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Comment on "General nonlocality in quantum fields"
In this paper, we first incorporate the weak interaction into the theory of
General Nonlocality by finding a appropriate metric for it. Accordingly, we
suggest the theoretical frame of General Nonlocality as the candidate theory of
unifying three microscope interactions in low energy limit. In this unifying
scenario, the essential role of photon field is stressed.Comment: Only partial content published in the following reference. The part
asserting the fermion mass problem now proved to be wrong, though remains in
the versio
On subgroups in division rings of type
Let be a division ring with center . We say that is a {\em
division ring of type } if for every two elements the division
subring is a finite dimensional vector space over . In this paper
we investigate multiplicative subgroups in such a ring.Comment: 10 pages, 0 figure
3D quantum Hall effect of Fermi arcs in topological semimetals
The quantum Hall effect is usually observed in 2D systems. We show that the
Fermi arcs can give rise to a distinctive 3D quantum Hall effect in topological
semimetals. Because of the topological constraint, the Fermi arc at a single
surface has an open Fermi surface, which cannot host the quantum Hall effect.
Via a "wormhole" tunneling assisted by the Weyl nodes, the Fermi arcs at
opposite surfaces can form a complete Fermi loop and support the quantum Hall
effect. The edge states of the Fermi arcs show a unique 3D distribution, giving
an example of (d-2)-dimensional boundary states. This is distinctly different
from the surface-state quantum Hall effect from a single surface of topological
insulator. As the Fermi energy sweeps through the Weyl nodes, the sheet Hall
conductivity evolves from the 1/B dependence to quantized plateaus at the Weyl
nodes. This behavior can be realized by tuning gate voltages in a slab of
topological semimetal, such as the TaAs family, CdAs, or NaBi. This
work will be instructive not only for searching transport signatures of the
Fermi arcs but also for exploring novel electron gases in other topological
phases of matter.Comment: 5 pages, 3 figure
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