TY - JOUR
T1 - Modulation of mechanical resonance by chemical potential oscillation in graphene
AU - Chen, Changyao
AU - Deshpande, Vikram V.
AU - Koshino, Mikito
AU - Lee, Sunwoo
AU - Gondarenko, Alexander
AU - Macdonald, Allan H.
AU - Kim, Philip
AU - Hone, James
N1 - Funding Information:
The authors thank N. Cooper, I. Aleiner, B. Skinner and G. Steele for helpful discussions; D. Heinz and A. Young for help in building the measurement set-up; N. Clay for fabrication support; K.-C. Fong, T. Heinz, A. Young and A.van der Zande for helpful comments. P.K. and J.H. acknowledge Air Force Office of Scientific Research Grant No. MURI FA955009-1-0705. A.H.M. was supported by the DOE Division of Materials Sciences and Engineering under Grant DE-FG03-02ER45958, and by the Welch Foundation under Grant TBF1473. P.K. acknowledges support from DOE (DE-FG02-05ER46215) for performing experiments and data analysis.
Funding Information:
The authors thank N. Cooper, I. Aleiner, B. Skinner and G. Steele for helpful discussions; D. Heinz and A. Young for help in building the measurement set-up; N. Clay for fabrication support; K.-C. Fong, T. Heinz, A. Young and A.van der Zande for helpful comments. P.K. and J.H. acknowledge Air Force O_ce of Scientific Research Grant No. MURI FA955009-1-0705. A.H.M. was supported by the DOE Division of Materials Sciences and Engineering under Grant DE-FG03-02ER45958, and by theWelch Foundation under Grant TBF1473. P.K. acknowledges support from DOE (DE-FG02-05ER46215) for performing experiments and data analysis.
Publisher Copyright:
© 2016 Macmillan Publishers Limited.
PY - 2016/3/1
Y1 - 2016/3/1
N2 - The classical picture of the force on a capacitor assumes a large density of electronic states, such that the electrochemical potential of charges added to the capacitor is given by the external electrostatic potential and the capacitance is determined purely by geometry. Here we consider capacitively driven motion of a nano-mechanical resonator with a low density of states, in which these assumptions can break down. We find three leading-order corrections to the classical picture: the first of which is a modulation in the static force due to variation in the internal chemical potential; the second and third are changes in the static force and dynamic spring constant due to the rate of change of chemical potential, expressed as the quantum (density of states) capacitance. As a demonstration, we study capacitively driven graphene mechanical resonators, where the chemical potential is modulated independently of the gate voltage using an applied magnetic field to manipulate the energy of electrons residing in discrete Landau levels. In these devices, we observe large periodic frequency shifts consistent with the three corrections to the classical picture. In devices with extremely low strain and disorder, the first correction term dominates and the resonant frequency closely follows the chemical potential. The theoretical model fits the data with only one adjustable parameter representing disorder-broadening of the Landau levels. The underlying electromechanical coupling mechanism is not limited by the particular choice of material, geometry, or mechanism for variation in the chemical potential, and can thus be extended to other low-dimensional systems.
AB - The classical picture of the force on a capacitor assumes a large density of electronic states, such that the electrochemical potential of charges added to the capacitor is given by the external electrostatic potential and the capacitance is determined purely by geometry. Here we consider capacitively driven motion of a nano-mechanical resonator with a low density of states, in which these assumptions can break down. We find three leading-order corrections to the classical picture: the first of which is a modulation in the static force due to variation in the internal chemical potential; the second and third are changes in the static force and dynamic spring constant due to the rate of change of chemical potential, expressed as the quantum (density of states) capacitance. As a demonstration, we study capacitively driven graphene mechanical resonators, where the chemical potential is modulated independently of the gate voltage using an applied magnetic field to manipulate the energy of electrons residing in discrete Landau levels. In these devices, we observe large periodic frequency shifts consistent with the three corrections to the classical picture. In devices with extremely low strain and disorder, the first correction term dominates and the resonant frequency closely follows the chemical potential. The theoretical model fits the data with only one adjustable parameter representing disorder-broadening of the Landau levels. The underlying electromechanical coupling mechanism is not limited by the particular choice of material, geometry, or mechanism for variation in the chemical potential, and can thus be extended to other low-dimensional systems.
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U2 - 10.1038/nphys3576
DO - 10.1038/nphys3576
M3 - Article
AN - SCOPUS:84959376247
VL - 12
SP - 240
EP - 244
JO - Nature Physics
JF - Nature Physics
SN - 1745-2473
IS - 3
ER -