Simulation of Chiral Topological Phases in Driven Low Dimensional Systems
Gloria Platero a
a Instituto de Ciencia de Materiales de Madrid, CSIC, Madrid, Spain
nanoGe Fall Meeting
Proceedings of nanoGe Fall Meeting19 (NGFM19)
#Sol2D19. Two Dimensional Layered Semiconductors
Berlin, Germany, 2019 November 3rd - 8th
Organizers: Efrat Lifshitz, Cristiane Morais Smith and Doron Naveh
Invited Speaker, Gloria Platero, presentation 317
Publication date: 16th July 2019

Recently, there is a big effort to implement long arrays of semiconductor quantum dots. The high tunnability of these systems allows to control the different parameters of the system, as the tunneling rates between dots. Therefore, they
become good quantum simulators of real molecules, as dimerized molecular chains.
A one-dimensional tight-binding model with alternating tunnel matrix elements, the SSH model, represents a simple description of a dimerized polymer. It is characterized by a topological invariant, the Zak phase which has been measured in cold atom systems[1]. For finite chains in the topologically nontrivial phase, a pair of exponentially decaying edge states emerges. In this talk I will discuss the dynamics of interacting electrons in a 1D chain of dimers and the role of edge states in the dynamics[2]. We extend our result for two strongly interacting electrons propagating in two dimensional lattices under the action of a periodic electric field both with and without a magnetic flux[3]. Finally we extend the analysis to include long range hopping in a dimer chain[4,5]. We show that a quantum simulator for 1D chiral topological phases can be obtained by periodically driving an array of quantum dots with long-range hopping. We propose a driving protocol which enables us to imprint bond-order in the lattice, while also offers tunability of the long-range hoppings[5]. This control can be used to tune the hopping amplitudes to configurations that would be unreachable otherwise, while preserving the fundamental symmetries which guarantee topological features. Thus, the driving protocol triggers topological behaviour in a trivial setup, opening the door to the simulation of different chiral topological phases. Furthermore, we also study the exact time-evolution for the case of two interacting electrons and show that the dynamics of different edge states modes can become highly correlated. This allows to discriminate between different topological phases and also opens up new possibilities for quantum state transfer protocols.

[1] M. Atala, et al. , Nat. Phys. 9, 795–800 (2013).
[2] M. Bello et al., Sci. Rep. 6, 22562, (2016).
[3] M. Bello et al., Phys Rev B , 95, 094303 (2017)
[4] B. Pérez-González et al., Phys. Rev. B, 99, 035146 (2019)
[5] B. Pérez-González et al., submitted, arXiv:1903.07678v1

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