Quantum friction of micromechanical resonators at low temperatures

Dissipation of micro- and nanoscale mechanical structures is dominated by quantum-mechanical tunneling of two-level defects intrinsically present in the system. We find that at high frequencies-usually, for smaller, micron-scale structures-a novel mechanism of phonon pumping of two-level defects gives rise to weakly temperature-dependent internal friction, Q-1, concomitant to the effects observed in recent experiments. Because of their size, comparable to or shorter than the emitted phonon wavelength, these structures suffer from superradiance-enhanced dissipation by the collective relaxation of a large number of two-level defects contained within the wavelength.     

Acoustic experiments on amorphous Pd30Zr70 and Cu30Zr70 in the superconducting and the normal state

Measurements of internal friction and sound velocity of amorphous Pd₃₀Zr₇₀ and Cu₃₀Zr₇₀ around 1 kHz and of Pd₃₀Zr₇₀ around 1 GHz are presented for both the superconducting and the normal state. Our experiments reveal several serious discrepancics with the predictions of the Tunneling Model and its extension to metallic glasses. Particularly from internal friction we conclude that the density of states of the tunneling systems is affected by the presence of conduction electrons. We discuss our results on the basis of recent theories which consider a slowing down of the tunneling motion due to the interaction with conduction electrons.Dedicated to K. Dransfeld on the occasion of his 60th birthday     

Acoustic properties of amorphous silica between 1 and 500 mK

We have made reliable measurements of the sound velocity delta v/v(0) and internal friction Q(-1) in vitreous silica at 1.03, 3.74, and 14.0 kHz between 1 mK and 0.5 K. In contrast with earlier studies that did not span as wide a temperature and frequency range, our measurements of Q(-1) reveal a crossover (as T decreases) only near 10 mK from the T(3) dependence predicted by the standard tunneling model to a T dependence predicted if interactions are accounted for. We find good fits at all frequencies using a single interaction parameter, the prefactor of the interaction-driven relaxation rate, in contrast to earlier claims of a frequency dependent power law. We also show that the discrepancy in the slopes d(delta v/v(0))/d(log(10)T) below and above the sound velocity maximum (1: -1 observed, 1: -2 predicted) can be resolved by assuming a modified distribution of tunneling states.     

Elastic properties of several amorphous solids and disordered crystals below 100 K

We have measured the internal friction and speed of sound variation at temperatures between 60 mK and room temperature for amorphous CdGeAs₂, Polystyrene, and Stycast 2850FT epoxy, and the disordered crystals (ZrO₂)_0.89(CaO)_0.11 and (CaF₂)_0.74(LaF₃)_0.26. A comparison of our results with an extensive review of previously published data shows a remarkable similarity in the internal friction of disordered solids below ～5 K. The low temperature elastic behavior of these solids is adequately described by the standard tunneling model, from which one finds a nearly universal density of tunneling states for glasses. Internal friction above ～10 K for different materials, however, displays a wide range of magnitudes and temperature dependence that is far from universal. Attempts to directly link the tunneling states observed by internal friction at low temperatures to configurational states of localized oscillators existing at high temperatures must take into account this striking variation among disordered solids above 10 K.     

Phonon transport in superconducting EuBa2Cu3O7−x

We have measured the thermal conductivity, Young modulus sound velocity and internal friction of a polycrystalline sample of the ceramic superconductor EuBa₂Cu₃O_7-x. The low temperature data can be quantitavely understood assuming the interaction of phonons with tunneling systems.     

On the low-frequency current 1f noise in metals

The spectral density of the resistivity noise caused by those relaxation mechanisms of the defects which are responsible for the low-frequency internal friction is calculated. The $\text{1}\text{f}$ noise is related to the magnitude of the background in the internal friction spectrum of the metal. The current noise arising from two-level tunneling systems is also evaluated.     

鋼中含氫所引起的内耗峯

钢的内部发裂已经公认为与钢中的氢气有关。现有的理论认为这是由于氢气聚集于钢中的内部缺陷产生破裂压力所引起,然而关于缺陷的性质和引起内部发裂的详细机构迄今还没有明确的了解。本文尝试用内耗测量的方法来研究这个问题。初步实验的结果指出:(1)氢在钢中可以引起内耗峰(将内耗表示为测量温度的函数时);(2)轻微冷加工或保温对于内耗峰的颠值温度有着显著的影响,这表示所得的内耗峰与钢中的缺陷和应力状态有关系;(3)所得的内耗峰表现有反常的振幅效应,即在一定的观测温度时,如将内耗表示为外加应力的函数,则也得到一个内耗峰。这与本文作者之一以前在铝铜合金中所观测到的反常内耗峰的性质和表现相同,因而所得的内耗峰可能是由于氢与钢中的原子脱节的交互作用所引起来的。     

Low frequency elastic properties of neutron-irradiated quartz. Comparison with glasses

