TY - JOUR
T1 - Topological number of edge states
AU - Hashimoto, Koji
AU - Kimura, Taro
N1 - Funding Information:
The work of K.H. was supported in part by JSPS KAKENHI Grants No. 15H03658 and No. 15K13483. The work of T.K. was supported in part by JSPS KAKENHI Grant No. 13J04302, and also by the MEXT-Supported Program for the Strategic Research Foundation at Private Universities Topological Science (Grant No. S1511006) and JSPS Grant-in-Aid for Scientific Research on Innovative Areas Topological Material Science (Grant No. 15H05855).
Publisher Copyright:
© 2016 American Physical Society.
PY - 2016/5/31
Y1 - 2016/5/31
N2 - We show that the edge states of the four-dimensional class A system can have topological charges, which are characterized by Abelian/non-Abelian monopoles. The edge topological charges are a new feature of relations among theories with different dimensions. From this novel viewpoint, we provide a non-Abelian analog of the TKNN number as an edge topological charge, which is defined by an SU(2) 't Hooft-Polyakov BPS monopole through an equivalence to Nahm construction. Furthermore, putting a constant magnetic field yields an edge monopole in a noncommutative momentum space, where D-brane methods in string theory facilitate study of edge fermions.
AB - We show that the edge states of the four-dimensional class A system can have topological charges, which are characterized by Abelian/non-Abelian monopoles. The edge topological charges are a new feature of relations among theories with different dimensions. From this novel viewpoint, we provide a non-Abelian analog of the TKNN number as an edge topological charge, which is defined by an SU(2) 't Hooft-Polyakov BPS monopole through an equivalence to Nahm construction. Furthermore, putting a constant magnetic field yields an edge monopole in a noncommutative momentum space, where D-brane methods in string theory facilitate study of edge fermions.
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U2 - 10.1103/PhysRevB.93.195166
DO - 10.1103/PhysRevB.93.195166
M3 - Article
AN - SCOPUS:84971571168
SN - 2469-9950
VL - 93
JO - Physical Review B
JF - Physical Review B
IS - 19
M1 - 195166
ER -