Corentin Morice

Jeudi 03 octobre 2019

2D to 3D crossover in topological insulators

At the heart of the study of topological insulators lies a fundamental
dichotomy : topological invariants are defined in infinite systems, but
their main footprint, surface states, only exists in finite systems.
In systems in the slab geometry, namely infinite in two dimensions and
finite in one, the 2D topological invariant was shown to display three
different types of behaviours. In the limit of zero Dirac velocity
along z, these behaviours extrapolate to the three 3D topological
phases : trivial, weak and strong topological insulators. We show
analytically that the boundaries of these regions are topological
phase transitions of particular significance, and allow one to fully
predict the 3D topological invariants from finite-thickness
information. Away from this limit, we show that a new phase arises,
which displays surface states but no band inversion at any finite
thickness, disentangling these two concepts closely linked in 3D.

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