Washboard Frequency Research Articles

Modulating Friction by the Phase of the Vertical Vibrational Excitation at Washboard Frequency.

Applying external vibrations at the resonant frequencies of the frictional system has been a highly effective approach to suppress friction but usually requires additional energy consumption. In this study, we find that in addition to exerting the vibration at the resonant frequency of the frictional system, the friction force on the atomically flat silicon surface can also present a local minimum when the oscillation frequency of the vertical vibrational excitation equals the washboard frequency with respect to the sliding velocity. Moreover, compared with the additional energy consumption at the resonant frequency, applying vertical vibrational excitation at the washboard frequency requires much less energy consumption. The study further shows that the friction force under the washboard frequency can be effectively mediated depending on how the initial phase angle of the vertical vibrational excitation affects the effective substrate potential barrier at the slip moment of the tip. We have also extended the proposed friction modulation technique on atomically flat surfaces to periodic textured surfaces and confirmed its practicality and great potential for controlling friction.

Noise and thermal depinning of Wigner crystals

We examine changes in the depinning threshold and conduction noise fluctuations for driven Wigner crystals in the presence of quenched disorder. At low temperatures there is a well defined depinning threshold and a strong peak in the noise power with noise characteristics. At higher temperatures, the depinning threshold shifts to lower drives and the noise, which is also reduced in power, becomes more white in character. At lower temperatures, a washboard frequency appears when the system depins elastically or forms a moving smectic state; however, this washboard signal is strongly reduced for higher temperatures and completely disappears above the melting temperature of a system without quenched disorder. Our results are in good agreement with recent transport and noise studies for systems where electron crystal depinning is believed to arise, and also show how noise can be used to distinguish between crystal, glass, and liquid phases.

Decoding the phonon transport of structural lubrication at silicon/silicon interface

Although the friction characteristics under different contact conditions have been extensively studied, the mechanism of phonon transport at the structural lubrication interface is not extremely clear. In this paper, we firstly promulgate that there is a 90°-symmetry of friction force depending on rotation angle at Si/Si interface, which is independent of normal load and temperature. It is further found that the interfacial temperature difference under incommensurate contacts is much larger than that in commensurate cases, which can be attributed to the larger interfacial thermal resistance (ITR). The lower ITR brings greater energy dissipation in commensurate sliding, and the reason for that is more effective energy dissipation channels between the friction surfaces, making it easier for the excited phonons at the washboard frequency and its harmonics to transfer through the interface. Nevertheless, the vibrational frequencies of the interfacial atoms between the tip and substrate during the friction process do not match in incommensurate cases, and there is no effective energy transfer channel, thus presenting the higher ITR and lower friction. Eventually, the number of excited phonons on contact surfaces reveals the amount of frictional energy dissipation in different contact states.

Velocity-dependent phononic friction in commensurate and incommensurate states

We investigate that multiple friction peaks occur with an increase in velocity in commensurate and incommensurate states between graphene layers. Fast Fourier transform analysis of instantaneous friction force confirms that frictional spectrum mainly distributes at washboard frequency of tip and its harmonics. When washboard frequency approaches natural frequency of tip and its fractional frequencies, resonance will occur in both contact cases, resulting in friction peaks. Further observations indicate that phonon spectra of tip and substrate match in commensurate state, thereby establishing effective energy dissipation channels; however, phonon spectra do not match in incommensurate state. Finally, we deduce a theoretical model for calculating number of excited phonons and quantitatively explain friction discrepancy in different contact states and velocities.

