Torsion, parity-odd response, and anomalies in topological states

被引:67
|
作者
Parrikar, Onkar [1 ]
Hughes, Taylor L. [1 ]
Leigh, Robert G. [1 ]
机构
[1] Univ Illinois, Dept Phys, Urbana, IL 61801 USA
来源
PHYSICAL REVIEW D | 2014年 / 90卷 / 10期
关键词
LOOP CALCULATIONS; INDEX THEOREM; RIEMANN; INSULATORS; SYMMETRY; FERMIONS; SPACE;
D O I
10.1103/PhysRevD.90.105004
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
We study the response of a class of topological systems to electromagnetic and gravitational sources, including torsion and curvature. By using the technology of anomaly polynomials, we derive the parity-odd response of a massive Dirac fermion in d = 2 + 1 and d = 4 + 1, which provides a simple model for a topological insulator. We discuss the covariant anomalies of the corresponding edge states, from a Callan-Harvey anomaly inflow, as well as a Hamiltonian spectral flow point of view. We also discuss the applicability of our results to other systems such as Weyl semimetals. Finally, using dimensional reduction from d = 4 + 1, we derive the effective action for a d = 3 + 1 time-reversal invariant topological insulator in the presence of torsion and curvature, and discuss its various physical consequences.
引用
收藏
页数:34
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