Current modulation at nano-scale level: A theoretical study Santanu K. Maiti 1 , 2 $^{1}$Theoretical Condensed Matter Physics Division, Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Kolkata-700 064, India $^{2}$Department of Physics, Narasinha Dutt College, 129 Belilious Road, Howrah-711 101, India We explore the possibilities of current modulation at nano-scale level using mesoscopic rings. A single mesoscopic ring or an array of such rings is used for current modulation where each ring is threaded by a time varying magnetic flux φ which plays the central role in the modulation action. Within a tight-binding framework, all the calculations are done based on the Green’s function for- malism. We present numerical results for the two-terminal conductance and current which support the essential features of current modulation. The analysis may be helpful in fabricating mesoscopic or nano-scale electronic devices. PACS numbers: 73.63.-b, 73.63.Rt, 81.07.Nb Furthermore, electron transport in the ring can also be modulated in other way by tuning the magnetic flux, the so-called Aharonov-Bohm (AB) flux, penetrated by the ring. Electron transport in low-dimensional systems has drawn much attention in the field of theoretical as well as experimental research due to flourishing development in nanotechnology and nano-scale device modeling. Low- dimensional model quantum systems are the basic build- ing blocks for future generation of nano-electronic de- vices. Several exotic features are observed in this length scale owing to the effect of quantum interference. This effect is generally observed in samples with size much smaller or comparable to phase coherence length L$_{φ}$ , while the effect disappears for larger systems. A nor- mal metal mesoscopic ring is a very good example to study the effect of quantum interference. Current trend of fabricating nano-scale devices has resulted much in- terest in characterization of ring type nanostructures. There are several methods for preparation of mesoscopic rings. For instance, gold rings can be designed using tem- plates of suitable structure in combination with metal deposition through ion beam etching [1, 2]. In a recent experiment, Yan et al. have proposed how gold rings can be prepared by selective wetting of porous templates using polymer membranes [3]. With such rings we can fabricate nano-scale electronic circuits which can be uti- lized for the operation of current modulation. To ex- plore this phenomenon the ring is coupled to two elec- trodes, to form an electrode-ring-electrode bridge, where the ring is penetrated by a time varying magnetic flux φ . Electron transport through a molecular bridge system was first studied theoretically by Aviram and Ratner [4] during 1970’s. Following this pioneering work, several experiments have been done using different bridge sys- tems to reveal the actual mechanism of electron trans- port. Though, to date a lot of theoretical [5–16] as well as experimental works [17–20] on two-terminal electron transport have been done addressing several important issues, yet the complete knowledge of conduction mech- anism in nano-scale systems is still unclear to us. Trans- port properties are characterized by several significant factors like quantization of energy levels, quantum inter- ference effect, ring-to-electrode interface geometry, etc. In the forthcoming two sub-sections we focus on two different circuit configurations, for our illustrative pur- poses, those are used for current modulation. Here we try to illustrate how a single mesoscopic ring or two such rings, where each ring is penetrated by a time varying magnetic flux φ , under a DC bias voltage can support an The scheme of the present paper is as follows. With the brief introduction (Section I), in Section II, we describe the model and theoretical formulations for our calcula- tions. Section III presents the significant results, and finally, we conclude our results in Section IV. Aim of the present paper is to illustrate the possibilities of current modulation at nano-scale level using simple mesoscopic rings. To achieve current modulation we de- sign an electronic circuit using a single mesoscopic ring or a cluster of such rings, where each ring is penetrated by a time varying magnetic flux φ which plays the central role for the modulation action. For a constant DC voltage, current through the circuit shows oscillatory behavior as a function of time t depending on the phase of the mag- netic flux φ passing through the ring. Therefore, current modulation can be achieved simply by tuning the phase of magnetic flux φ threaded by the ring. Within a tight- binding framework, a simple parametric approach [21–29] is given and all the calculations are done through single particle Green’s function technique to reveal the electron transport. Here we present numerical results for the two- terminal conductance and current which clearly describe the essential features of current modulation. Our exact analysis may be helpful for designing mesoscopic or nano- scale electronic devices. To the best of our knowledge the modulation action using such simple mesoscopic rings has not been addressed earlier in the literature. arXiv:1001.2184v1 [cond-mat.mes-hall] 13 Jan 2010 I. INTRODUCTION II. MODEL AND SYNOPSIS OF THE THEORETICAL FORMULATION