Flat bands with higher Chern number in pyrochlore slabs

A large number of recent works point to the emergence of intriguing analogs of fractional quantum Hall states in lattice models due to effective interactions in nearly flat bands with Chern number C=1. Here, we provide an intuitive and efficient construction of almost dispersionless bands with higher Chern numbers. Inspired by the physics of quantum Hall multilayers and pyrochlore-based transition-metal oxides, we study a tight-binding model describing spin-orbit coupled electrons in N parallel kagome layers connected by apical sites forming N-1 intermediate triangular layers (as in the pyrochlore lattice). For each N, we find finite regions in parameter space giving a virtually flat band with C=N. We analytically express the states within these topological bands in terms of single-layer states and thereby explicitly demonstrate that the C=N wave functions have an appealing structure in which layer index and translations in reciprocal space are intricately coupled. This provides a promising arena for new collective states of matter.Comment: 5+3 pages. Title extended, as publishe

Inclusion as Critique. Deconstructionist Approaches Exemplified through ‘Care’ of People with Cognitive Disabilities in Germany

The article builds on a reformulation of disability that construes disability as ‘discoursive disability’ (Trescher 2017d) and develops a conception of inclusion, which may be thought of as a deconstruction of barriers to participate in discourses and that aims at enabling access to discourses. I develop this perspective against the background of stationary housing in disability care. In this context, I refer to results of my study ‚Living space as pedagogic challenge. Institutional arrangement of residential home for people with disabilities’ (Trescher 2017c), which documents that external and internal, (in)formally assigned practices manifest as ‘disabling’ and ultimately lead to a bureaucratic overdetermination of subjects. Inclusion in this regard means to deconstruct disabling practices, such as bureaucratic overdetermination, and thus constitutes a process, which runs counter to disability. Inclusion is critical, because it deconstructs barriers to participate in discourses and therefore ultimately transforms society

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$X$.Comment: 24 pages, 17 figure

Topology and Interactions in a Frustrated Slab: Tuning from Weyl Semimetals to C > 1 Fractional Chern Insulators

We show that, quite generically, a [111] slab of spin-orbit coupled pyrochlore lattice exhibits surface states whose constant energy curves take the shape of Fermi arcs, localized to different surfaces depending on their quasimomentum. Remarkably, these persist independently of the existence of Weyl points in the bulk. Considering interacting electrons in slabs of finite thickness, we find a plethora of known fractional Chern insulating phases, to which we add the discovery of a new higher Chern number state which is likely a generalization of the Moore-Read fermionic fractional quantum Hall state. By contrast, in the three-dimensional limit, we argue for the absence of gapped states of the flat surface band due to a topologically protected coupling of the surface to gapless states in the bulk. We comment on generalizations as well as experimental perspectives in thin slabs of pyrochlore iridates.Comment: Published. 6+4 page

Behinderung als Praxis

How do »mental handicaps« become a social reality? An analysis on the basis of documented biographies.Welche Alltagspraxen führen dazu, dass sich behinderte Identitäten ausbilden? Durch die Dokumentation der 16 Lebensgeschichten und -entwürfe von Menschen mit geistiger Behinderung geht Hendrik Trescher der Frage nach, wie diese ihren Alltag erfahren. Er legt dar, wie diese Menschen in ihrem Lebenslauf immer wieder an Diskursteilhabebarrieren stoßen und so letztlich behindert werden. Wie komplex und gleichsam radikal wirkmächtig solche Barrieren sein können, zeigt er u.a. durch Aufdecken der Zusammenhänge zwischen Behinderung und der Funktionslogik von Hilfestrukturen, die – häufig auch in ihrer Ausprägung als pädagogische Protektorate – letztlich selbst behindernd wirken