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  • 1. A. Madsen, Kevin
    et al.
    J. Bergholtz, Emil
    Stockholm University, Faculty of Science, Department of Physics.
    Brouwer, Piet W.
    Josephson effect in a Weyl SNS junction2017In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 95, no 6, article id 064511Article in journal (Refereed)
    Abstract [en]

    We calculate the Josephson current density j (phi) for a Weyl superconductor-normal-metal-superconductor junction for which the outer terminals are superconducting Weylmetals and the normal layer is a Weyl (semi) metal. We describe the Weyl (semi) metal using a simple model with two Weyl points. The model has broken time-reversal symmetry, but inversion symmetry is present. We calculate the Josephson current for both zero and finite temperature for the two pairing mechanisms inside the superconductors that have been proposed in the literature, zero-momentum BCS-like pairing and finite-momentum FFLO-like pairing, and assuming the short-junction limit. For both pairing types we find that the current is proportional to the normal-state junction conductivity, with a proportionality coefficient that shows quantitative differences between the two pairing mechanisms. The current for the BCS-like pairing is found to be independent of the chemical potential, whereas the current for the FFLO-like pairing is not.

  • 2.
    Bergholtz, Emil Johansson
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Hansson, Thors Hans
    Stockholm University, Faculty of Science, Department of Physics.
    Hermanns, Maria
    Stockholm University, Faculty of Science, Department of Physics.
    Karlhede, Anders
    Stockholm University, Faculty of Science, Department of Physics.
    Viefers, Susanne
    Quantum Hall hierarchy wave functions: From conformal correlators to Tao-Thouless states2008In: Physical Review B Condensed Matter, ISSN 0163-1829, E-ISSN 1095-3795, Vol. 77, no 16, p. 165325-1-165325-9Article in journal (Refereed)
    Abstract [en]

    Laughlin’s wave functions, which describe the fractional quantum Hall effect at filling factorsν=1/(2k+1), can be obtained as correlation functions in a conformal field theory, and recently, this construction was extended to Jain’s composite fermion wave functions at filling factors ν=n/(2kn+1). Here, we generalize this latter construction and present ground state wave functions for all quantum Hall hierarchy states that are obtained by successive condensation of quasielectrons (as opposed to quasiholes) in the original hierarchy construction. By considering these wave functions on a cylinder, we show that they approach the exact ground states, which are the Tao-Thouless states, when the cylinder becomes thin. We also present wave functions for the multihole states, make the connection to Wen’s general classification of Abelian quantum Hall fluids, and discuss whether the fractional statistics of the quasiparticles can be analytically determined. Finally, we discuss to what extent our wave functions can be described in the language of composite fermions.

  • 3. Budich, Jan Carl
    et al.
    Carlström, Johan
    Stockholm University, Faculty of Science, Department of Physics.
    Kunst, Flore K.
    Stockholm University, Faculty of Science, Department of Physics.
    Bergholtz, Emil J.
    Stockholm University, Faculty of Science, Department of Physics.
    Symmetry-protected nodal phases in non-Hermitian systems2019In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 99, no 4, article id 041406Article in journal (Refereed)
    Abstract [en]

    Non-Hermitian (NH) Hamiltonians have become an important asset for the effective description of various physical systems that are subject to dissipation. Motivated by recent experimental progress on realizing the NH counterparts of gapless phases such as Weyl semimetals, here we investigate how NH symmetries affect the occurrence of exceptional points (EPs), that generalize the notion of nodal points in the spectrum beyond the Hermitian realm. Remarkably, we find that the dimension of the manifold of EPs is generically increased by one as compared to the case without symmetry. This leads to nodal surfaces formed by EPs that are stable as long as a protecting symmetry is preserved, and that are connected by open Fermi volumes. We illustrate our findings with analytically solvable two-band lattice models in one and two spatial dimensions, and show how they are readily generalized to generic NH crystalline systems.

  • 4.
    Carlström, Johan
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Bergholt, Emil J.
    Stockholm University, Faculty of Science, Department of Physics.
    Strongly interacting Weyl semimetals: Stability of the semimetallic phase and emergence of almost free fermions2018In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 98, no 24, article id 241102Article in journal (Refereed)
    Abstract [en]

    Using a combination of analytical arguments and state-of-the-art diagrammatic Monte Carlo simulations, we show that the corrections to the dispersion in interacting Weyl semimetals are determined by the ultraviolet cutoff and the inverse screening length. If both of these are finite, then the diagrammatic series is convergent even in the low-temperature limit, which implies that the semimetallic phase remains stable. Meanwhile, the absence of a UV cutoff or screening results in logarithmic divergences at zero temperature. These results highlight the crucial impact of Coulomb interactions and screening, mediated, e.g., through the presence of parasitic bands, which are ubiquitous effects in real-world materials. Also, despite sizable corrections from Coulomb forces, the contribution from the frequency-dependent part of the self-energy remains extremely small, thus giving rise to a system of effectively almost free fermions with a strongly renormalized dispersion.

