A great variety of topological phases have been classified as a consequence of discovery of the quantum Hall effect, but this work has recently led to discovery of some topologically non-trivial phases of matter, which contradict key assumptions of established classification schemes. These phases, which are the topological skyrmion phases of matter, multiplicative topological phases of matter, and finite-size topological phases of matter, necessitate a paradigm shift from the quantum Hall effect framework to that of the quantum skyrmion Hall effect, in which the point charges of the quantum Hall effect are generalised to compactified p-branes. For compactification via fuzzification, these compactified p-branes carrying charge are necessarily expressed in terms of angular momentum as quantum skyrmions. Ostensibly (d+1)-dimensional systems, based on the number of Cartesian coordinates they possess, can then in fact have D additional dimensions encoded in (pseudo)spin degrees of freedom, and realize intrinsically (D+d+1)-dimensional topological states, a finding supported by results in lattice tight-binding models.
Bio:
Ashley Cook is a junior group leader at Max Planck Dresden.
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2024-09-05T10:00:002024-09-05T11:00:00Quantum skyrmion Hall effectEvent Information:
Abstract:
A great variety of topological phases have been classified as a consequence of discovery of the quantum Hall effect, but this work has recently led to discovery of some topologically non-trivial phases of matter, which contradict key assumptions of established classification schemes. These phases, which are the topological skyrmion phases of matter, multiplicative topological phases of matter, and finite-size topological phases of matter, necessitate a paradigm shift from the quantum Hall effect framework to that of the quantum skyrmion Hall effect, in which the point charges of the quantum Hall effect are generalised to compactified p-branes. For compactification via fuzzification, these compactified p-branes carrying charge are necessarily expressed in terms of angular momentum as quantum skyrmions. Ostensibly (d+1)-dimensional systems, based on the number of Cartesian coordinates they possess, can then in fact have D additional dimensions encoded in (pseudo)spin degrees of freedom, and realize intrinsically (D+d+1)-dimensional topological states, a finding supported by results in lattice tight-binding models.
Bio:
Ashley Cook is a junior group leader at Max Planck Dresden.Event Location:
AMPEL 311