Non-abelian topological states of matter are of great interest in condensed matter physics,
both due to their extraordinary fundamental properties and to their possible use for quantum
computation. The insensitivity of their topological characteristics to disorder, noise,
and interaction with the environment may lead to realization of quantum computers with
very long coherence times. The realization of a quantum computer ranks among the foremost
outstanding problems in physics, particularly in light of the revolutionary rewards
the achievement of this goal promises.
The proposed theoretical study is multi-dimensional. On the methodological side the
multi-dimensionality is in the breadth of the studies we discuss, ranging all the way from
phenomenology to mathematical physics. We will aim at detailed understanding of present
and future experimental results. We will analyze experimental setups designed to identify,
characterize and manipulate non-abelian states. And we will propose and classify novel
non-abelian states. On the concrete side, the multi-dimensionality is literal. The systems
we consider include quantum dots, one dimensional quantum wires, two dimensional planar
systems, and surfaces of three dimensional systems.
Our proposal starts with Majorana fermions in systems where spin-orbit coupling, Zeeman
fields and proximity coupling to superconductivity are at play. It continues with “edge
anyons”, non-abelian quasiparticles residing on edges of abelian Quantum Hall states. It
ends with open issues in the physics of the Quantum Hall Effect.
We expect that this study will result in clear schemes for unquestionable experimental
identification of Majorana fermions, new predictions for more of their measurable consequences,
understanding of the feasibility of fractionalized phases in quantum wires, feasible
experimental schemes for realizing and observing edge anyons, steps towards their classification,
and better understanding of quantum Hall interferometry.
Fields of science
- natural sciencesmathematicsapplied mathematicsmathematical physics
- natural sciencesphysical sciencestheoretical physicsparticle physicsfermion
- engineering and technologyelectrical engineering, electronic engineering, information engineeringelectronic engineeringcomputer hardwarequantum computer
- natural sciencesphysical sciencescondensed matter physics
Call for proposal
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