We argue that a correlated fluid of electrons and holes can exhibit a fractional quantum Hall effect at zero magnetic field analogous to the Laughlin state at filling $1/m$. We introduce a variant of the Laughlin wave function for electrons and holes and show that for $m=1$ it is the exact ground state of a free fermion model that describes $p_x+i{p}_y$ excitonic pairing. For $m>1$ we develop a simple composite fermion mean field theory, and we present evidence that our wave function correctly describes this phase. We derive an interacting Hamiltonian for which our wave function is the exact ground state, and we present physical arguments that the $m=3$ state can be realized in a system in which energy bands with angular momentum that differ by 3 cross at the Fermi energy. This leads to a gapless state with $(p_x+i{p}_y{)}^3$ excitonic pairing, which we argue is conducive to forming the fractional excitonic insulator in the presence of interactions. Prospects for numerics on model systems and band structure engineering to realize this phase in real materials are discussed.

中文翻译：

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小数激子绝缘子

我们认为，电子和空穴的相关流体可以在零磁场下表现出分数量子霍尔效应，类似于填充时的劳克林态。 $\mathrm{1个}/米$。我们介绍了Laughlin波函数对电子和空穴的一个变体，并证明了$米=\mathrm{1个}$ 自由费米子模型的确切基态描述了 $p_X+\mathrm{一世}{p}_{ÿ}$激子配对。为了$米>\mathrm{1个}$我们建立了一个简单的复合费米子平均场理论，并提供了证明我们的波函数正确描述了该相位的证据。我们推导了一个相互作用的哈密顿量，其波动函数是确切的基态，并且我们提出了物理论证，即$米=3$可以在一个系统中实现这种状态，在该系统中，角动量相差3的能带在费米能量处相交。这导致了无间隙状态$（p_X+\mathrm{一世}{p}_{ÿ}{）}^3$激子配对，我们认为这有助于在存在相互作用的情况下形成分数次激子绝缘子。讨论了用于在实际材料中实现此阶段的模型系统和能带结构工程中的数值的前景。