  • 5.
    Carlström, Johan
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Bergholtz, Emil J.
    Stockholm University, Faculty of Science, Department of Physics.
    Exceptional links and twisted Fermi ribbons in non-Hermitian systems2018In: Physical Review A: covering atomic, molecular, and optical physics and quantum information, ISSN 2469-9926, E-ISSN 2469-9934, Vol. 98, no 4, article id 042114Article in journal (Refereed)
    Abstract [en]

    The generic nature of band touching points in three-dimensional band structures is at the heart of the rich phenomenology, topological stability, and novel Fermi arc surface states associated with Weyl semimetals. Here we report on the corresponding scenario emerging in systems effectively described by non-Hermitian Hamiltonians. Remarkably, three-dimensional non-Hermitian systems have generic band touching along one-dimensional closed contours, forming exceptional rings and links in reciprocal space. The associated Seifert surfaces support open Fermi ribbons where the real part of the energy gap vanishes, providing a novel class of higher-dimensional bulk generalizations of Fermi arcs which are characterized by an integer twist number. These results have possible applications to a plethora of physical settings, ranging from mechanical systems and optical metamaterials with loss and gain to heavy fermion materials with finite-lifetime quasiparticles. In particular, photonic crystals provide fertile ground for simulating the exuberant phenomenology of exceptional links and their concomitant Fermi ribbons.

  • 6.
    Carlström, Johan
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Bergholtz, Emil J.
    Stockholm University, Faculty of Science, Department of Physics.
    Symmetry-enforced stability of interacting Weyl and Dirac semimetals2018In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 97, no 16, article id 161102Article in journal (Refereed)
    Abstract [en]

    The nodal and effectively relativistic dispersion featuring in a range of novel materials including two-dimensional graphene and three-dimensional Dirac and Weyl semimetals has attracted enormous interest during the past decade. Here, by studying the structure and symmetry of the diagrammatic expansion, we show that these nodal touching points are in fact perturbatively stable to all orders with respect to generic two-body interactions. For effective low-energy theories relevant for single and multilayer graphene, type-I and type-II Weyl and Dirac semimetals, as well as Weyl points with higher topological charge, this stability is shown to be a direct consequence of a spatial symmetry that anticommutes with the effective Hamiltonian while leaving the interaction invariant. A more refined argument is applied to the honeycomb lattice model of graphene showing that its Dirac points are also perturbatively stable to all orders. We also give examples of nodal Hamiltonians that acquire a gap from interactions as a consequence of symmetries different from those of Weyl and Dirac materials.

  • 7.
    Carlström, Johan
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Stålhammar, Marcus
    Stockholm University, Faculty of Science, Department of Physics.
    Budich, Jan Carl
    Bergholtz, Emil J.
    Stockholm University, Faculty of Science, Department of Physics.
    Knotted non-Hermitian metals2019In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 99, no 16, article id 161115Article in journal (Refereed)
    Abstract [en]

    We report on the occurrence of knotted metallic band structures as stable topological phases in non-Hermitian (NH) systems. These knotted NH metals are characterized by open Fermi surfaces, known in mathematics as Seifert surfaces, that are bounded by knotted lines of exceptional points. Quite remarkably, and in contrast to the situation in Hermitian systems, no fine tuning or symmetries are required in order to stabilize these exotic phases of matter. By explicit construction, we derive microscopic tight-binding models hosting knotted NH metals with strictly short-ranged hopping, and investigate the stability of their topological properties against perturbations. Building up on recently developed experimental techniques for the realization of NH band structures, we discuss how the proposed models may be experimentally implemented in photonic systems.