Nonlinear dynamics, avalanches, and noise for driven Wigner crystals

We consider the driven dynamics of Wigner crystals interacting with random disorder. Using numerical simulations, we find a rich variety of transport phenomena as a function of charge density, drive, and pinning strength. For weak pinning, the system forms a defect free crystal that depins elastically. When the pinning is stronger, a pinned glass phase appears that depins into a filamentary flow state, transitions at higher drives into a disordered flow phase, and finally forms a moving smectic. Within the filamentary flow phase, the conduction curves can show switching dynamics as well as negative differential conductivity in which switching events cause some flow channels to be blocked. The velocity noise in the filamentary flow regime exhibits narrow band characteristics due to the one-dimensional nature of the motion, while the moving smectic has narrow band velocity noise with a washboard frequency. In the disordered flow state, the noise power reaches a peak value and the noise has a $1/f$ character. Our transport results are consistent with recent experimental transport studies in systems where Wigner crystal states are believed to be occurring. Below the conduction threshold, we find that avalanches with a power law size distribution appear when there are sudden local rearrangements of charges from one pinned configuration to another.

Effects of the normal load on the excited phonons in atomic friction

Although the quantitative relationship between the normal load and the induced friction force has been established from the phenomenological laws of friction, it does not answer the question of how mechanical energy is dissipated into heat by exciting phonons. In this study, the effects of normal load on the friction force of a relatively sliding graphene film are investigated by molecular dynamics simulations. The results show that the excited phonon modes couple with the resonant frequency of the entire frictional system, and the enhancement of the normal load is equivalent to the increase of the resonant frequency of the frictional system. It is also found that the relative intensity of the resonant peaks in the vibrational density of states is a key factor affecting the friction force, which can explain the variation of friction force with the normal load. Moreover, under a certain normal load, the friction force can reach its maximum value when the washboard frequency equals the resonant frequency of the frictional system. Our work establishes the relationship between the normal load and the frictional force from the phonon level, which provides a method for regulating atomic friction and energy dissipation by considering both washboard frequency and contact resonant frequency.

Frictional Energy Dissipation due to Phonon Resonance in Two-Layer Graphene System

The frictional energy dissipation mechanism of a supported two-layer graphene film under the excitation of the model washboard frequency is investigated by molecular dynamics simulations. The results show that two local maxima in the energy dissipation rate occur at special frequencies as the excitation frequency increases from 0.1 to 0.6 THz. By extracting the vibrational density of states of the graphene, it is found that large numbers of phonons with frequencies equal to the excitation frequency are produced. A two-degree of freedom mass-spring model is proposed to explain the molecular dynamics results. Since the washboard frequency for atomically surfaces in wearless dry friction can be analogous to the excitation frequency in the molecular dynamics simulations, our study indicates that the phonon resonance would occur once the washboard frequency is close to the natural frequency of the frictional system, leading to remarkable local maxima in energy dissipation.Graphical Abstract

Phononic origin of structural lubrication

Atomistic mechanisms of frictional energy dissipation have attracted significant attention. However, the dynamics of phonon excitation and dissipation remain elusive for many friction processes. Through systematic fast Fourier transform analyses of the frictional signals as a silicon tip sliding over a graphite surface at different angles and velocities, we experimentally demonstrate that friction mainly excites non-equilibrium phonons at the washboard frequency and its harmonics. Using molecular dynamics simulations, we further disclose the phononic origin of structural lubrication, i.e., the drastic reduction of friction force as the contact angle between two commensurate surfaces changes. In commensurate contacting states, friction excites a large amount of phonons at the washboard frequency and many orders of its harmonics that perfectly match each other in the sliding tip and substrate, while for incommensurate cases, only limited phonons are generated at mismatched washboard frequencies and few low order harmonics in the tip and substrate.

Nanoscale friction behavior of monolayer MoxW1−xS2 alloy

We synthesized MoxW1−xS2 alloy by chemical vapor deposition. Raman characterization results showed that the sample is a monolayer with a special structure which transforms from MoS2 to WS2. Atomic force microscopy measurements suggested that the friction force decreases from MoS2 region to WS2 region. Molecular dynamics simulations verified that interfacial interaction is the determining factor resulting in the variation in the friction properties of monolayer MoxW1−xS2. Green’s function calculations demonstrated that phonons are excited at both washboard frequency and its harmonics. Besides, the number and total energy of the excited phonons were calculated. The decreasing of the number and total energy of the excited phonons with the weakening interfacial interaction, leading to the decreasing dissipated energy and reduced friction force.

