2,342 research outputs found
Anatomy of Topological Surface States: Exact Solutions from Destructive Interference on Frustrated Lattices
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 non-interacting
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. 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 various
recently synthesized pyrochlore iridate slabs. Remarkably, each of the
pyrochlore slabs exhibit Fermi arcs although only the ones with a magnetic
one-in-three-out configuration feature bulk Weyl nodes in realistic parameter
regimes. Our approach furthermore signal the absence of topological surface
states, which we illustrate for a class of models akin to the trivial surface
of Hourglass materials KHg.Comment: 24 pages, 17 figure
Extended Bloch theorem for topological lattice models with open boundaries
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 insulators with open boundaries of co-dimension 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
Boundaries of boundaries: a systematic approach to lattice models with solvable boundary states of arbitrary codimension
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 non-topological phases as well as the transitions between them
in a particularly illuminating and transparent manner.Comment: 19 pages, 12 figure
Symmetry-protected nodal phases in non-Hermitian systems
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.Comment: Editors' Suggestio
Beyond the picturesque.
Amongst the work shown as part of a group exhibition in Gent entitled "Beyond the picturesque" whose main theme was exploring concepts and influences of the picturesque in contemporary art were the following: Another Country XII (2001), Colony 13 (2006) and Google Painting Grid (2007-9) by John Timberlake. The exhibition subsequently toured to Marta museum, Herford, Germany.
Some of this work was previously exhibited in other public and commercial galleries before being selected to form part of this exhibition
Exact solutions from destructive interference on frustrated lattices
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 bulk-boundary 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
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