Washboard Frequency Research Articles

Vortex matter driven through mesoscopic channels

The dynamics of vortex matter confined to mesoscopic channels has been investigated by means of mode locking experiments. When vortices are coherently driven through the potential provided by static vortices pinned in the channel edges, interference between the washboard frequency of the moving vortex lattice and the frequency of the superimposed rf-drive causes (Shapiro-like) steps in the dc- I– V curves. The position of the voltage steps uniquely determines the number of moving rows in each channel. It also shows how the frustration between row spacing and channel width behaves as a function of magnetic field. Maxima in flow stress (∼ I c) occur at mismatch conditions. They are related to the traffic-jam-like flow impedance caused by the disorder in the edges. At higher fields, near the 2D-melting line B m( T), the mode-locking interference characteristic for crystalline motion, strongly depends on the velocity, i.e. the applied frequency at which the vortex motion is probed. The minimum velocity at which coherent motion could be observed, diverges when the melting line is approached from below. Above the melting line interference is absent for any frequency. These observations give the first direct evidence for a dynamic phase transition of vortex matter driven through a disorder potential as predicted by Koshelev and Vinokur.

Mode-locking and dynamic melting of vortex matter driven through mesoscopic channels

We investigated the dynamics of vortex matter confined to mesoscopic channels by means of mode locking experiments. When vortices move coherently through the pinning (shear) potential provided by static vortices in the channel edges, interference between the washboard frequency of the lattice and the frequency of superimposed rf-currents causes (Shapiro-like) steps in the dc-IV curves. These steps allow to trace directly how the number of moving rows in each channel and the frustration between row spacing and channel width, varies with magnetic field. The flow stress (~ I,) surprisingly exhibits maxima for mismatching (defective) structures, originating from traftic-jam-like flow due to disorder in the edges. We then focus on the behavior for higher fields, approaching the 2D melting field Bm. In this regime the presence of the interference phenomenon, characteristic for crystalline motion, strongly depends on the velocity (applied frequency) at which vortices are probed. The minimum velocity to observe coherent, solid-like motion is found to diverge when the field is increased towards $E_{''}$ above which the interference is absent for any frequency. This provides the first direct evidence for a velocity dependent, dynamic phase transition of vortex matter moving through disorder, as predicted by Koshelev and Vinokur.

Collective motion of Josephson vortex lattice in long stacked junction fabricated from Bi-2212 whisker

We study the I– V characteristics of long Bi-2212 stacked junctions in the Josephson flux-flow regime in parallel magnetic field ( B∥ b). We measure both voltage position of the flux-flow step, V ff, corresponding to the maximum velocity of Josephson vortex lattice, and the flux-flow resistivity, ρ ff, as a function of magnetic field B=0.1–4 T. We found plateau-like features of constant V ff on dependence V ff( B) corresponding to washboard frequencies 600 GHz and 3 THz. We discuss these features as mode locking of washboard frequency with active intrinsic modes of the stack. We found also that field dependence of flux-flow resistivity can be well described by a recent model [A. Koshelev, Phys. Rev. B 62 (2000) R3616] which takes into account both out-of-plane and in-plane dissipation.

Conduction noise in Bi 2Sr 2CaCu 2O y

We investigated the velocity fluctuations of driven vortices in Bi 2Sr 2CaCu 2O y (Bi2212) by means of the conduction noise measurement. Velocity modulations of the driven vortices at the washboard frequency were observed below the first-order vortex lattice phase transition (FOT). This is the first observation of the washboard modulation in the flow regime of the driven vortices system, which strongly supports the well-development of the coherece in the vortices around the FOT.