Resonance in Atomic-Scale Sliding Friction.

Friction represents a major energy dissipation mode, yet the atomistic mechanism of how friction converts mechanical motion into heat remains elusive. It has been suggested that excess phonons are mainly excited at the washboard frequency, the fundamental frequency at which relative motion excites the interface atoms, and the subsequent thermalization of these nonequilibrium phonons completes the energy dissipation process. Through combined atomic force microscopy measurements and atomistic modeling, here we show that the nonlinear interactions between a sliding tip and the substrate can generate excess phonons at not only the washboard frequency but also its harmonics. These nonequilibrium phonons can induce resonant vibration of the tip and lead to multiple peaks in the friction force as the tip sliding velocity ramps up. These observations disclose previously unrecognized energy dissipation channels associated with tip vibration and provide insights into engineering friction force through adjusting the resonant frequency of the tip-substrate system.

Radiofrequency generation by coherently moving fluxons

A lattice of Abrikosov vortices in type II superconductors is characterized by a periodic modulation of the magnetic induction perpendicular to the applied magnetic field. For a coherent vortex motion under the action of a transport current, the magnetic induction at a given point of the sample varies in time with a washboard frequency fWB = v/d, where v is the vortex velocity and d is the distance between the vortices in the direction of motion. Here, by using a spectrum analyzer connected to a 50 nm-wide Au nanowire meander near the surface of a superconducting Nb film, we detect an ac voltage induced by coherently moving fluxons. The voltage is peaked at the washboard frequency, fWB, and its subharmonics, fTOF = fWB/5, determined by the antenna width. By sweeping the dc current value, we reveal that fWB can be tuned from 100 MHz to 1.5 GHz, thereby demonstrating that patterned normal metal/superconductor nanostructures can be used as dc-tunable generators operating in the radiofrequency range.

Optimization of the THz radiation from superconductor at non-laminar regime

The THz radiation due to the flux flow in a superconductor slab at non-laminar regime has been investigated and the radiated power spectrum has been calculated. The parameter (τ) is defined to show amount of non-laminarity. The results reveal that for small values of τ, the system radiated at the harmonics of famous washboard frequency. However, for large values of τ, the radiation spectrum will be changed and for extreme values of τ, the peaks will be flat. Therefore the washboard picture is not valid anymore. The results show that the radiation power is optimum for the special value of τ. Also, the results compared with other theoretical and experimental data.

Shapiro steps for skyrmion motion on a washboard potential with longitudinal and transverse ac drives

We numerically study the behavior of two-dimensional skyrmions in the presence of a quasi-one-dimensional sinusoidal substrate under the influence of externally applied dc and ac drives. In the overdamped limit, when both dc and ac drives are aligned in the longitudinal direction parallel to the direction of the substrate modulation, the velocity-force curves exhibit classic Shapiro step features when the frequency of the ac drive matches the washboard frequency that is dynamically generated by the motion of the skyrmions over the substrate, similar to previous observations in superconducting vortex systems. In the case of skyrmions, the additional contribution to the skyrmion motion from a non-dissipative Magnus force shifts the location of the locking steps to higher dc drives, and we find that the skyrmions move at an angle with respect to the direction of the dc drive. For a longitudinal dc drive and a perpendicular or transverse ac drive, the overdamped system exhibits no Shapiro steps; however, when a finite Magnus force is present we find pronounced transverse Shapiro steps along with complex two-dimensional periodic orbits of the skyrmions in the phase-locked regimes. Both the longitudinal and transverse ac drives produce locking steps whose widths oscillate with increasing ac drive amplitude. We examine the role of collective skyrmion interactions and find that additional fractional locking steps occur for both longitudinal and transverse ac drives. At higher skyrmion densities, the system undergoes a series of dynamical order-disorder transitions, with the skyrmions forming a moving solid on the phase locking steps and a fluctuating dynamical liquid in regimes between the steps.