  • 8.
    Edvardsson, Elisabet
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Kunst, Flore K.
    Stockholm University, Faculty of Science, Department of Physics.
    Bergholtz, Emil J.
    Stockholm University, Faculty of Science, Department of Physics.
    Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence2019In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 99, no 8, article id 081302Article in journal (Refereed)
    Abstract [en]

    Non-Hermitian Hamiltonians, which describe a wide range of dissipative systems, and higher-order topological phases, which exhibit novel boundary states on corners and hinges, comprise two areas of intense current research. Here we investigate systems where these frontiers merge and formulate a generalized biorthogonal bulk-boundary correspondence, which dictates the appearance of boundary modes at parameter values that are, in general, radically different from those that mark phase transitions in periodic systems. By analyzing the interplay between corner/hinge, edge/surface and bulk degrees of freedom we establish that the non-Hermitian extensions of higher-order topological phases exhibit an even richer phenomenology than their Hermitian counterparts and that this can be understood in a unifying way within our biorthogonal framework. Saliently this works in the presence of the non-Hermitian skin effect, and also naturally encompasses genuinely non-Hermitian phenomena in the absence thereof.

  • 9.
    El Hassan, Ashraf
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Kunst, Flore K.
    Stockholm University, Faculty of Science, Department of Physics.
    Moritz, Alexander
    Stockholm University, Faculty of Science, Department of Physics.
    Andler, Guillermo
    Stockholm University, Faculty of Science, Department of Physics.
    Bergholtz, Emil J.
    Stockholm University, Faculty of Science, Department of Physics.
    Bourennane, Mohamed
    Stockholm University, Faculty of Science, Department of Physics.
    Corner states of light in photonic waveguides2019In: Nature Photonics, ISSN 1749-4885, E-ISSN 1749-4893, Vol. 13, no 10, p. 697-700Article in journal (Refereed)
    Abstract [en]

    The recently established paradigm of higher-order topological states of matter has shown that not only edge and surface states(1,2) but also states localized to corners, can have robust and exotic properties(3-9). Here we report on the experimental realization of novel corner states made out of visible light in three-dimensional photonic structures inscribed in glass samples using femtosecond laser technology(10,11). By creating and analysing waveguide arrays, which form two-dimensional breathing kagome lattices in various sample geometries, we establish this as a platform for corner states exhibiting a remarkable degree of flexibility and control. In each sample geometry we measure eigenmodes that are localized at the corners in a finite frequency range, in complete analogy with a theoretical model of the breathing kagome(7-9,12-14). Here, measurements reveal that light can be 'fractionalized,' corresponding to simultaneous localization to each corner of a triangular sample, even in the presence of defects.

  • 10. Ferreiros, Yago
    et al.
    Kedem, Yaron
    Stockholm University, Faculty of Science, Department of Physics.
    Bergholtz, Emil J.
    Stockholm University, Faculty of Science, Department of Physics.
    Bardarson, Jens H.
    Mixed Axial-Torsional Anomaly in Weyl Semimetals2019In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 122, no 5, article id 056601Article in journal (Refereed)
    Abstract [en]

    We show that Weyl semimetals exhibit a mixed axial-torsional anomaly in the presence of axial torsion, a concept exclusive of these materials with no known natural fundamental interpretation in terms of the geometry of spacetime. This anomaly implies a nonconservation of the axial current-the difference in the current of left- and right-handed chiral fermions-when the torsion of the spacetime in which the Weyl fermions move couples with opposite sign to different chiralities. The anomaly is activated by driving transverse sound waves through a Weyl semimetal with a spatially varying tilted dispersion, which can be engineered by applying strain. This leads to a sizable alternating current in the presence of a magnetic field that provides a clear-cut experimental signature of our predictions.

  • 11.
    Hermanns, Maria
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Suorsa, Juha
    Bergholtz, Emil Johansson
    Stockholm University, Faculty of Science, Department of Physics.
    Hansson, Thors Hans
    Karlhede, Anders
    Stockholm University, Faculty of Science, Department of Physics.
    Quantum Hall wave functions on the torus2008In: Physical Review B Condensed Matter, ISSN 0163-1829, E-ISSN 1095-3795, Vol. 77, no 12, p. 125321-1-125321-16Article in journal (Refereed)
    Abstract [en]

    We present explicit expressions for a large set of hierarchy wave functions on the torus. Included are the Laughlin states, the states in the positive Jain series, and recently observed states at, e.g., ν=4∕11. The techniques we use constitute a nontrivial extension of the conformal field theory methods developed earlier to construct the corresponding wave functions in disk geometry.

