FLEET seminar: Zero-energy states in 2D 2nd-order topological insulator flakes

Michele Governale’s research focuses on the theory of quantum transport in nanostructures, spin-dependent phenomena, hybrid normal-superconducting systems, and topological phases of matter.

Prof. Michele Governale, Victoria University, Wellington (New Zealand) and Principal Investigator at the MacDiarmid Institute for Advanced Materials and Nanotechnology.

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Two-dimensional second-order topological insulators are characterized by the presence of topologically protected zero-energy states localized at the corners of a flake [Nat. Rev. Phys].

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 [Phys. Rev. B]. We consider two different models for the second-order topological insulators, both belonging to Cartan class AIII, i.e. time-reversal and charge-conjugation symmetries are broken but there is an additional chiral 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. We discuss how the location and properties of the corner states can be controlled, for example by rotating an in-plane magnetic field or by changing the orientation of the flake with respect to the crystal axes.

Finally, we study the effect of the corner states on the electronic transport through a flake of second order topological insulator. We consider a finite region of rectangular shape of a two-dimensional topological insulator in the presence of an in-plane magnetic field [Poata, Taddei, and Governale, in preparation]. This system has been shown to be a second-order topological insulator and therefore it exhibits corner states at its boundary [Phys. Rev. B]. In the leads, we assume that the magnetic field is absent and therefore they exhibit helical one-dimensional propagating states characteristic of the spin-Hall effect. In a two-terminal configuration, we show that transport can be turned on/off by a rotation of the in-plane magnetic field, and we provide the analytical expression for the scattering matrix of this setup. Similarly, in a three-terminal configuration, the in-plane magnetic field can be used to turn on/off the transmission between neighbouring contacts.

Both setups work therefore as topological switches. The switching functionality is robust to both disorder and non-ideal contacts between the leads and the scattering region, due to the topological nature of the states participating in the electron transport.

Michele Governale is Professor of Physics at Victoria University of Wellington and a Principal Investigator at the MacDiarmid Institute for Advanced Materials and Nanotechnology. After obtaining his Ph.D. from the University of Pisa in Italy in 2001, he held postdoctoral positions at the University of Karlsruhe (now KIT), Scuola Normale Superiore in Pisa, Ruhr-Unversität Bochum, and Duisburg-Essen University. Since 2009 he has been based at Victoria University where his research focuses on the theory of quantum transport in nanostructures, spin-dependent phenomena, hybrid normal-superconducting systems, and topological phases of matter.