only in photoemission experiments, is the presence of open constant-energy contours at the boundary --- the so-called Fermi arcs. In this work, we establish the universal characteristics of Fermi-arc contributions to surface quasiparticle interference. Using a general phenomenological model, we determine the defining interference patterns stemming from the existence of Fermi arcs in a surface band structure. We then trace these patterns in both simple tight-binding models and realistic ab initio calculations. Our results show that definitive signatures of Fermi arcs can be observed in existing and proposed Weyl semimetals using scanning tunneling spectroscopy.

cond-mat.mes-hall↗
arXiv2016

Boson Condensation in Topologically Ordered Quantum Liquids

Boson condensation in topological quantum field theories (TQFT) has been previously investigated through the formalism of Frobenius algebras and the use of vertex lifting coefficients. While general, this formalism is physically opaque and computationally arduous: analyses of TQFT condensation are practically performed on a case by case basis and for very simple theories only, mostly not using the Frobenius algebra formalism. In this paper we provide a new way of treating boson condensation that is computationally efficient. With a minimal set of physical assumptions, such as commutativity of lifting and the definition of confined particles, we can prove a number of theorems linking Boson condensation in TQFT with chiral algebra extensions, and with the factorization of completely positive matrices over the nonnegative integers. We present numerically efficient ways of obtaining a condensed theory fusion algebra and S matrices; and we then use our formalism to prove several theorems for the S and T matrices of simple current condensation and of theories which upon condensation result in a low number of confined particles. We also show that our formalism easily reproduces results existent in the mathematical literature such as the noncondensability of 5 and 10 layers of the Fibonacci TQFT.

cond-mat.str-el↗
arXiv2015

Shiba chains of scalar impurities on unconventional superconductors

We show that a chain of nonmagnetic impurities deposited on a fully gapped two- or three-dimensional superconductor can become a topological one-dimensional superconductor with protected Majorana bound states at its end. A prerequisite is that the pairing potential of the underlying superconductor breaks the spin-rotation symmetry, as it is generically the case in systems with strong spin-orbit coupling. We illustrate this mechanism for a spinless triplet-superconductor p+ip and a time-reversal symmetric Rashba superconductor with a mixture of singlet and triplet pairing. For the latter, we show that the impurity chain can be topologically nontrivial even if the underlying superconductor is topologically trivial.

cond-mat.supr-con↗
arXiv2015

Type-II Weyl Semimetals

Fermions in nature come in several types: Dirac, Majorana and Weyl are theoretically thought to form a complete list. Even though Majorana and Weyl fermions have for decades remained experimentally elusive, condensed matter has recently emerged as fertile ground for their discovery as low energy excitations of realistic materials. Here we show the existence of yet another particle - a new type of Weyl fermion - that emerges at the boundary between electron and hole pockets in a new type of Weyl semimetal phase of matter. This fermion was missed by Weyl in 1929 due to its breaking of the stringent Lorentz symmetry of high-energy physics. Lorentz invariance however is not present in condensed matter physics, and we predict that an established material, WTe$_2$, is an example of this novel type of topological semimetal hosting the new particle as a low energy excitation around a type-2 Weyl node. This node, although still a protected crossing, has an open, finite-density of states Fermi surface, likely resulting in a plethora physical properties very different from those of standard point-like Fermi surface Weyl points.

cond-mat.mes-hall↗
arXiv2015

Detection of Majorana Kramers pairs using a quantum point contact

We propose a setup that integrates a quantum point contact (QPC) and a Josephson junction on a quantum spin Hall sample, experimentally realizable in InAs/GaSb quantum wells. The confinement due to both the QPC and the superconductor results in a Kramers pair of Majorana zero-energy bound states when the superconducting phases in the two arms differ by an odd multiple of $π$ across the Josephson junction. We investigate the detection of these Majorana pairs with the integrated QPC, and find a robust switching from normal to Andreev scattering across the edges due to the presence of Majorana Kramers pairs. This transport signature is expected to be exhibited in measurements of differential conductance and/or current cross-correlation at low bias.

cond-mat.mes-hall↗
arXiv2015

Matrix product state representation of non-Abelian quasiholes

We provide a detailed explanation of the formalism necessary to construct matrix product states for non-Abelian quasiholes in fractional quantum Hall model states. Our construction yields an efficient representation of the wave functions with conformal-block normalization and monodromy, and complements the matrix product state representation of fractional quantum Hall ground states.

cond-mat.str-el↗
arXiv2015

Parafermionic phases with symmetry-breaking and topological order

Parafermions are the simplest generalizations of Majorana fermions that realize topological order. We propose a less restrictive notion of topological order in 1D open chains, which generalizes the seminal work by Fendley [J. Stat. Mech., P11020 (2012)]. The first essential property is that the groundstates are mutually indistinguishable by local, symmetric probes, and the second is a generalized notion of zero edge modes which cyclically permute the groundstates. These two properties are shown to be topologically robust, and applicable to a wider family of topologically-ordered Hamiltonians than has been previously considered. An an application of these edge modes, we formulate a new notion of twisted boundary conditions on a closed chain, which guarantees that the closed-chain groundstate is topological, i.e., it originates from the topological manifold of degenerate states on the open chain. Finally, we generalize these ideas to describe symmetry-breaking phases with a parafermionic order parameter. These exotic phases are condensates of parafermion multiplets, which generalizes Cooper pairing in superconductors. The stability of these condensates are investigated on both open and closed chains.

cond-mat.str-el↗
arXiv2015

Projective construction of the $\mathbb{Z}_k$ Read-Rezayi fractional quantum Hall states and their excitations on the torus geometry

Multilayer fractional quantum Hall wave functions can be used to construct the non-Abelian states of the $\mathbb{Z}_k$ Read-Rezayi series upon symmetrization over the layer index. Unfortunately, this construction does not yield the complete set of $\mathbb{Z}_k$ ground states on the torus. We develop an alternative projective construction of $\mathbb{Z}_k$ Read-Rezayi states that complements the existing one. On the multi-layer torus geometry, our construction consists of introducing twisted boundary conditions connecting the layers before performing the symmetrization. We give a comprehensive account of this construction for bosonic states, and numerically show that the full ground state and quasihole manifolds are recovered for all computationally accessible system sizes. Furthermore, we analyze the neutral excitation modes above the Moore-Read on the torus through an extensive exact diagonalization study. We show numerically that our construction can be used to obtain excellent approximations to these modes. Finally, we extend the new symmetrization scheme to the plane and sphere geometries.

cond-mat.str-el↗