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Recently, quantum oscillation of the resistance in insulating monolayerWTe$_2$ was reported. An explanation in terms of gap modulation in thehybridized Landau levels of an excitonic insulator was also proposed by one ofus. However, the previous picture of gap modulation in the Landau levelsspectrum was built on a pair of well nested electron and hole Fermi surfaces,while the monolayer WTe$_2$ has one hole and two electron Fermi pockets withrelative anisotropy. Here we demonstrate that for system like monolayerWTe$_2$, the excitonic insulating state arising from the coupled one hole andtwo electron pockets possesses a finite region in interaction parameter spacethat shows gap modulation in a magnetic field. In this region, the thermallyactivated conductivity displays the $1/B$ periodic oscillation and it canfurther develop into discrete peaks at low temperature, in agreement with theexperimental observation. We show that the relative anisotropy of the bands isa key parameter and the qunatum oscillations decrease rapidly if the anisotropyincreases further than the realistic value for monolayer WTe$_2$.

Quantum Oscillation of Thermally Activated Conductivity in a Monolayer WTe$_2$-like Excitonic Insulator