Neutron-irradiated quartz is a promising model system to learn more about the low-energy excitations (tunneling states) in vitreous silica and in similar glasses. We present the first systematic study of the elastic properties of neutron-irradiated quartz at low frequencies and very low temperatures. Using the vibrating reed technique at frequencies of several kHz we have measured the sound velocity and internal friction of six quartz crystals irradiated with different neutron doses over a wide range of temperatures (7 mK-300 K). The results are analyzed using the tunneling model and several extensions of this theory. Comparisons are made with recent low-frequency measurements on normal and compacted vitreous silica and with ultrasound experiments on neutron-irradiated quartz. Received 23 October 1998     

扩展位错低频内耗的模型

本文提出面心立方合金中扩展位错引起低频内耗峰的一个模型,用来解释高浓度Cu-Al和Cu-Zn合金经过冷加工后在210K附近出现的弛豫型内耗峰(测量频率约为1Hz)。文中指出,扩展位错在外力作用下的运动,可以分解为相对运动(两个部分位错之间的相对位移)和整体运动(扩展位错中心的位移)。除了考虑两个部分位错之间交互作用引起的回复力和位错线张力引起的回复力以外,本文引入了邻近位错之间长程交互作用引起的回复力,并且论证了这种回复力只影响扩展位错的整体运动,但不影响其相对运动。扩展位错的相对运动和整体运动,分别导致相对运动内耗峰和整体运动内耗峰。二者峰温相近。实验上观察到的内耗峰是这两个内耗峰的叠加。本文模型的推论与实验结果相符。 关键词：     

Innere Reibung durch Mitschleppen von Punktfehlern. II

The internal friction caused by dragging of mobile point defects is examined for the case of strong point defect dislocation interaction. For the amplitude independent internal friction and for the amplitude dependent internal friction with low point defect concentration this yields qualitatively the same results as the opposite case of weak interaction. For large point defect concentration there is an additional damping by hysteresis.     

Chemical reaction rates and solvent friction

The role of the dynamic solvent friction in influencing the rates of chemical reactions in solution is described. Features considered include (a) the bias of the reaction coordinate toward a direction of lesser friction in the diffusive limit, (b) the importance of frequency-dependent friction in atom transfers, tunneling reactions and isomerizations, (c) the dynamic nonequilibrium solvation in charge transfers which leads to a polar solvent molecule reorientation time dependence for the rate, and (d)the importance of internal degrees of freedom in the location of the Kramers turnover for isomerizations.     

Sound propagation in metallic glasses—a new look at the tunneling model

A variety of amorphous metals exhibit a characteristic behavior in their acoustic properties at low frequencies which differs from the predictions of the standard tunneling model. We point out that a lower cut-off _min for the tunnel matrix element, which is needed for consistency of the tunneling model, leads to an upper bound on relaxation times induced by the conduction electrons. We derive explicit expressions for the velocity shift and internal friction for the normalconducting and superconducting case. It is shown that a maximum relaxation time plays an essential role at audio frequencies. The corresponding change of the acoustic properties is in qualitative agreement with vibrating reed experiments.     

INTERNAL FRICTION AND ULTRASONIC ATTENUATION RELATED TO CARRIERS IN HIGH Tc SUPERCONDUCTORS

For both BiSrCaCuO and TlBaCaCuO samples, internal frictions (Q^-1) in the kHz range reveal a plateau (Q^-1_p) above T_c and a rapid drop below T_c with the turning points located just at T_c for various samples with different T_c. This anomaly cannot be observed in non-superconducting samples. The ultrasonic attenuation (α) in TlBaCaCuO displays similar results to the internal friction. Moreover, it is discovered that the Q^-1_p is nearly proportional to the carrier density for Y(Pr)BaCuO and Gd(Pr)BaCuO with different Pr contents. These results show that the drop of Q^-1 and a below T_c is closely related to superconducting condensation. The Q^-1_p and α_p can be explained using coupling-model of carriers with local dynamic distortion because high T_c superconductors are strong-correlation systems. Furthermore, by taking account of the smearing of superconducting gap structure resulting from the recombination of quasi-particles and by modifying the BCS relative jump rate as S(E, E', Γ) = Re{1-Δ²/[(E-iΓ)(E'-iΓ)]}, the calculated results of internal friction and ultrasonic attenuation below T_c are in good agreement with the experimental data. The superconducting gap Δ and the damping rate Γ for both BiSrCaCuO and TlBaCaCuO have also been obtained, they are in accordance with those got by tunneling spectrum and NMR methods, etc.     

Effect of the electric current on the Casimir force between graphene sheets

The dependence of the thermal component of the Casimir force and Casimir friction between graphene sheets on the drift velocity of charge carriers in one of the sheets has been analyzed. It has been shown that the drift motion results in the measurable change in the thermal Casimir force owing to the Doppler effect. The thermal Casimir force, as well as Casimir friction, increases strongly in the case of resonant photon tunneling, when the energy of an emitted photon coincides with the excitation energy of an electron-hole pair. In the case of resonant photon tunneling, the dominant contribution to the Casimir friction even at temperatures above room temperature comes from quantum friction caused by quantum fluctuations. Quantum friction can be detected in an experiment on the friction drag between graphene sheets in a high electric field.     

