Persistent currents in distorted quantum ring

Abstract

Abstract. Persistent currents in distorted narrow mesoscopic rings threaded by the magnetic flux of the Aharonow Bohm type are investigated. It is shown that the ring distortions can be modelled by an appropriate potential term. The cases with a single and multiple distortions are considered. The single distortion opens a gap in the electron energy spectrum of a ring and decreases the amplitude of persistent currents. It is shown that in the ring with multiple distortions, under some geometrical conditions, there is an enhancement of the persistent current and some of the electronic states remain degenerated. The possible application of the model to the formation of a qubit is discussed. IntroductionDuring the last 20 years, persistent currents (PC) in mesoscopic rings have attracted significant interest both theoretically and experimentally [1][2][3][4]. PC in small quantum rings threaded by a magnetic flux are a manifestation of quantum coherence in a submicron system. If the ring circumference L is smaller than the phase coherence L φ the electron wave function may extend coherently over L even in the presence of elastic scatterers. In other words a normal loop with L < L φ has a nontrivial ground state with a circulating PC.In this paper we present theoretical study of persistent currents in the quantum ring. We consider a narrow ring with two distortions of uniform cross section lying on a plane (Fig. 1). We show that quantum tunneling between states with nearly equal energy and PC can lead to a formation of a qubit. The paper is organized as follows. In Sec. 2, we write down and disscus the Schrödinger equation for one electron in the ring with two distoritons in the presence of a magnetic flux. We show that the curvature of distorted ring enters into the Schrödinger equation via a geometrical potential term [5]. We demonstrate that the factorization of the wave function leads to two separate eigenequations in transverse and longitudinal directions. In Sec. 3 we analyze a distorted quantum ring consisting of eight constant-curvature segments and we find the energy spectrum of such a ring. We show that the geometrical potential V g opens gaps in the electron energy spectrum with the exception of the case when distortions are symmetrically placed. Next, in section 4 we perform analitycal calculations and computer simulations to analyze the effect of distortions on the persistent currents. We show that in the case of a small one-dimensional ring the presence of distortions significantly changes the currents and especially how the currents are affected by various configuration of distortions. In Sec. 5 we show that distorted quantum ring can be useful for quantum computing hardware. Conclusions are presented in Sec. 6.

Teoria quântica em uma subvariedade: Efeitos clássicos, quânticos e térmicos

“…This simple rule explains all the observed spectra considered here and is consistent with previous results in 1D [28,30,107,118] and 2D [109,113,117] QRs with cyclic symmetries.…”

“…In non-relativistic quantum mechanics the confining potential approach has been used mainly in the context of condensed matter physics, in order to study the quantum dynamics of a particle confined to a low-dimensional space [7,10,11,[15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. For example, it has been studied the influence of the geometric potential in the electronic properties and bound-state formation in curved nanostructures [22], geometry-induced charge separation on helicoidal ribbon [20], mechanical-quantum-bit states [23], effects of periodic curvature on the electrical resistivity of corrugated semiconductor films [24,25], curvature-induced p-n junctions in bilayer graphene [32], distorted quantum rings [10,28,30,33] as well as geometry-driven shift in the Tomonaga-Luttinger liquid [26].…”

“…where g 1/2 (ϕ) = ds(ϕ) dϕ = dr(ϕ) dϕ 6 . Theoretical efforts have been focused on how deformations and external fields modify the energy spectrum of one-dimensional [28,33,103] and two-dimensional QRs [28,33,100,[104][105][106][107][108][109][110][111][112][113]. The study of deformed QRs has been concentrated mainly on elliptical deformations [104,107,109,[112][113][114][115][116], Cassini ovals [117] and limaçon-shaped [107].…”

“…In this geometry, the extrinsic curvature is piecewise constant, and so the effective potential is analogous to the Kronig-Penney Model in a finite interval. This kind of effective potential also appears in distorted QRs with single [28,33], double [28] and multiple distortions [30]. Here, inspired by on the classic vibrational modes of a ring, we consider the following family of curves with non-constant extrinsic curvature,…”

Controlling the magnetic susceptibility in an artificial elliptical quantum ring by magnetic flux and external Rashba effect

“…[11][12][13][14][15][16][17][18][19][20][21] The quantum interferences are affected by the symmetry of the structure which is disturbed by the disorder. [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] For instance, Maiti has studied the sign of the currents in a one-dimensional (1D) quantum ring in the presence of impurity. 38 He found that the sign of the currents strongly depends on the total number of electrons and also on the disordered configurations of these systems.…”