  • 12.
    Kunst, Flore K.
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Edvardsson, Elisabet
    Stockholm University, Faculty of Science, Department of Physics.
    Budich, Jan Carl
    Bergholtz, Emil J.
    Stockholm University, Faculty of Science, Department of Physics.
    Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems2018In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 121, no 2, article id 026808Article in journal (Refereed)
    Abstract [en]

    Non-Hermitian systems exhibit striking exceptions from the paradigmatic bulk-boundary correspondence, including the failure of bulk Bloch band invariants in predicting boundary states and the (dis) appearance of boundary states at parameter values far from those corresponding to gap closings in periodic systems without boundaries. Here, we provide a comprehensive framework to unravel this disparity based on the notion of biorthogonal quantum mechanics: While the properties of the left and right eigenstates corresponding to boundary modes are individually decoupled from the bulk physics in non-Hermitian systems, their combined biorthogonal density penetrates the bulk precisely when phase transitions occur. This leads to generalized bulk-boundary correspondence and a quantized biorthogonal polarization that is formulated directly in systems with open boundaries. We illustrate our general insights by deriving the phase diagram for several microscopic open boundary models, including exactly solvable non-Hermitian extensions of the Su-Schrieffer-Heeger model and Chern insulators.

  • 13.
    Kunst, Flore K.
    et al.
    Stockholm University, Faculty of Science, Department of Physics. Freie Universität Berlin, Germany.
    Trescher, Maximilian
    Bergholtz, Emil J.
    Stockholm University, Faculty of Science, Department of Physics. Freie Universität Berlin, Germany.
    Anatomy of topological surface states: Exact solutions from destructive interference on frustrated lattices2017In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 96, no 8, article id 085443Article in journal (Refereed)
    Abstract [en]

    The hallmark of topological phases is their robust boundary signature whose intriguing properties-such as the one-way transport on the chiral edge of a Chern insulator and the sudden disappearance of surface states forming open Fermi arcs on the surfaces of Weyl semimetals-are impossible to realize on the surface alone. Yet, despite the glaring simplicity of noninteracting topological bulk Hamiltonians and their concomitant energy spectrum, the detailed study of the corresponding surface states has essentially been restricted to numerical simulation. In this work, however, we show that exact analytical solutions of both topological and trivial surface states can be obtained for generic tight-binding models on a large class of geometrically frustrated lattices in any dimension without the need for fine-tuning of hopping amplitudes. Our solutions derive from local constraints tantamount to destructive interference between neighboring layer lattices perpendicular to the surface and provide microscopic insights into the structure of the surface states that enable analytical calculation of many desired properties including correlation functions, surface dispersion, Berry curvature, and the system size dependent gap closing, which necessarily occurs when the spatial localization switches surface. This further provides a deepened understanding of the bulkboundary correspondence. We illustrate our general findings on a large number of examples in two and three spatial dimensions. Notably, we derive exact chiral Chern insulator edge states on the spin-orbit-coupled kagome lattice, and Fermi arcs relevant for recently synthesized slabs of pyrochlore-based Eu2Ir2O7 and Nd2Ir2O7, which realize an all-in-all-out spin configuration, as well as for spin-ice-like two-in-two-out and one-in-three-out configurations, which are both relevant for Pr2Ir2O7. Remarkably, each of the pyrochlore examples exhibit clearly resolved Fermi arcs although only the one-in-three-out configuration features bulk Weyl nodes in realistic parameter regimes. Our approach generalizes to symmetry protected phases, e.g., quantum spin Hall systems and Dirac semimetals with time-reversal symmetry, and can furthermore signal the absence of topological surface states, which we illustrate for a class of models akin to the trivial surface of Hourglass materials KHgX where the exact solutions apply but, independently of Hamiltonian details, yield eigenstates delocalized over the entire sample.

  • 14.
    Kunst, Flore K.
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    van Miert, Guido
    Bergholtz, Emil J.
    Stockholm University, Faculty of Science, Department of Physics.
    Boundaries of boundaries: A systematic approach to lattice models with solvable boundary states of arbitrary codimension2019In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 99, no 8, article id 085426Article in journal (Refereed)
    Abstract [en]

    We present a generic and systematic approach for constructing D−dimensional lattice models with exactly solvable d−dimensional boundary states localized to corners, edges, hinges, and surfaces. These solvable models represent a class of “sweet spots” in the space of possible tight-binding models—the exact solutions remain valid for any tight-binding parameters as long as they obey simple locality conditions that are manifest in the underlying lattice structure. Consequently, our models capture the physics of both (higher order) topological and nontopological phases as well as the transitions between them in a particularly illuminating and transparent manner.

