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Dive into the research topics where Aaron Farrell is active.

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Featured researches published by Aaron Farrell.


Physical Review B | 2016

Edge-state transport in Floquet topological insulators

Aaron Farrell; Tami Pereg-Barnea

Floquet topological insulators are systems in which the topology emerges only when a time-periodic perturbation is applied. In these systems one can define quasienergy states which replace the equilibrium stationary states. The system exhibits its nontrivial topology by developing edge-localized quasienergy states which lie in a gap of the quasienergy spectrum. These states represent a nonequilibrium analog of the topologically protected edge states in equilibrium topological insulators which exhibit an edge conductance of


Physical Review B | 2014

Entanglement spectrum as a probe for the topology of a spin-orbit-coupled superconductor

Jan Borchmann; Aaron Farrell; Shunji Matsuura; T. Pereg-Barnea

2{e}^{2}/h


Physical Review B | 2016

Anderson topological superconductor

Jan Borchmann; Aaron Farrell; Tami Pereg-Barnea

. Here we explore the transport properties of the edge states in a Floquet topological insulator. In stark contrast to the equilibrium result, we find that the two-terminal conductivity of these edge states is significantly different from


Physical Review B | 2016

Incommensurate spin density wave as a signature of spin-orbit coupling and precursor of topological superconductivity

Aaron Farrell; P.-K. Wu; Ying-Jer Kao; Tami Pereg-Barnea

2{e}^{2}/h


Physical Review B | 2014

Strong coupling expansion of the extended Hubbard model with spin-orbit coupling

Aaron Farrell; Tami Pereg-Barnea

. This fact notwithstanding, we find that for certain external potential strengths the conductivity is smaller than


Physical Review B | 2016

Dirac cones, Floquet side bands, and theory of time-resolved angle-resolved photoemission

Aaron Farrell; A. Arsenault; Tami Pereg-Barnea

2{e}^{2}/h


Physical Review B | 2014

Zeeman-field-induced nontrivial topology in a spin-orbit-coupled superconductor

Aaron Farrell; Tami Pereg-Barnea

and robust to the effects of disorder and smooth changes to the Hamiltonians parameters. This robustness is reminiscent of the robustness found in equilibrium topological insulators. We provide an intuitive understanding of the reduction of the conductivity in terms of a picture where electrons in edge states are scattered by photons. We also consider the Floquet sum rule [A. Kundu and B. Seradjeh, Phys. Rev. Lett. 111, 136402 (2013)], which was proposed in a different context. The summed conductivity recovers the equilibrium value of


Physical Review B | 2015

Quasiparticle interference patterns in a topological superconductor

Aaron Farrell; Maxime Beaudry; Marcel Franz; Tami Pereg-Barnea

2{e}^{2}/h


Physical Review B | 2013

Topological superconductivity without proximity effect

Aaron Farrell; Tami Pereg-Barnea

whenever edge states are present. We show that this sum rule holds in our system using both numerical and analytic techniques.


arXiv: Strongly Correlated Electrons | 2015

Anderson Topological Superconductor and Entanglement Entropy

Jan Borchmann; Aaron Farrell; Tami Pereg-Barnea

The classification of electron systems according to their topology has been at the forefront of condensed matter research in recent years. It has been found that systems of the same symmetry, previously thought of as equivalent, may in fact be distinguished by their topological properties. Moreover, the non-trivial topology found in some insulators and superconductors has profound physical implications that can be observed experimentally and can potentially be used for applications. However, characterizing a systems topology is not always a simple task, even for a theoretical model. When translation and other symmetries are present in a quadratic model the topological invariants are readily defined and easily calculated in a variety of symmetry classes. However, once interactions or disorder come into play the task becomes difficult, and in many cases prohibitively so. The goal of this paper is to suggest alternatives to the topological invariants which are based on the entanglement spectrum and entanglement entropy. Using quadratic models of superconductors we demonstrate that these entanglement properties are sensitive to changes in topology. We choose quadratic models since the topological phase diagram can be mapped using the topological invariants and then compared to the entanglement entropy/spectrum features. This work sets the stage for learning about topology in interacting and disordered systems through their entanglement properties.

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Tami Pereg-Barnea

University of British Columbia

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Marcel Franz

University of British Columbia

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Ying-Jer Kao

National Taiwan University

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