Yukawa particles confined in a channel and subject to a periodic potential: Ground state and normal modes

Abstract

We consider a classical system of two-dimensional (2D) charged particles, interacting through a repulsive Yukawa potential exp(−r/λ)/r, and confined in a parabolic channel that limits the motion of the particles in the y direction. Along the x direction, the particles are subject to a periodic potential. The ground-state configurations and the normal-mode spectra of the system are obtained as a function of the periodicity and strength of the periodic potential (V 0 ) and density. An interesting set of tunable ground-state configurations are found, with firstor second-order structural transitions between them. A configuration with particles aligned, perpendicular to the x direction, in each minimum of the periodic potential is obtained for V 0 larger than some critical value that has a power-law dependence on the density. The phonon spectrum of different configurations was also calculated. A localization of the modes into a small frequency interval is observed for sufficiently large strength of the periodic potential, and a tunable gap in the phonon spectrum is found as a function of V 0 .

Diffusion in a quasi-one-dimensional system on a periodic substrate

“…Previously we found that, at zero temperature with n = 1.0 and L/a 0 = 1, the particle configuration consists of two chains where its internal structure strongly depends on the strength of the periodic substrate V 0 [22]. In Fig.…”

“…Taking the same units of energy and distance from Ref. [22], i.e., E 0 = (mω 0 2 q 4 /2 2 ) 1/3 and r 0 = (2q 2 / mω 2 0 ) 1/3 , Eq. (2) can be rewritten in a dimensionless form as…”

“…The simulations were performed for = 10 and = 100, which correspond to a weakly correlated situation and a strongly correlated situation, respectively. Further, the system is defined by V 0 , L, and the particle density n, which is the ratio between the number of chains N ch and a 0 , i.e., n = N ch /a 0 , where a 0 is the average separation between particles along the chain, calculated when the substrate is not present [22], i.e., when V 0 = 0. Examples of particle positions taken over a large time interval are shown in Fig.…”

“…Inspired by our previous work on the ground state configuration of charged colloids subjected to a periodic substrate [22], we start with the simplest case where n = 0.5 and L/a 0 = 1.0 for which a single-chain configuration was found as the ordered phase. For this parameter set, exactly one particle is positioned at each minimum of the periodic potential.…”

“…1 together with the three different diffusion regimes. In a recent work [22] we studied the zero temperature ground state structures and normal mode spectra of the model system proposed in this paper. That is, we investigated a classical 2D system of charged particles interacting through a repulsive Yukawa potential, e −r/λ /r, and confined in a parabolic channel which limits the motion of the particles in the y direction.…”