799 research outputs found
Topological origin of edge states in two-dimensional inversion-symmetric insulators and semimetals
Symmetries play an essential role in identifying and characterizing
topological states of matter. Here, we classify topologically two-dimensional
(2D) insulators and semimetals with vanishing spin-orbit coupling using
time-reversal () and inversion () symmetry. This
allows us to link the presence of edge states in and
symmetric 2D insulators, which are topologically trivial
according to the Altland-Zirnbauer table, to a topological
invariant. This invariant is directly related to the quantization of the Zak
phase. It also predicts the generic presence of edge states in Dirac
semimetals, in the absence of chiral symmetry. We then apply our findings to
bilayer black phosphorus and show the occurrence of a gate-induced topological
phase transition, where the invariant changes
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
On the topological immunity of corner states in two-dimensional crystalline insulators
A higher-order topological insulator (HOTI) in two dimensions is an insulator
without metallic edge states but with robust zero-dimensional topological
boundary modes localized at its corners. Yet, these corner modes do not carry a
clear signature of their topology as they lack the anomalous nature of helical
or chiral boundary states. Here, we demonstrate using immunity tests that the
corner modes found in the breathing kagome lattice represent a prime example of
a mistaken identity. Contrary to previous theoretical and experimental claims,
we show that these corner modes are inherently fragile: the kagome lattice does
not realize a higher-order topological insulator. We support this finding by
introducing a criterion based on a corner charge-mode correspondence for the
presence of topological midgap corner modes in n-fold rotational symmetric
chiral insulators that explicitly precludes the existence of a HOTI protected
by a threefold rotational symmetry.Comment: 10 pages, 5 figures. Accepted for publication in NPJ Quantum
Material
Trommius’s Travelogue: Learned Memories of Erasmus and Scaliger and Scholarly Identity in the Republic of Letters
On the basis of the autobiography of the orthodox Calvinist minister Abraham Trommius (1633-1719), this article argues that the Republic of Letters created its own cultures of memory. The very use of the word ‘Republic’ begs the question whether there was some kind of early modern ‘state building’ at play within the networks of learned men and women. Although sentiments of religious and political alliance cannot be ruled out in the practices of learned memories, the identity arising from these cultures aimed at stressing learning, friendship and communication. Its acts of memory were localized instances of learned identity formation across borders, serving travelling students regardless of their political and confessional affiliations. This article argues that memories of learning or learned memories present a new logical, although hitherto ignored, line of research, to complement well-studied political and confessional memories. Trommius draws particular attention to Erasmus and to Joseph Scaliger and his father Julius Caesar Scaliger. The article also discusses the broader memory of these towering figures to exemplify the study of early modern learned identity formation by means of cultures of memory
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