Dissipation due to tunneling two-level systems in gold nanomechanical resonators

We present measurements of the dissipation and frequency shift in gold nanomechanical resonators at temperatures down to 10 mK. The resonators were fabricated as doubly clamped beams above a GaAs substrate and actuated magnetomotively. Measurements on beams with frequencies 7.95 and 3.87 MHz revealed that from 30 to 500 mK the dissipation increases with temperature as $T^{0.5}$, with saturation occurring at higher temperatures. The relative frequency shift of the resonators increases logarithmically with temperature up to at least 400 mK. Similarities with the behavior of bulk amorphous solids suggest that the dissipation in our resonators is dominated by two-level systems.

Figure 1

(Color online) (a) Detection setup used to perform the magnetomotive measurements. A SEM micrograph of one of the samples is also shown. (b) Typical ring-down data for the 3.87 MHz device taken at 1 T, the smooth lines are exponential fits to the envelope (the data sets are displaced for clarity). (c) $Q^{-1}$ versus $B^2$ for the 3.87 MHz device at three different temperatures; the lines are linear fits to the data.

Figure 2

(Color online) 7.95 MHz resonator: (a) $Q_0^{-1}$ as a function of temperature, on a log-log scale (main plot) and a linear scale (inset). The full line (curve in the inset) is a guide to the eye $\propto T^{0.5}$. The dashed line is the average of the five points with the highest temperatures. (b) $\delta f/f_0$, as a function of temperature. The line is a logarithmic fit to the data marked with full circles (i.e., excluding the two points below 30 mK). Note that the data were collected in two runs and a frequency jump of 20.4 kHz that occurred during thermal cycling between the runs has been subtracted from the low-temperature data.

Figure 3

(Color online) 3.87 MHz resonator: (a) $Q_0^{-1}$ as a function of temperature, on a log-log scale (main plot) and a linear scale (inset). The full line (curve in inset) is a guide to the eye $\propto T^{0.5}$. The dashed line is the average of the five points with the highest temperatures. Only the 1 T ring-down data are shown in the inset for clarity. (b) $\delta f/f_0$, as a function of temperature (cw data at 2 T). The line is a logarithmic fit to the subset of data points marked with full circles.