Conformational changes of single molecules induced by scanning tunneling microscopy manipulation: a route to molecular switching

A detailed experimental and theoretical investigation of the processes involved in the manipulation of individual specially designed porphyrin-based molecules by scanning tunneling microscopy at low temperature is presented. On a stepped Cu(211) surface, the interaction between tip and molecule was used to locally modify in a reversible way the internal configuration of a single molecule, thus drastically changing the tunneling current passing through it. Model calculations confirm that this manipulation realizes the principle of a conformational molecular switch.     

Low temperature acoustic properties of amorphous silica and the tunneling model

Internal friction and speed of sound were measured on a-SiO2 above 6 mK using a torsional oscillator at 90 kHz, controlling for thermal decoupling, vibrational heating, background losses, and nonlinear effects. Strain amplitudes epsilon(A) = 10(-8) mark the transition between the linear and nonlinear regimes. In the former, agreement with the tunneling model was observed for both internal friction and speed of sound above 25 mK. The observed deviations in the speed of sound below 25 mK can be described with a cutoff energy of Delta(0, min)/k(B) = 6+/-0.5 mK. In the nonlinear regime, above 10 mK the behavior was typical for nonlinear harmonic oscillators, while below 10 mK different behavior was found.     

与位错和点缺陷的交互作用有关的低温内耗峰

系统研究了出现在经冷加工处理的Al-Mg固溶体中的低温内耗峰。当测量频率约为1Hz时,分别在-70℃(P_L2峰)和-50℃(P_L1峰)观察到了两个内耗峰。详细研究了镁(Mg)含量,冷加工量,冷加工模式,不同合金元素(Ga,Zn),退火等诸因素对这两个内耗峰的出现及特性的影响。得出了P_L2峰与位错和“Mg原子-双空位”对的交互作用有关以及P_L1峰与位错和“Mg原子-单空位”对的交互作用有关的结论。 关键词：     

Laser fluence dependence of the elastic properties of diamond-like carbon films prepared by pulsed-laser deposition

We studied the temperature dependence of internal friction of variety of amorphous diamond-like carbon films prepared by pulsed-laser deposition. Like the most of amorphous solids, the internal friction below 10 K exhibits a temperature independent plateau, which is caused by the atomic tunnelling states—a measure of structure disorder. In this work, we have varied the concentration of sp³ versus sp² carbon atoms by increasing laser fluence from 1.5 to 30 J/cm². Our results show that the internal friction has a nonmonotonic dependence on sp³/sp² ratio with the values of the internal friction plateaus varying between 6×10⁻⁵ and 1.1×10⁻⁴. We explain our findings as a result of a possible competition between the increase of atomic bonding and the increase of internal strain in the films, both of which are important in determining the tunneling states in amorphous solids. The importance of the internal strain in diamond-like carbon films is consistent with our previous study on laser fluence, doping, and annealing, which we will review as well. In contrast, no significant dependence of laser fluence is found in shear moduli of the films, which vary between 220 and 250 GPa.     

Low frequency acoustic and dielectric measurements on glasses

The acoustic and dielectric properties of different glasses at audio frequencies and temperatures below 1 K have been investigated with the vibrating reed and a capacitance bridge technique. We found the temperature dependence of the absorption of vitreous silica (Suprasil W) to agree with the predictions of the tunneling model which is commonly used to explain the low temperature behaviour of amorphous materials. The variation of the sound velocity and of the dielectric constant, however, shows significant deviations from the expected behaviour which cannot be accounted for by a simple modification of the model. Instead, it seems to be necessary to introduce a temperature dependence of some relevant model parameters. Moreover, at very low temperatures (T < 0.1 K) the sound velocity strongly depends on the excitation levels. The absence of this effect at higher temperatures proves that it can be ascribed to a nonlinear response of tunneling systems. Similar results were found in sound velocity measurements on a cover glass and on a superconducting metallic glass (Pd₃₀Zr₇₀, T_c = 2.6 K), which indicates that these features are a general aspect of the dynamics of tunneling states in glasses. In contrast to the insulating glasses we found that in Pd₃₀Zr₇₀ also the internal friction is strain dependent.     

Quantum stochastic synchronization

We study, within the spin-boson dynamics, the synchronization of a quantum tunneling system with an external, time-periodic driving signal. As a main result, we find that at a sufficiently large system-bath coupling strength (i.e., for a friction strength alpha > 1) the thermal noise plays a constructive role in yielding forced synchronization. This noise-induced synchronization can occur when the driving frequency is larger than the zero-temperature tunneling rate. As an application evidencing the effect, we consider the charge transfer dynamics in molecular complexes.