Coexistence of diffusive resistance and ballistic persistent current in disordered metallic rings with rough edges: Possible origin of puzzling experimental values

Abstract

Typical persistent current (Ityp) in a mesoscopic normal metal ring with disorder due to rough edges and random grain boundaries is calculated by a scattering matrix method. In addition, resistance of a corresponding metallic wire is obtained from the Landauer formula and the electron mean free path (l) is determined. If disorder is due to the rough edges, a ballistic persistent current Ityp ≃ evF /L is found to coexist with the diffusive resistance (∝ L/l), where vF is the Fermi velocity and L ≫ l is the ring length. This ballistic current is due to a single electron that moves almost in parallel with the rough edges and thus hits them rarely (it is shown that this parallel motion exists in the ring geometry owing to the Hartree-Fock interaction). Our finding agrees with a puzzling experimental result Ityp ≃ evF /L, reported by Chandrasekhar et al. [Phys. Rev. Lett. 67, 3578 (1991)] for metallic rings of length L ≃ 100l. If disorder is due to the grain boundaries, our data reproduce theoretical result Ityp ≃ (evF /L)(l/L) that holds for the white-noise-like disorder and has been observed in recent experiments. Thus, result Ityp ≃ evF /L in a disordered metallic ring of length L ≫ l is as normal as result Ityp ≃ (evF /L)(l/L). Which result is observed depends on the nature of disorder. Experiments that would determine Ityp and l in correlation with the nature of disorder can be instructive.

Reflection resonances in surface-disordered waveguides: strong higher-order effects of the disorder

“…We consider a simple, non-trivial model consisting of a quasi-1D corrugated waveguide (or conducting wire) with discrete steps in the surface profile. This rough waveguide of length L and average width d L ≪ is attached to infinite leads of width d on the left and right (see Altogether three different cases will be considered in terms of the symmetries of the boundary profiles with respect to the horizontal center axis at y = 0: Following the assumptions adopted in a few recent papers [20,26,[36][37][38][39], the functions x ( ) i σξ are chosen as sequences of horizontal steps of constant width Δ and random heights,…”

“…Following the assumptions adopted in a few recent papers [20,26,35,36,37,38], the functions σξ i (x) are chosen as sequences of horizontal steps of constant width ∆ and random heights, uniformly distributed in an interval [−δ/2, δ/2] around the upper (lower) boundary of the attached leads. In our numerical analysis we set d = 1 and δ = 0.04, resulting in a variance of the disorder, σ 2 = δ 2 /12, which is small compared to the width of the waveguide, σ ≪ d.…”

“…Phenomena induced by surface corrugations play a major role in the study of acoustic, electromagnetic, and matter waves alike and appear in macroscopic domains such as acoustic oceanography and atmospheric sciences [5,6], but also emerge on much smaller length scales, e.g., for photonic crystals [7], optical fibers and waveguides [8,9], surface plasmon polaritons [10], metamaterials [11], thin metallic films [12-14], layered structures [15], graphene nanoribbons [16,17], nanowires [18][19][20], and confined quantum systems [21,22]. While having a detrimental effect on the performance of many of the above systems, surface roughness can also be put to use, e.g., for the fabrication of high-performance thermoelectric devices [23,24] and for light trapping in silicon solar cells [25]; rough surfaces cause anomalously large persistent currents in metallic rings [26] and provide the necessary scattering potential to manipulate ultra-cold neutrons which are bound by the earthʼs gravity potential [27].In view of this sizeable research effort, it might come as a surprise that even quite fundamental effects emerging in surface-disordered systems are still not fully understood. Consider here, in particular, the problem of wave transmission through a surface-corrugated guiding system which we will study in the following.…”

“…In these waveguides (see figure 1), the surface disorder features steps of random height (in the direction transverse to propagation) and of constant width (in longitudinal direction). Such waveguides have been considered in quite a few recent studies [20,26,[36][37][38][39], as they are attractive model systems both for an experimental implementation as well as for a numerical computation. This is because waveguides with the above specifics can be easily built up by combining a series of rectangular waveguide stubs, each of which has no surface disorder but a randomly chosen height.…”