Electronic circuit analogs of non-hermitian topological edge states
In this pro ject, we devise a technique to simulate tight-binding lattices of infinite size with circuitry. Each atom in the lattice is mo delled by a parallel LC resonator; the hoppings between atoms are modelled by a capacitor that connects the pairs of nodes. We devise a setup that introduces a...
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| Format: | Final Year Project |
| Language: | English |
| Published: |
2018
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10356/76191 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | In this pro ject, we devise a technique to simulate tight-binding lattices of infinite size with circuitry.
Each atom in the lattice is mo delled by a parallel LC resonator; the hoppings between atoms are
modelled by a capacitor that connects the pairs of nodes. We devise a setup that introduces a
tunable momentum parameter, enabling the simulation of infinitely large lattices. In the first
half of the paper. we shows how this technique works by applying it to specific examples in one
and two dimensions - to a 1D tight-binding chain and graphene with zigzag edge, respectively.
The dispersion relation is successfully reproduced in these two examples. In the second half of
the paper, we propose a two-dimensional non-Hermitian tight-binding model that reduces to a
previously studied continuum Hamiltonian and that exhibits topological edge states. This tight
binding model can also be simulated with circuits using the same procedure outline in the previous
sections. It is left for future work to construct the corresponding non-Hermitian circuitry lattice
to find experimental evidences for the predicted edge states. |
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