Electron binding energy of a donor in bilayer graphene with gate-tunable gap
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arXiv
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2024
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| author | Gorbar, E. V. Gusynin, V. P. Oriekhov, D. O. Shklovskii, B. I. |
| author_facet | Gorbar, E. V. Gusynin, V. P. Oriekhov, D. O. Shklovskii, B. I. |
| contents | In gapped bilayer graphene, similarly to conventional semiconductors, Coulomb impurities (such as nitrogen donors) may determine the activation energy of its conductivity and provide low temperature hopping conductivity. However, in spite of the importance of Coulomb impurities, nothing is known about their electron binding energy $E_b$ in the presence of gates. To close this gap, we study numerically the electron binding energy $E_b$ of a singly charged donor in BN-enveloped bilayer graphene with the top and bottom gates at distance $d$ and gate-tunable gap $2Δ$. We show that for $10 < d < 200$ nm and $1 < Δ< 100$ meV the ratio $E_b/Δ$ changes from 0.4 to 1.5. The ratio $E_b/Δ$ stays close to unity because of the dominating role of the bilayer polarization screening which reduces the Coulomb potential well depth to values $\sim Δ$. Still the ratio $E_b/Δ$ somewhat decreases with growing $Δ$, faster at small $Δ$ and slower at large $Δ$. On the other hand, $E_b/Δ$ weakly grows with $d$, again faster at small $Δ$ and slower at large $Δ$. We also studied the effect of trigonal warping and found only a small reduction of $E_b/Δ$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_09389 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Electron binding energy of a donor in bilayer graphene with gate-tunable gap Gorbar, E. V. Gusynin, V. P. Oriekhov, D. O. Shklovskii, B. I. Mesoscale and Nanoscale Physics In gapped bilayer graphene, similarly to conventional semiconductors, Coulomb impurities (such as nitrogen donors) may determine the activation energy of its conductivity and provide low temperature hopping conductivity. However, in spite of the importance of Coulomb impurities, nothing is known about their electron binding energy $E_b$ in the presence of gates. To close this gap, we study numerically the electron binding energy $E_b$ of a singly charged donor in BN-enveloped bilayer graphene with the top and bottom gates at distance $d$ and gate-tunable gap $2Δ$. We show that for $10 < d < 200$ nm and $1 < Δ< 100$ meV the ratio $E_b/Δ$ changes from 0.4 to 1.5. The ratio $E_b/Δ$ stays close to unity because of the dominating role of the bilayer polarization screening which reduces the Coulomb potential well depth to values $\sim Δ$. Still the ratio $E_b/Δ$ somewhat decreases with growing $Δ$, faster at small $Δ$ and slower at large $Δ$. On the other hand, $E_b/Δ$ weakly grows with $d$, again faster at small $Δ$ and slower at large $Δ$. We also studied the effect of trigonal warping and found only a small reduction of $E_b/Δ$. |
| title | Electron binding energy of a donor in bilayer graphene with gate-tunable gap |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2401.09389 |