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The classical picture of the force on a capacitor assumes a large density ofelectronic states, such that the electrochemical potential of charges added tothe capacitor is given by the external electrostatic potential and thecapacitance is determined purely by geometry. Here we consider capacitivelydriven motion of a nano-mechanical resonator with a low density of states, inwhich these assumptions can break down. We find three leading-order correctionsto the classical picture: the first of is a modulation in the static force dueto variation in the internal chemical potential, the second and third arechange in static force and dynamic spring constant due to the rate of change ofchemical potential, expressed as the quantum (density of states) capacitance.As a demonstration, we study a capacitively driven graphene mechanicalresonators, where the chemical potential is modulated independently of the gatevoltage using an applied magnetic field to manipulate the energy of electronsresiding in discrete Landau levels. In these devices, we observe large periodicfrequency shifts consistent with the three corrections to the classicalpicture. In devices with extremely low strain and disorder, the firstcorrection term dominates and the resonant frequency closely follows thechemical potential. The theoretical model fits the data with only oneadjustable parameter representing disorder-broadening of the Landau levels. Theunderlying electromechanical coupling mechanism is not limited the particularchoice of material, geometry, or mechanism for variation in chemical potential,and can thus be extended to other low-dimensional systems.

Modulation of mechanical resonance by chemical potential oscillation in graphene