  • 15.
    Kunst, Flore K.
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    van Miert, Guido
    Bergholtz, Emil J.
    Stockholm University, Faculty of Science, Department of Physics.
    Extended Bloch theorem for topological lattice models with open boundaries2019In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 99, no 8, article id 085427Article in journal (Refereed)
    Abstract [en]

    While the Bloch spectrum of translationally invariant noninteracting lattice models is trivially obtained by a Fourier transformation, diagonalizing the same problem in the presence of open boundary conditions is typically only possible numerically or in idealized limits. Here we present exact analytic solutions for the boundary states in a number of lattice models of current interest, including nodal-line semimetals on a hyperhoneycomb lattice, spin-orbit coupled graphene, and three-dimensional topological insulators on a diamond lattice, for which no previous exact finite-size solutions are available in the literature. Furthermore, we identify spectral mirror symmetry as the key criterium for analytically obtaining the entire (bulk and boundary) spectrum as well as the concomitant eigenstates, and exemplify this for Chern and Z2 insulators with open boundaries of codimension one. In the case of the two-dimensional Lieb lattice, we extend this further and show how to analytically obtain the entire spectrum in the presence of open boundaries in both directions, where it has a clear interpretation in terms of bulk, edge, and corner states.

  • 16.
    Kunst, Flore K.
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    van Miert, Guido
    Bergholtz, Emil J.
    Stockholm University, Faculty of Science, Department of Physics.
    Lattice models with exactly solvable topological hinge and corner states2018In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 97, no 24, article id 241405Article in journal (Refereed)
    Abstract [en]

    We devise a generic recipe for constructing D-dimensional lattice models whose d-dimensional boundary states, located on surfaces, hinges, corners, and so forth, can be obtained exactly. The solvability is rooted in the underlying lattice structure and as such does not depend on fine tuning, allowing us to track their evolution throughout various phases and across phase transitions. Most saliently, our models provide boundary solvable examples of the recently introduced higher-order topological phases. We apply our general approach to breathing and anisotropic kagome and pyrochlore lattices for which we obtain exact corner eigenstates, and to periodically driven two-dimensional models as well as to three-dimensional lattices where we present exact solutions corresponding to one-dimensional chiral states at the hinges of the lattice. We relate the higher-order topological nature of these models to reflection symmetries in combination with their provenance from lower-dimensional conventional topological phases.

  • 17. Liu, Zhao
    et al.
    Bergholtz, Emil J.
    Stockholm University, Faculty of Science, Department of Physics.
    Fractional quantum Hall states with gapped boundaries in an extreme lattice limit2019In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 99, no 19, article id 195122Article in journal (Refereed)
    Abstract [en]

    We present a detailed microscopic investigation of fractional quantum Hall states with gapped boundaries in a coupled bilayer lattice model featuring holes whose counterpropagating chiral edge states are hybridized and gapped out. We focus on an lattice limit for cold-atom experiments, in which each hole just consists of a single removed site. Although the holes distort the original band structure and lead to in-gap remnants of the continuum edge modes, we find that the lowest nearly flat band representing a higher-genus system may naturally form by controlling the local hopping terms that gap out the boundaries. Remarkably, local interactions in this new flat band lead to various Abelian and non-Abelian fractional quantum Hall states with gapped boundaries residing on emergent higher-genus surfaces, which we identify by extracting the nontrivial topological ground-state degeneracies and the fractional statistics of quasiparticles. These results demonstrate the feasibility of realizing novel fractional quantum Hall states with gapped boundaries even in the extreme lattice limit, thus enabling a possible new route towards universal topological quantum computation.

  • 18. Liu, Zhao
    et al.
    Bergholtz, Emil J.
    Stockholm University, Faculty of Science, Department of Physics.
    Romito, Alessandro
    Meidan, Dganit
    Interacting Majorana chain: Transport properties and signatures of an emergent two-dimensional weak topological phase2017In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 96, no 20, article id 205442Article in journal (Refereed)
    Abstract [en]

    We study a one-dimensional chain of 2N Majorana bound states, which interact through a local quartic interaction. This model describes for example the edge physics of a quasi-one-dimensional (1D) stack of 2N Kitaev chains with modified time-reversal symmetry T gamma iT-1 = gamma(i), which precludes the presence of quadratic coupling. The ground state of our 1D Majorana chain displays a fourfold periodicity in N, corresponding to the four distinct topological classes of the stacked Kitaev chains. We analyze the transport properties of the 1D Majorana chain, when probed by local conductors located at its ends. We find that for finite but large N, the scattering matrix partially reflects the fourfold periodicity, and the chain exhibits strikingly different transport properties for different chain lengths. In the thermodynamic limit, the 1D Majorana chain hosts a robust many-body zero mode, which indicates that the corresponding stacked two-dimensional bulk system realizes a weak topological phase.

