Observation of Aharonov-Bohm Electron Interference Effects with Periodsheandh2ein Individual Micron-Size, Normal-Metal Rings

Abstract

We report resistance oscillations as a function of magnetic field for individual aluminum and silver thin-film rings, 1-2 /u,m in diameter, between 1.2 and 10 K. This is the first observation in single rings of oscillations with a flux period of h/2e predicted by Al'tshuler et al Oscillations periodic in hi e are also seen in the l-/xm Ag rings at higher fields. These electron interference effects in metal rings are the solid-state analog of the Aharonov-Bohm effect for electrons in vacuum. PACS numbers: 71.55.Jv, 72.15.Lh, 73.60.Dt In recent years there has been major interest, and a dramatic advance, in the understanding of electron transport in random systems, especially those of reduced dimensionality. 1 The early studies of one-and two-dimensional systems verified the picture, originally proposed by Thouless, of localization effects which reduce the conductivity at T-• 0. It is now clear that localization phenomena result from electron interference: Coherent backscattering adds quantum corrections to the classical electron-diffusion results. 1 Localization experiments confirm the striking result that the length over which electrons can retain phase memory and interfere is the inelastic diffusion length //, which can be > 1 ftm at low temperatures. (1 /xm= 10 4 A.) In contrast, the mean o free path / in typical metal films is of order 10 to 100 A.Recently there have been predictions 2 " 5 that explicit, oscillatory electron interference effects should be seen in the macroscopic electrical properties of small metal rings and cylinders in a perpendicular (axial) magnetic field B ( = VxA). The vector potential A adds to the quantum phase along a path from a to b by an amount (in mks units) A</ > = 27r(e//?) f A-rfl. J aFor electrons in vacuum this leads to the well-known Aharonov-Bohm interference effect 6 for the electron intensity, where the electron travels on either of two paths which enclose a magnetic flux <& [see Fig. 1(a)]. The flux is given by <I > = B x area = 0 A • d\. The flux periodicity of the resulting intensity is h/e. Aharonov-Bohm resistance oscillations have been reported in very pure single-crystal cylinders with long mean free paths, 3 with a period of h/e. Observation of such interference effects in a ring of disordered metal (with significant elastic scattering) would demonstrate elegantly the connection between macroscopic transport and the essentially quantum-mechanical behavior at the microscopic level.The first prediction of interference effects in disordered normal-metal rings and cylinders was by Al'tshuler et al 2 They predicted that the low-temperature resistance would be a periodic function of the enclosed flux, with a period of h/2e. This periodicity results from the interference paths shown in Fig. Kb). 7 Different theoretical arguments, which start with a model of a closed chain of atoms, also predict a flux periodicity of h/2e for various physical quantities. 5

Characteristic molecular properties of one-electron double quantum rings under magnetic fields

“…Refs. [35,36,37,38]), to composite systems, which may unveil subtleties of these purely quantum mechanical phenomena. As a matter of fact, here we show that, unlike in single QRs [19,20], AB effects in composite systems need no finite net magnetic flux to take place.…”

Aharonov-Bohm oscillation in a ferromagnetic ring

“…The non-magnetic part, ℓ ϕ , would be identical as in the non-magnetic systems, i.e., the contribution is mainly from the electron-electron interaction at low temperatures [1,5] (say, T < ∼ 1K). Experimentally ℓ ϕ is estimated to be 1 ∼ 2µm in Al and Ag [9,15], which is long enough for submicron rings. The spin-orbit interaction may be different in magnetic case, but is estimated in Ag as ℓ so = 1/ √ Dτ so ∼ 0.47µm [9].…”

Fractionally Charged Zero-Energy Single-Particle Excitations in a Driven Fermi Sea

“…I discuss also how to address separately electron-hole pairs and a fractionally charged zero-energy excitation in experiment. Introduction.-Recent realization of a triggered singleelectron source [1-10] opens a new era for a coherent electronics [11][12][13][14][15][16][17][18] by allowing it to go quantum much like a quantum optics. The analogues of the famous quantum optics effects were successfully demonstrated with single electrons in solid state circuits such as partitioning of electrons [7,[19][20][21] in Hanbury-Brown and Twiss geometry and quantum-statistical repulsion of electrons [7,22] in Hong-Ou-Mandel geometry.…”