Correlated topological insulators and the fractional magnetoelectric effect
Correlated topological insulators and the fractional magnetoelectric effect
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相关拓扑绝缘体和分数磁电效应
DOI：
10.1103/physrevb.83.195139
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发表时间：
2010
影响因子：
3.7
通讯作者：
T. Senthil
中科院分区：
文献类型：
--
作者：
Brian Swingle;M. Barkeshli;J. McGreevy;T. Senthil
拓扑绝缘体的特征是存在受时间反转对称性保护的无间隙表面模式。在三个空间维度中，磁电响应用电磁场的整体数学项来描述。在这里，我们构造了这样的相的理论例子，这些相不能顺利地连接到任何带绝缘子。这种相关的拓扑绝缘体允许分数磁电响应的可能性，由分数$\EnsureMatha/\EnsureMath{\pi}$描述。我们证明，只有在有间隙的玻色子或费米子的时间反转不变系统中，如果系统在拓扑非平凡空间上也有解受限的分数激发和相关的简并基态，分数数学才是可能的。我们用关联玻色子的时间逆对称拓扑绝缘体$\ensuremath{\theta}=\frac{\ensuremath{\pi}}{4}$.的一个具体例子来说明这一结果简要介绍了对电子分数级拓扑绝缘子的扩展。
Topological insulators are characterized by the presence of gapless surface modes protected by time-reversal symmetry. In three space dimensions the magnetoelectric response is described in terms of a bulk $\ensuremath{\theta}$ term for the electromagnetic field. Here we construct theoretical examples of such phases that cannot be smoothly connected to any band insulator. Such correlated topological insulators admit the possibility of fractional magnetoelectric response described by fractional $\ensuremath{\theta}/\ensuremath{\pi}$. We show that fractional $\ensuremath{\theta}/\ensuremath{\pi}$ is only possible in a gapped time-reversal-invariant system of bosons or fermions if the system also has deconfined fractional excitations and associated degenerate ground states on topologically nontrivial spaces. We illustrate this result with a concrete example of a time-reversal-symmetric topological insulator of correlated bosons with $\ensuremath{\theta}=\frac{\ensuremath{\pi}}{4}$. Extensions to electronic fractional topological insulators are briefly described.