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Engineering Topological Quantum States :

From 1D to 2D.


University of Basel

I will present results on exotic states in one-dimensional (Majorana fermions and parafermions) and two-dimensional (edge states in topological insulators) condensed matter systems that have attracted wide attention due to their promise of non-Abelian statistics believed to be useful for topological quantum computing. I discuss systems in which topological properties could be engineered per demand in semiconducting systems. For example, Majorana fermions can emerge in hybrid systems with proximity pairing in which the usually weak Rashba spin-orbit interaction is replaced by magnetic textures. Here, I will discuss candidate materials such as semiconducting nanowires, graphene nanoribbons, atomic magnetic chains or magnetic semiconductors [1]. One further goal is to go beyond Majorana fermions and to identify systems that can host quasiparticles with more powerful non-Abelian statistics such as parafermions in double semiconducting wires coupled by crossed Andreev reflections [2,3]. In the second part of my talk, I will focus on ’strip of stripes model’ consisting of weakly coupled one-dimensional semiconducting wires [4-6], where interaction effects in the wires can be treated non-perturbatively via bosonization. I will demonstrate that such systems can exhibit the integer or fractional quantum Hall effect [4], spin Hall effect [5], and anomalous Hall effect [6]. In the fractional regimes, the quasiparticles have fractional charges and non-trivial Abelian braid statistics.
[1] J. Klinovaja and D. Loss, Phys. Rev. B 86, 085408 (2012) ; J. Klinovaja and D. Loss, Phys. Rev. X 3, 011008 (2013) ; J. Klinovaja and D. Loss, Phys. Rev. B 88, 075404 (2013) ; J. Klinovaja, P. Stano, A. Yazdani, and D. Loss, Phys. Rev. Lett. 111, 186805 (2013). [2] J. Klinovaja and D. Loss, Phys. Rev. B 90, 045118 (2014). [3] J. Klinovaja, A. Yacoby, and D. Loss, Phys. Rev. B 90, 155447 (2014). [4] J. Klinovaja and D. Loss, Phys. Rev. Lett. 111, 196401 (2013) ; J. Klinovaja and D. Loss, Eur. Phys. J. B 87, 171 (2014). [5] J. Klinovaja and Y. Tserkovnyak, Phys. Rev. B 90, 115426 (2014). [6] J. Klinovaja, Y. Tserkovnyak, and D. Loss, Phys. Rev. B 91, 085426 (2015).

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