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In this lecture, we introduce the basic idea of topology as it manifests in condensed matter systems.
The video lecture is divided into three parts, corresponding to the three sections in the lecture notes. You can also check out the video lectures at our Vimeo showcase.
In this part of the lecture, we introduce topology in the context of two-dimensional surfaces, and discuss how certain ideas abstracted from that setup apply to condensed matter systems.
In this first perspective on topology, we discuss homotopy between 0-dimensional free fermion Hamiltonians and the notion of spectral flattening.
In this section, we start off with a recap of tight-binding models and then introduce the Su-Schrieffer-Heeger model. This model is shown to have two topologically distinct gapped phases by mapping this system to an geometric picture in two dimensions.
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