  • 19. Liu, Zhao
    et al.
    Möller, Gunnar
    Bergholtz, Emil J.
    Stockholm University, Faculty of Science, Department of Physics.
    Exotic Non-Abelian Topological Defects in Lattice Fractional Quantum Hall States2017In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 119, no 10, article id 106801Article in journal (Refereed)
    Abstract [en]

    We investigate extrinsic wormholelike twist defects that effectively increase the genus of space in lattice versions of multicomponent fractional quantum Hall systems. Although the original band structure is distorted by these defects, leading to localized midgap states, we find that a new lowest flat band representing a higher genus system can be engineered by tuning local single-particle potentials. Remarkably, once local many-body interactions in this new band are switched on, we identify various Abelian and non-Abelian fractional quantum Hall states, whose ground-state degeneracy increases with the number of defects, i.e, with the genus of space. This sensitivity of topological degeneracy to defects provides a "proof of concept" demonstration that genons, predicted by topological field theory as exotic non-Abelian defects tied to a varying topology of space, do exist in realistic microscopic models. Specifically, our results indicate that genons could be created in the laboratory by combining the physics of artificial gauge fields in cold atom systems with already existing holographic beam shaping methods for creating twist defects.

  • 20.
    Mohamed El Hassan, Ashraf
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Kunst, Flore
    Stockholm University, Faculty of Science, Department of Physics.
    Moritz, Alexander
    Stockholm University, Faculty of Science, Department of Physics.
    Andler, Guillermo
    Stockholm University, Faculty of Science, Department of Physics.
    Bergholtz, Emil
    Stockholm University, Faculty of Science, Department of Physics.
    Bourennane, Mohamed
    Stockholm University, Faculty of Science, Department of Physics.
    Corner state of light in photonic waveguides2018In: Article in journal (Refereed)
  • 21. Nietner, A.
    et al.
    Krumnow, C.
    Johansson Bergholtz, Emil
    Stockholm University, Faculty of Science, Department of Physics. Freie Universität Berlin, Germany.
    Eisert, J.
    Composite symmetry-protected topological order and effective models2017In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 96, no 23, article id 235138Article in journal (Refereed)
    Abstract [en]

    Strongly correlated quantum many-body systems at low dimension exhibit a wealth of phenomena, ranging from features of geometric frustration to signatures of symmetry-protected topological order. In suitable descriptions of such systems, it can be helpful to resort to effective models, which focus on the essential degrees of freedom of the given model. In this work, we analyze how to determine the validity of an effective model by demanding it to be in the same phase as the original model. We focus our study on one-dimensional spin-1/2 systems and explain how nontrivial symmetry-protected topologically ordered (SPT) phases of an effective spin-1 model can arise depending on the couplings in the original Hamiltonian. In this analysis, tensor network methods feature in two ways: on the one hand, we make use of recent techniques for the classification of SPT phases using matrix product states in order to identify the phases in the effective model with those in the underlying physical system, employing Kunneth's theorem for cohomology. As an intuitive paradigmatic model we exemplify the developed methodology by investigating the bilayered Delta chain. For strong ferromagnetic interlayer couplings, we find the system to transit into exactly the same phase as an effective spin-1 model. However, for weak but finite coupling strength, we identify a symmetry broken phase differing from this effective spin-1 description. On the other hand, we underpin our argument with a numerical analysis making use of matrix product states.

  • 22. Sbierski, Bjoern
    et al.
    Trescher, Maximilian
    Bergholtz, Emil J.
    Stockholm University, Faculty of Science, Department of Physics. Freie Universität Berlin, Germany.
    Brouwer, Piet W.
    Disordered doubleWeyl node: Comparison of transport and density of states calculations2017In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 95, no 11, article id 115104Article in journal (Refereed)
    Abstract [en]

    Double Weyl nodes are topologically protected band crossing points which carry chiral charge +/- 2. They are stabilized by C-4 point-group symmetry and are predicted to occur in SrSi2 or HgCr2Se4. We study their stability and physical properties in the presence of a disorder potential. We investigate the density of states and the quantum transport properties at the nodal point. We find that, in contrast to their counterparts with unit chiral charge, double Weyl nodes are unstable to any finite amount of disorder and give rise to a diffusive phase, in agreement with the predictions of Goswami and Nevidomskyy [Phys. Rev. B 92, 214504 (2015)] and Bera, Sau, and Roy [Phys. Rev. B 93, 201302 (2016)]. However, for finite system sizes a crossover between pseudodiffusive and diffusive quantum transport can be observed.

