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Article overview
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Edge states and topological pumping in elastic lattices with periodically modulated coupling | | Matheus I. N. Rosa
; Raj Kumar Pal
; José R. F. Arruda
; Massimo Ruzzene
; | | Date: |
6 Nov 2018 | | Abstract: | We investigate the dispersion topology of elastic lattices characterized by
spatial stiffness modulation. The modulation is defined by the sampling of a
two-dimensional surface, which provides the lattices with topological
properties that are usually attributed to two-dimensional crystals. We show
that the cyclic variation of the phase of the stiffness modulation leads to a
Berry phase accumulation for the Bloch eigenmodes, which is characterized by
integer valued Chern numbers for the bands and associated gap labels. The
resulting non-trivial gaps are spanned by edge modes localized at one of the
boundaries of the considered 1D lattices. The edge mode location is governed by
the phase of the stiffness distribution, whose spatial modulation drives these
modes to transition from one edge to the other, through a bulk state that
occurs when the corresponding dispersion branch touches the bulk bands. This
property enables the implementation of a topological pump that is obtained by
stacking and coupling a family of modulated 1D lattices along a second spatial
dimension. The gradual variation of the stiffness phase modulation drives the
adiabatic transition of the edge states, which transition from their localized
state at one boundary, to a bulk mode and, finally, to another localized state
at the opposite boundary. Similar effects were illustrated under the assumption
of quasiperiodic modulation of the lattice interactions. We here demonstrate
that a topological pump can be achieved also in periodic media, and illustrate
this for the first time in elastic discrete lattices. | | Source: | arXiv, 1811.2637 | | Services: | Forum | Review | PDF | Favorites | |
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