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[CMT Seminar] Adrien Bouhon – Weyl nodes with non-Abelian charges

2019-09-17 @ 10:30 - 12:00

Speaker: Adrien Bouhon from Nordita
Title: Weyl nodes with non-Abelian charges
Time:  Tuesday
17th of September, Fika 10:30-11:00, Seminar 11:00-12:00,
Place: Nordita South, room 112:028 .

Weyl points trapped within a C_2T-symmetric plane (C2 = 180 degrees rotation, and T = time reversal) possess non-Abelian topological charges on top of their chirality. E.g. three-level systems realize the quaternion group. This picture requires to go beyond the modeling of a band structure as a Grassmannian (where a single spectral gap is specified). The non-Abelian nature of Weyl points implies new types of obstruction, where, for instance, two Weyl points with opposite chiralities may not annihilate. Also, the non-Abelian charges can be converted through the braiding of Weyl points in momentum space.
I will review three different yet equivalent ways of computing the non-Abelian charges: (i) as a non-cyclic phase defined from the parallel transport of the Hamiltonian along a base loop, (ii) as the Euler class of a two-band subspace over a patch bounded by the base loop, and (iii) as the winding number of the Pfaffian of the Wilsonnian Hamiltonian – of the two-band subspace – as the base loop flows over the patch. 
[Remark: 50% of the material I will present is new as compared to the talk I gave at the Nordita workshop in beginning of August.]


10:30 - 12:00
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