  • 23.
    Stålhammar, Marcus
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Rødland, Lukas
    Arone, Gregory
    Stockholm University, Faculty of Science, Department of Mathematics.
    Budich, Jan Carl
    Bergholtz, Emil J.
    Stockholm University, Faculty of Science, Department of Physics.
    Hyperbolic nodal band structures and knot invariants2019In: SciPost Physics, E-ISSN 2542-4653, Vol. 7, no 2, article id 019Article in journal (Refereed)
    Abstract [en]

    We extend the list of known band structure topologies to include a large family of hyperbolic nodal links and knots, occurring both in conventional Hermitian systems where their stability relies on discrete symmetries, and in the dissipative non-Hermitian realm where the knotted nodal lines are generic and thus stable towards any small perturbation. We show that these nodal structures, taking the forms of Turk's head knots, appear in both continuum- and lattice models with relatively short-ranged hopping that is within experimental reach. To determine the topology of the nodal structures, we devise an efficient algorithm for computing the Alexander polynomial, linking numbers and higher order Milnor invariants based on an approximate and well controlled parameterisation of the knot.

  • 24. Trescher, Maximilian
    et al.
    Bergholtz, Emil J.
    Stockholm University, Faculty of Science, Department of Physics.
    Knolle, Johannes
    Quantum oscillations and magnetoresistance in type-II Weyl semimetals: Effect of a field-induced charge density wave2018In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 98, no 12, article id 125304Article in journal (Refereed)
    Abstract [en]

    Recent experiments on type-II Weyl semimetals such as WTe2 , MoTe2 , MoxW1-xTe2 , and WP2 reveal remarkable transport properties in the presence of a strong magnetic field, including an extremely large magnetoresistance and an unusual temperature dependence. Here, we investigate magnetotransport via the Kubo formula in a minimal model of a type-II Weyl semimetal taking into account the effect of a charge density wave (CDW) transition, which can arise even at weak coupling in the presence of a strong magnetic field because of the special Landau level dispersion of type-II Weyl systems. Consistent with experimental measurements we find an extremely large magnetoresistance with close to B-2 scaling at particle-hole compensation, while in the extreme quantum limit there is a transition to a qualitatively new scaling with approximately B-0.75 . We also investigate the Shubnikov-de Haas effect and find that the amplitude of the resistivity quantum oscillations are greatly enhanced below the CDW transition temperature which is accompanied by an unusual nonmonotonous (non-Lifshitz-Kosevich) temperature dependence.

  • 25. Trescher, Maximilian
    et al.
    Bergholtz, Emil J.
    Stockholm University, Faculty of Science, Department of Physics.
    Udagawa, Masafumi
    Knolle, Johannes
    Charge density wave instabilities of type-II Weyl semimetals in a strong magnetic field2017In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 96, no 20, article id 201101Article in journal (Refereed)
    Abstract [en]

    Shortly after the discovery of Weyl semimetals, properties related to the topology of their bulk band structure have been observed, e.g., signatures of the chiral anomaly and Fermi arc surface states. These essentially single particle phenomena are well understood, but whether interesting many-body effects due to interactions arise in Weyl systems remains much less explored. Here, we investigate the effect of interactions in a microscopic model of a type-II Weyl semimetal in a strong magnetic field. We identify a charge density wave (CDW) instability even for weak interactions stemming from the emergent nesting properties of the type-II Weyl Landau level dispersion. We map out the dependence of this CDW on magnetic field strength. Remarkably, as a function of decreasing temperature, a cascade of CDW transitions emerges and we predict characteristic signatures for experiments.

