Luis Foà Torres

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# Floquet Topological Insulators

This article is about *Floquet Topological Insulators. *Topological Insulators (TIs) are a recent family of exotic materials with a few intriguing properties. They are insulators in the bulk but their edges support propagating states bridging the bulk band-gap, much like the states emerging in the **Quantum Hall effect** discovered by Klaus von Klitzing in 1980 but in the case of TIs this happens without a magnetic field thanks to spin-orbit interaction. Recently, a new way of achieving properties akin those found in quantum Hall systems started to gain attention: using a time-dependent potential to harness *tunable* topological properties.

**Floquet Topological Insulators**[1,2] can be made out of normal materials which develop properties akin those in the quantum Hall regime, for example, upon illumination with a laser field. In

*“Floquet chiral edge states in graphene”*[3] we offered the first analytical solution for the topological states as well as numerics proving their chirality [A simple analysis for bilayer graphene can be found in [4]]. This study has been followed up in [5] with a few additional twists.

More recently, we tackled the multiterminal conductance of such systems and found more surprises: Notably, the usual connection between counting the number/chirality of the edge states and the Hall conductance breaks down, not all the chiral edge states contribute equally to the Hall response as in the case of time-dependent systems [7].

As a side note, one of the simplest possible systems showing Floquet topological states and transitions between trivial and non-trivial band-structure is the driven Su-Schrieffer-Heeger model analyzed in [8]. Besides the creation of Floquet topological states, the SSH model allows to study the interplay between the native topology and the driving. The driving a 3D topological insulator was studied in [9].

The field of *Floquet Topological Insulators* is just starting to flourish.

Update:

**Multiterminal Conductance of a Floquet Topological Insulator**

L. E. F. Foa Torres, P. M. Perez-Piskunow, C. A. Balseiro, and G. Usaj

Physical Review Letters,** 113**, 266801 (2014). [pdf]

References

[1] T. Oka and H. Aoki, *“Photovoltaic Hall effect in graphene”*, Phys. Rev. B **79**, 081406(R) (2009). link

[2] N. H. Lindner, Gil Refael, and V. Galitski, *“Floquet topological insulator in semiconductor quantum wells”*, Nature Physics **7**, 490–495 (2011). link

[3] P. M. Perez-Piskunow, G. Usaj, C. A. Balseiro, L. E. F. Foa Torres, *“Floquet chiral edge states in graphene”*, Physical Review B, **89**, 121401(R) (2014). link pdf

[4] E. Suárez Morell and L. E. F. Foa Torres, *“Radiation effects on the electronic structure of bilayer graphene”*, Physical Review B **86**, 125449 (2012). link [pdf]

[5] G. Usaj, P. M. Perez-Piskunow, L. E. F. Foa Torres, C. A. Balseiro, *“Irradiated graphene as a tunable Floquet topological insulator”*, Physical Review B **90**, 115423 (2014). [link]

[6] H. L. Calvo, H. M. Pastawski, S. Roche, and L. E. F. Foa Torres, *“Tuning laser-induced band gaps in graphene”*, Appl. Phys. Lett. **98**, 232103 (2011).[pdf]

[7] L. E. F. Foa Torres, P. M. Perez-Piskunow, C. A. Balseiro, and G. Usaj, “Multiterminal Conductance of a Floquet Topological Insulator”, Physical Review Letters,** 113**, 266801 (2014). [pdf]

[8] V. Dal Lago, M. Atala, and L. E. F. Foa Torres, “Floquet topological transitions in a driven one-dimensional topological insulator”, Physical Review A 92, 023624 (2015).

[9] H. L. Calvo et al., Physical Review B 91, 241404(R) (2015).

Commentaries/Notes/Other

The quest for new materials: Can any material become topological?