THz Radiation of Vortex Flux Flow in Superconductor Media at the Approximately Non-Laminar Regime

The electromagnetic radiation due to flux flow from type II superconductors has been investigated. The effect of small non-laminar flux motion is simulated, and the radiation power is calculated and analyzed. The calculations show that for a little non-laminar effect, the harmonic frequencies do not change, but the power will be changed proportional to this effect. Therefore, the system will radiate at the harmonics of the famous washboard frequency with a widening of its frequency. Considering this unwanted effect is necessary for optimization and modeling of flux flow based devices, especially THz devices. The behavior of the obtained power is similar to the experimental results.

A Superconductor THz Modulator Based on Vortex Flux Flow

A terahertz modulator based on the Type-II superconductor flux flow oscillator has been proposed. Analytical calculations are presented and the effects of intrinsic and extrinsic parameters such as disorder strength of crystal, penetration depth, frequency, and amplitude of the modulated current on the radiation power spectrum have been studied. The proposed structure also exhibits a mixer-like behavior, in the sense that its output harmonics range from the washboard frequency up to the superconductor gap frequency, so the input signal is practically mixed with the washboard frequency and its harmonics. The modulation index for each harmonic of this modulator has also been investigated. This well-featured modulator has a potential to be used in next-generation terahertz integrated transceivers.

Time resolved study of non-coherent oscillations produced by a moving charge density wave in -

A time resolved study of the signal produced by a moving charge density wave shows, along with the fundamental (washboard frequency) and its harmonics, the presence of a rather strong non-coherent component. In this work we report on a phase analysis of non-coherent component and its relation to the narrow band noise signal.

Electromagnetic Radiation from Vortex Flow in Type-II Superconductors

We show that a moving vortex lattice, as it comes to a crystal edge, radiates into a free space the harmonics of the washboard frequency, omega(0)=2pi v/a, up to a superconducting gap, Delta/variant Planck's over 2pi. Here v is the velocity of the vortex lattice and a is the intervortex spacing. We compute radiation power and show that this effect can be used for the generation of terahertz radiation and for characterization of moving vortex lattices.

Effects of magnetic excitations on the I–V characteristic of magnetic superconductors

The coupling between magnetic and superconducting degrees of freedom in magnetic superconductors leads to subgap resonances in the I–V characteristic. We study two mechanisms of coupling: the spin-assisted cotunneling (in layered magnetic superconductors) and the interaction mediated by the ac magnetic field of a moving vortex lattice. The latter mechanism we study in both layered and moderately anisotropic superconductors. At resonance conditions the dynamics of vortices in magnetic superconductors changes drastically, resulting in strong peaks in the dc I–V characteristic at voltages at which the washboard frequency of vortex lattice matches the spin wave frequency ω s ( g ) , where g are the reciprocal vortex lattice vectors. We show that for a high enough washboard frequency, peaks in the I–V characteristic in borocarbides and cuprate layered magnetic superconductors are strong enough to be observed on the quasiparticle background. To cite this article: M. Hruška, L.N. Boulaevskii, C. R. Physique 7 (2006).

Spectroscopy of Magnetic Excitations in Magnetic Superconductors Using Vortex Motion

In magnetic superconductors a moving vortex lattice is accompanied by an ac magnetic field which leads to the generation of spin waves. At resonance conditions the dynamics of vortices in magnetic superconductors changes drastically, resulting in strong peaks in the dc I-V characteristics at voltages at which the washboard frequency of the vortex lattice matches the spin wave frequency omegaS(g), where g are the reciprocal vortex lattice vectors. We show that if the washboard frequency lies above the magnetic gap, measurement of the I-V characteristics provides a new method to obtain information on the spectrum of magnetic excitations in borocarbides and cuprate layered magnetic superconductors.

Numerical observation of the washboard noise of a driven vortex lattice in high- Tc superconductors

The dynamics of vortex matter in high- T c superconductors is studied numerically. The power spectra of voltage noise are calculated for a fixed current at various temperatures. Well-developed peaks appear evidently at the washboard frequency below the melting temperature. It follows that the washboard noise is observed in three-dimensional numerical simulations.