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...

Full description

Saved in:
Bibliographic Details
Main Author: Trung, Ha Quang
Other Authors: Chong Yidong
Format: Final Year Project
Language:English
Published: 2018
Subjects:
Online Access:http://hdl.handle.net/10356/76191
Tags: Add Tag
No Tags, Be the first to tag this record!
Institution: Nanyang Technological University
Language: English
id sg-ntu-dr.10356-76191
record_format dspace
spelling sg-ntu-dr.10356-761912023-02-28T23:11:18Z Electronic circuit analogs of non-hermitian topological edge states Trung, Ha Quang Chong Yidong School of Physical and Mathematical Sciences DRNTU::Science::Physics 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. Bachelor of Science in Physics 2018-11-27T07:28:04Z 2018-11-27T07:28:04Z 2018 Final Year Project (FYP) http://hdl.handle.net/10356/76191 en 33 p. application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic DRNTU::Science::Physics
spellingShingle DRNTU::Science::Physics
Trung, Ha Quang
Electronic circuit analogs of non-hermitian topological edge states
description 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.
author2 Chong Yidong
author_facet Chong Yidong
Trung, Ha Quang
format Final Year Project
author Trung, Ha Quang
author_sort Trung, Ha Quang
title Electronic circuit analogs of non-hermitian topological edge states
title_short Electronic circuit analogs of non-hermitian topological edge states
title_full Electronic circuit analogs of non-hermitian topological edge states
title_fullStr Electronic circuit analogs of non-hermitian topological edge states
title_full_unstemmed Electronic circuit analogs of non-hermitian topological edge states
title_sort electronic circuit analogs of non-hermitian topological edge states
publishDate 2018
url http://hdl.handle.net/10356/76191
_version_ 1759853294313799680