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Using a variational approach, the binding energies $E_b$ of the lowest boundexcitons in Xenes under varying electric field are investigated. The internalexciton motion is described both by Dirac electron dispersion and ineffective-mass approximation, while the screened electron-hole attraction ismodeled by a Rytova-Keldysh potential with a 2D electronic polarizability$\alpha_{2{\rm D}}$. The most important parameters as spin-orbit-induced gap$E_g$, Fermi velocity $v_F$ and $\alpha_{2{\rm D}}$ are taken from ab initiodensity functional theory calculations. In addition, $\alpha_{2{\rm D}}$ isapproximated in two different ways. The relation of $E_b$ and $E_g$ is ruled bythe screening. The existence of an excitonic insulator phase with $E_b>E_g$sensitively depends on the chosen $\alpha_{2{\rm D}}$. The values of $E_g$ and$\alpha_{2{\rm D}}$ are strongly modified by a vertical external electric bias$U$, which defines a transition from the topological into a trivial insulatorat $U=E_g/2$, with the exception of plumbene. Within the Dirac approximation,but also within the effective mass description of the kinetic energy, thetreatment of screening dominates the appearance or non-appearance of anexcitonic insulator phase. Gating does not change the results: the predictiondone at zero electric field is confirmed when a vertical electric field isapplied. Finally, Many-Body perturbation theory approaches based on the Green'sfunction method, applied to stanene, confirm the absence of an excitonicinsulator phase, thus validating our results obtained by ab initio modeling of$\alpha_{2{\rm D}}$.

scipost physics

Transitions in Xenes between excitonic, topological and trivial  insulator phases: influence of screening, band dispersion and external  electric field