强关联拓扑绝缘体中的指数定理、自旋Chern Simons理论和分数磁电效应
Index theorem, spin Chern Simons theory and fractional magnetoelectric effect in strongly correlated topological insulators
摘要：
利用指数定理和自旋Chern Simons理论，在不存在时间反演对称破缺的情况下，构造了强关联拓扑绝缘体与具有相互作用常数$ g $的非交换规范场$ SU(N) $耦合的有效拓扑场论.如果$ N $和$ g $允许我们定义一个有效耦合的t 'Hooft参数$ λ$为$ λ= N g^{2} $，那么我们的构造导致了具有霍尔电导$ σ_{H}^{s} = \frac{1}{4λ} \frac{e^{2}}{h} $的表面上的分数量子霍尔效应。对于由体轴子角$ θ$描述的磁电响应，我们提出，如果强关联玻色子或费米子在具有有效轴子角$ θ_{eff} = \fracπ{2 λ} $的拓扑非平凡空间上具有分数激发和简并基态，那么在强关联玻色子或费米子的带隙时间反演不变拓扑绝缘体中可以实现分数磁电效应.在$ e_{eff} = \frac{e}{\sqrt{2 λ}} $给出有效电荷的条件下，证明了$ σ_{H}^{s} = \frac{e_{eff}^{2}}{2h} $，从而得到了具有$ e_{eff} $和纯轴子角$ θ= π$的无带隙费米子的表面霍尔电导.
英文摘要：
Making use of index theorem and spin Chern Simons theory, we construct an effective topological field theory of strongly correlated topological insulators coupling to a nonabelian gauge field $ SU(N) $ with an interaction constant $ g $ in the absence of the time-reversal symmetry breaking. If $ N $ and $ g $ allow us to define a t'Hooft parameter $ λ$ of effective coupling as $ λ= N g^{2} $, then our construction leads to the fractional quantum Hall effect on the surface with Hall conductance $ σ_{H}^{s} = \frac{1}{4λ} \frac{e^{2}}{h} $. For the magnetoelectric response described by a bulk axion angle $ θ$, we propose that the fractional magnetoelectric effect can be realized in gapped time reversal invariant topological insulators of strongly correlated bosons or fermions with an effective axion angle $ θ_{eff} = \fracπ{2 λ} $ if they can have fractional excitations and degenerate ground states on topologically nontrivial and oriented spaces. Provided that an effective charge is given by $ e_{eff} = \frac{e}{\sqrt{2 λ}} $, it is shown that $ σ_{H}^{s} = \frac{e_{eff}^{2}}{2h} $, resulting in a surface Hall conductance of gapless fermions with $ e_{eff} $ and a pure axion angle $ θ= π$.
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