Shallow donor states and interlevel transitions in gapped graphene bilayers

Abstract A variational calculation for the energies of the ground and first excited states of a shallow donor impurity in bilayer graphene (BLG) with an open energy gap is presented in this study. It is shown that the binding energies of the lowest states and the distance between them can be tuned in the region of few tens of meV by changing the gap and tight binding parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>γ</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> , which is responsible for the nearest neighboring interlayer coupling. Based on the results obtained, the optical transition of an impurity electron from the ground to the first excited state in BLG is investigated. We find that the oscillator strength of the transition between the lowest energy states <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mi>S</mml:mi> <mml:mo accent="false" stretchy="false">→</mml:mo> <mml:mn>2</mml:mn> <mml:mrow> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>x</mml:mi> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> of a shallow donor also depends on the gap and tight binding parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>γ</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> , but is not sensitive to the value of the cutting parameter of the soft Coulomb potential that is proposed. The transitions between shallow impurity levels in BLG can serve as an alternative tunable source of terahertz radiation. The possibility to tune the energy levels of hydrogenic-like impurities can open new ways for either the creation of coherent superpositions of the energy states or the coherent population transfer between them by applying laser pulses.