#### Alladi Ramakrishnan Hall

#### "Cornering" the electrons on a topological insulator - Higher order topological insulators

#### Ranjani Seshadri

##### IISc Bangalore

*In this talk, I will be presenting a recent work on a new entrant to the field of topology in condensed matter physics called higher order topological insulators (HOTIs). Usually, TIs in two-dimensions are known to host robust one-dimensional edge modes. These are related to the bulk properties via the topological invariant called the Chern number. However, in HOTIs, there are zero-dimensional corner modes, which, in case of a square-shaped sample, say, are confined to the four vertices of the square. Here, a variant of the well-known BHZ model is used to construct a two-dimensional HOTI. This model, in equilibrium, has both topological and non-topological phases depending on the different parameter values. By introducing anisotropy into this, we find edge states with interesting behaviours as well as corner modes in certain parameter regimes. When the system is driven periodically by a sequence of two pulses, multiple corner states may appear 'depending on the driving frequency and we try to understand the
bulk-boundary correspondence associated with these corner modes.
Reference: R. Seshadri, A. Dutta and D. Sen arXiv:1901.10495
<arxiv.org/abs/1901.10495>*

Done