Nanomechanical damping via electron-assisted relaxation of two-level systems

Abstract

We report on measurements of dissipation and frequency noise at millikelvin temperatures of nanomechanical devices covered with aluminum. A clear excess damping is observed after switching the metallic layer from superconducting to the normal state with a magnetic field. Beyond the standard model of internal tunneling systems coupled to the phonon bath, here we consider the relaxation to the conduction electrons together with the nature of the mechanical dispersion laws for stressed/unstressed devices. With these key ingredients, a model describing the relaxation of two-level systems inside the structure due to interactions with electrons and phonons with well separated timescales captures the data. In addition, we measure an excess 1/f -type frequency noise in the normal state, which further emphasizes the impact of conduction electrons.

Soft-clamped silicon nitride string resonators at millikelvin temperatures

“…Further cooling to the base temperature of the refrigerator (T mc = 30 mK) leads to another steep increase of Q for the localized mode of device C reaching up to Q = 2 × 10 9 . The heating experiment has exclusively been conducted with device C. A similar increase has been reported for metal-coated silicon strings [26] and with silicon nitride membrane resonators [15][16][17][18], but its microscopic origin remains unclear. To confirm the validity of our result, we performed careful studies as a function of average optical power and mixing chamber temperature that we present in the following.…”

“…The comparison of experimental data to the STM has produced a variety of results in the past. With a range of different materials, measurements of quasi-onedimensional devices were approximated as Γ m ∝ T ν with ν = 1/3 [35][36][37], ν = 2/3 [38], or ν = 1 [26,32]. A saturation of Γ m towards low temperatures was accounted for by the form Γ m ∝ (1 + (T /T 0 ) ν ), with the free parameters T 0 = 0.3 K and ν = 1.6 [22,30].…”

Dimensional control of tunneling two level systems in nanoelectromechanical resonators

“…At the lowest temperatures, coupling between different TTLS may also play a role [40]. This wide range of conditions leads to the qualitatively different behavior of damping in mechanical resonators hosting TTLS observed in different works [19][20][21][22][23][24][25][26][27][28][29][30][31][32][41][42][43]. Our work clearly demonstrates the transition from one-dimensional to two-dimensional behavior with increasing device size in devices supporting flexural phonon modes.…”

“…where N F is the electron density of states at the Fermi energy (accounting for both spin orientations), K is a coupling constant describing the interaction between TTLS and electrons and V e ∼ 1 nm 3 is the interaction volume of electrons. Inserting values d = 100 nm and K = 0.1 eV [30], we get Γ el /Γ rel,2D ∼ 10 5 . Thus, the electronic contribution should dominate if TTLS couple to electrons.…”

“…While many experimental works address TTLS in NEMS and MEMS resonators with reduced dimensions, Refs. [19][20][21][22][23][24][25][26][27][28][29][30][31][32], the experimental demonstration and matching with the theory, both in 1D and in 2D cases, in the devices of the same type have so far been missing.…”