Ginzburg-Landau theory of the zigzag transition in quasi-one-dimensional classical Wigner crystals

Abstract

We present a mean-field description of the zig-zag phase transition of a quasi-one-dimensional system of strongly interacting particles, with interaction potential r −n e −r/λ , that are confined by a power-law potential (y α ). The parameters of the resulting one-dimensional Ginzburg-Landau theory are determined analytically for different values of α and n. Close to the transition point for the zig-zag phase transition, the scaling behavior of the order parameter is determined. For α = 2 the zig-zag transition from a single to a double chain is of second order, while for α > 2 the one chain configuration is always unstable and for α < 2 the one chain ordered state becomes unstable at a certain critical density resulting in jumps of single particles out of the chain.

Generic ordering of structural transitions in quasi-one-dimensional Wigner crystals

“…As was analytically demonstrated in Refs. [12,13], the stability of the one-chain configuration as the GS is only guaranteed for the case of α = 2, while for larger values of α the onechain configuration is no longer found as the GS. This result is represented in Fig.…”

“…For α > 2 and small η, the two-chain configuration is the GS of the system even at low densities, where the inter-chain distance (i.e., the order parameter c 21 ) slowly decreases but never becomes exactly zero 13 except for η → 0. This behavior is illustrated in the right-hand side inset in Fig.…”

“…The GS of the system of interacting particles in a Q1D channel consists of chain-like structures [12][13][14][15] , and the transitions between them are of first order 10,22,23 , with the exception of the zigzag transition between 1 to 2 chains which is of second order 12,13 . Some typical chainlike configurations are shown in Fig.…”

“…The structural transition from twoto four-chain configuration occurs, in case of a non-SOT, through a zigzag transition of each of the two chains and a simultaneous small shift along the chain, which makes it a discontinuous transition 10 . The only second order transition in this sequence is the zigzag transition between one-and two-chain configuration, which has been extensively studied in classical [12][13][14][15][16] and quantum 6,[17][18][19][20][21] systems. A detailed analysis of the structural transitions for larger number of chains has to a lesser extent also been addressed 9,10,22,23 .…”

Orientational ordering, buckling, and dynamic transitions for vortices interacting with a periodic quasi-one-dimensional substrate

“…Between these limits, the vortices could exhibit buckling transitions by forming zig-zag patterns within individual potential troughs, so that for increasing vortex density there could be a series of transitions at which increas-ing numbers of rows of vortices appear in the potential troughs. Transitions from 1D rows of particles to zigzag states or multiple rows have been studied for particles in single q1D trough potentials in the context of vortices [68][69][70] , Wigner crystals [71][72][73] , colloids 75,[75][76][77] , q1D dusty plasmas 78,79 , ions in q1D traps [80][81][82] , and other systems 83,84 where numerous structural transitions, diffusion behavior and dynamics can occur. In the case of a periodic array of channels such as shown in Fig.…”