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<i>Ab initio</i>calculation of low-energy collective charge-density excitations in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mtext>MgB</mml:mtext></mml:mrow><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>
We present ab initio time-dependent density-functional theory calculation results for low-energy collective electron excitations in ${\text{MgB}}_{2}$. The existence of a long-lived collective excitation corresponding to coherent charge density fluctuations between the boron $\ensuremath{\sigma}$ and $\ensuremath{\pi}$ bands ($\ensuremath{\sigma}\ensuremath{\pi}$ mode) is demonstrated. This mode has a sine-like oscillating dispersion for energies below …