  • 26. Trescher, Maximilian
    et al.
    Sbierski, Björn
    Brouwer, Piet W.
    J. Bergholtz, Emil
    Stockholm University, Faculty of Science, Department of Physics. Freie Universität Berlin, Germany.
    Tilted disordered Weyl semimetals2017In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 95, no 4, p. 1-8, article id 045139Article in journal (Refereed)
    Abstract [en]

    Although Lorentz invariance forbids the presence of a term that tilts the energy-momentum relation in the Weyl Hamiltonian, a tilted dispersion is not forbidden and, in fact, generic for condensed matter realizations of Weyl semimetals. We here investigate the combined effect of such a tilted Weyl dispersion and the presence of potential disorder. In particular, we address the influence of a tilt on the disorder-induced phase transition between a quasiballistic phase at weak disorder, in which the disorder is an irrelevant perturbation, and a diffusive phase at strong disorder. Our main result is that the presence of a tilt leads to a reduction of the critical disorder strength for this transition or, equivalently, that increasing the tilt at fixed disorder strength drives the system through the phase transition to the diffusive strong-disorder phase. Notably this obscures the tilt-induced Lifshitz transition to an overtilted type II Weyl phase at any finite disorder strength. Our results are supported by analytical calculations using the self-consistent Born approximation and numerical calculations of the density of states and of transport properties.

  • 27. Udagawa, M.
    et al.
    Bergholtz, Emil J.
    Stockholm University, Faculty of Science, Department of Physics. Freie Universität Berlin, Germany.
    Field-Selective Anomaly and Chiral Mode Reversal in Type-II Weyl Materials2016In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 117, no 8, article id 086401Article in journal (Refereed)
    Abstract [en]

    Three-dimensional condensed matter incarnations of Weyl fermions generically have a tilted dispersion-in sharp contrast to their elusive high-energy relatives where a tilt is forbidden by Lorentz invariance, and with the low-energy excitations of two-dimensional graphene sheets where a tilt is forbidden by either crystalline or particle-hole symmetry. Very recently, a number of materials (MoTe2, LaAlGe, and WTe2) have been identified as hosts of so-called type-IIWeyl fermions whose dispersion is so strongly tilted that a Fermi surface is formed, whereby the Weyl node becomes a singular point connecting electron and hole pockets. We here predict that these systems have remarkable properties in the presence of magnetic fields. Most saliently, we show that the nature of the chiral anomaly depends crucially on the relative angle between the applied field and the tilt, and that an inversion-asymmetric overtilting creates an imbalance in the number of chiral modes with positive and negative slopes. The field-selective anomaly gives a novel magneto-optical resonance, providing an experimental way to detect concealed Weyl nodes.

  • 28.
    Åsman, Barbro
    et al.
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Bendtz, Katarina
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Bohm, Christian
    Stockholm University, Faculty of Science, Department of Physics.
    Clément, Christophe
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Eriksson, Daniel
    Stockholm University, Faculty of Science, Department of Physics.
    Gellerstedt, Karl
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Hellman, Sten
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Holmgren, Sven-Olof
    Stockholm University, Faculty of Science, Department of Physics.
    Johansen, Marianne
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Johansson, K. Emil
    Stockholm University, Faculty of Science, Department of Physics.
    Jon-And, Kerstin
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Khandanyan, Hovhannes
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Kim, Hyeon
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Klimek, Pawel
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Lundberg, Johan
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Lundberg, Olof
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Milstead, David A.
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Moa, Torbjörn
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Papadelis, Aras
    Stockholm University, Faculty of Science, Department of Physics.
    Sellden, Björn
    Stockholm University, Faculty of Science, Department of Physics.
    Silverstein, Samuel B.
    Stockholm University, Faculty of Science, Department of Physics.
    Sjölin, Jörgen
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Strandberg, Sara
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Tylmad, Maja
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Yang, Zhaoyu
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    A Particle Consistent with the Higgs Boson Observed with the ATLAS Detector at the Large Hadron Collider2012In: Science, ISSN 0036-8075, E-ISSN 1095-9203, Vol. 338, no 6114, p. 1576-1582Article in journal (Refereed)
    Abstract [en]

    Nearly 50 years ago, theoretical physicists proposed that a field permeates the universe and gives energy to the vacuum. This field was required to explain why some, but not all, fundamental particles have mass. Numerous precision measurements during recent decades have provided indirect support for the existence of this field, but one crucial prediction of this theory has remained unconfirmed despite 30 years of experimental searches: the existence of a massive particle, the standard model Higgs boson. The ATLAS experiment at the Large Hadron Collider at CERN has now observed the production of a new particle with a mass of 126 giga-electron volts and decay signatures consistent with those expected for the Higgs particle. This result is strong support for the standard model of particle physics, including the presence of this vacuum field. The existence and properties of the newly discovered particle may also have consequences beyond the standard model itself.

1 - 28 of 28
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