Disorder-induced transitions in layered Coulomb gases and application to flux lattices in superconductors

Abstract

A layered system of charges with logarithmic interaction parallel to the layers and random dipoles in each layer is studied via a variational method and an energy rationale. These methods reproduce the known phase diagram for a single layer where charges unbind by increasing either temperature or disorder, as well as a freezing first order transition within the ordered phase. Increasing interlayer coupling leads to successive transitions in which charge rods correlated in N Ͼ 1 neighboring layers are unbounded by weaker disorder. Increasing disorder leads to transitions between different N phases. The method is applied to flux lattices in layered superconductors in the limit of vanishing Josephson coupling. The unbinding charges are point defects in the flux lattice, i.e., vacancies or interstitials. We show that short range disorder generates random dipoles for these defects. We predict and accurately locate a disorder-induced defect-unbinding transition with loss of superconducting order, upon increase of disorder. While N = 1 charges dominate for most system parameters, we propose that in multilayer superconductors defect rods can be realized.

Gauge field induced by ripples in graphene

“…To the same accuracy this formula holds for all T < T m /2 where T m = K 0 a 2 /(16π) is the KTHNY melting temperature of a pure 2d crystal, with K 0 = 4µ(µ + λ)/(µ + 2λ), while the threshold decreases asσ c (T ) = 4σ c T Tm (1 − T Tm ) at higher T . Forσ >σ c and at T = 0 the scale L above which dislocation first appear can be estimated as in 41 and corresponds to the total energy cost . Because of logarithms this scale can be large hence it can alternatively be viewed as defining an effective size dependent thresholdσ c (L).…”

Depinning in a two-layer model of plastic flow

“…This approach was successful to treat disorder in the statics, where it leads to solvable limits for e.g., the Bragg glass phase, 82,83 the decoupling transition for magnetically coupled superconductors. 84 It is also studied to describe interacting quantum systems such as the sliding Luttinger liquid. 85 Recently a similar strategy was applied to describe plastic flow and depinning ͑see Refs.…”

Gauge field induced by ripples in graphene

“…To the same accuracy this formula holds for all T < T m /2 where T m = K 0 a 2 /(16π) is the KTHNY melting temperature of a pure 2d crystal, with K 0 = 4µ(µ + λ)/(µ + 2λ), while the threshold decreases as σc (T ) = 4σ c T Tm (1 − T Tm ) at higher T . For σ > σc and at T = 0 the scale L above which dislocation first appear can be estimated as in 41 and corresponds to the total energy cost K0a 2 8π (1 − σ/σ c ) ln(L/l 0 ) + E c becoming negative. We have taken into account the dislocation core energy E c = E 0 c + K0a 2 8π ln(l 0 /a) at scale l 0 (E 0 c denotes the bare core energy).…”