Transport results from untwinned YBCO: Washboard frequency of the vortex lattice, and the quasiparticle mean free path

The “washboard frequency” ω of the moving vortex lattice in untwinned YBa2 Cu3 O6.93 may be observed through mode-locking to an externally applied ac current of frequency ωext. The interference between ω and ωext results in jumps in the dc current-voltage characteristics when ω and ωext are harmonically related1. The interference effect disappears in the vortex liquid state. The Hall conductivity σxy below Tc in YBCO contains contributions2 from a positive quasiparticle (qp) term (∼H) and a negative vortex term (∼1/H). The qp term is surprisingly large well below Tc and implies a large gap anisotropy and a long qp mean free path (mfp). The thermal Hall effect3 κxy is closely related to the qp σxy; κxy is produced by asymmetric scattering of qp by pinned vortices. The qp mfp at H = 0, extracted from σxy and extended to low T by κxy, increases remarkably from 90 A at Tc to more than 0.5μm at 22 K.

AC and DC responses of the sliding CDW in the low-temperature switching state of K 0.3MoO 3

The dc response and ac response up to 15 MHz were studied in the low-temperature switching state in K 0.3MoO 3. The conductivity of the switched-on state increases with decreasing temperature. This suggests that the dominant mechanism of the damping for sliding charge-density wave (CDW) in the highly conductive state in this temperature region is different from that in the higher-temperature sliding state. The ac conductivity of the sliding state in this region exhibits a Drude-like structure, whose crossover frequency is the so-called washboard frequency, besides the peak structure due to the interference effect between the external rf field and the inherent periodicity of the CDW. This structure represents the inherent ac response of the sliding CDW in this region.

Noise, intermittency, and mode locking in sliding-charge-density-wave conductors.

Noise-induced intermittency is observed as a precursor to mode locking of the washboard frequency to an external ac field in the charge-density-wave conductor Nb${\mathrm{Se}}_{3}$. The experimental results illustrate that mode locking proceeds via a competition between the deterministic dynamics and a stochastic broad-band $\frac{1}{f}$-like noise.

Electric Response of Sliding CDW in Blue Bronzes

The narrow band noise and pulse response measurements were done in the blue bronzes (K0.3MoO3, Rb0.3MoO3) to investigate the sliding motion of CDW. From noise spectra under dc bias current, the ratio of washboard frequency to the CDW carrying current density F1/JCDW was obtained as 11 and 14 kHz/A cm-2 in K0.3MoO3 and Rb0.3MoO3 and Rb0.3MoO3, respectively. These values well agree with the calculated ones due to the washboard model (F1/JCDW=1/enλ) and indicate that the CDW is sliding uniformly in a whole crystal. The transient oscillation of voltage response to a current pulse was also observed in the same samples and their frequencies were about twice as large as those of the narrow band noise. This suggests that the CDW begins to slide through limited cross sectional area at the initial stage of sliding CDW relaxes to the uniformly sliding state, which is stationary state under dc bias current.

Low-temperature divergence of the charge-density-wave viscosity in K0.30MoO3, (TaSe4)2I, and TaS3.

We have measured the temperature dependence of the low-field, linear conductivity and the high-field, nonlinear conductivity resulting from charge-density-wave (CDW) motion in ${\mathrm{K}}_{0.30}$${\mathrm{MoO}}_{3}$, ${\mathrm{TaS}}_{3}$, and (${\mathrm{TaSe}}_{4}$${)}_{2}$I at zero frequency. In ${\mathrm{K}}_{0.30}$${\mathrm{MoO}}_{3}$ and (${\mathrm{TaSe}}_{4}$${)}_{2}$I, the nonlinear conductivity has a thermally activated behavior over an extended temperature range with activation energies which are nearly equal to that of the linear portion of the conductivity. In ${\mathrm{TaS}}_{3}$ the analysis is more complicated due to a large maximum in the threshold field, perhaps resulting from a commensurate-incommensurate transition, near 75 K. In ${\mathrm{TaS}}_{3}$, the nonlinear fraction of the conductivity has the same temperature dependence as the linear portion over a limited temperature range. In all materials the nonlinear conductivity vanishes at low temperatures. The charge carried by the CDW, measured by the current dependence of the ``washboard frequency,'' is relatively constant as function of temperature. These results indicate that viscous forces resulting from low-frequency damping of the CDW motion diverge as the temperature is lowered. We have also calculated the temperature dependence of the CDW relaxation time and static dielectric constant using experimental parameters. The excellent agreement attained gives strong support to a classical description of CDW transport in these materials.