Zero-energy states in flakes of two-dimensional second-order topological insulators

  • Seminar
Speaker
Michele Governale
Affiliation
Victoria University of Wellington, New Zealand
Date
2023-06-22
Time
11:00
Venue
ONSITE: NEST meeting room – ONLINE: https://tinyurl.com/MicheleGovernale Once connected, please switch off your microphone and camera. If you have questions, please use the chat to ask for attention.
Host
Fabio Taddei

Abstract:

Two-dimensional second-order topological insulators are characterized by the presence of topologically protected zero-energy bound states localized at the corners of a flake [1]. In this talk, we present a theoretical study of the occurrence and features of such corner states inside flakes in the shape of a convex polygon [2].
We consider two different models for the second-order topological insulators, the first obeying inversion symmetry and the other obeying a combined π/4 rotation symmetry and time-reversal symmetry. We derive an analytical effective model of an edge corresponding to a massive Dirac fermion and determine the presence of a corner state between two given edges by studying the sign of their induced masses. In particular, we find that the number of corner states in a flake is always two in the first model, while in the second model there are either 0, 2 or 4 corner states.
To corroborate our findings, we focus on flakes of specific shapes (a triangle and a square) and use a numerical finite-difference approach to determine the features of the corner states in terms of their probability density. In the case of a triangular flake, we can change the position of corner states by rotating the flake with respect to the crystal axes in the first model, while in the second model we can also change their number. Remarkably, when the induced mass of an edge is zero the corresponding corner state becomes delocalized along the edge.
Finally, if time allows, we will discuss electronic transport through flakes of second-order topological insulator.
 
[1] B. Xie, H.-X. Wang, X. Zhang, P. Zhan, J.-H. Jiang, M. Lu, and Y. Chen, Higher-order band topology, Nat. Rev. Phys. 3, 520 (2021).
[2] J. Poata, F. Taddei, and M. Governale, On the corner states of two-dimensional second-order topological insulators, arXiv:2304.06854 (2023).

Istituto Nanoscienze 

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Istituto Nanoscienze Consiglio Nazionale delle Ricerche

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Pisa NEST

Piazza San Silvestro 12, I
56127 Pisa

phone +39 050 509525/418

fax +39 050 509550

Modena S3

via Campi 213/A, I 

41125 Modena 7

phone +39 059 2055629

fax +39 059 2055651″