Multiple-path Quantum Interference Effects in a Double-Aharonov-Bohm Interferometer
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- Yang, X. & Liu, Y. Nanoscale Res Lett (2010) 5: 1228. doi:10.1007/s11671-010-9631-0
We investigate quantum interference effects in a double-Aharonov-Bohm (AB) interferometer consisting of five quantum dots sandwiched between two metallic electrodes in the case of symmetric dot-electrode couplings by the use of the Green’s function equation of motion method. The analytical expression for the linear conductance at zero temperature is derived to interpret numerical results. A three-peak structure in the linear conductance spectrum may evolve into a double-peak structure, and two Fano dips (zero conductance points) may appear in the quantum system when the energy levels of quantum dots in arms are not aligned with one another. The AB oscillation for the magnetic flux threading the double-AB interferometer is also investigated in this paper. Our results show the period of AB oscillation can be converted from 2π to π by controlling the difference of the magnetic fluxes threading the two quantum rings.
KeywordsAharonov-Bohm interferometer Fano effects Quantum dots Transport properties
Thanks to rapid developments in the fabrication and self-assembly techniques, the electrical transport through nanoscale quantum systems such as a single quantum dot, multiple quantum dots, atoms or molecules coupled to metallic electrodes has been an interesting subject in recent years [1, 2, 3, 4, 5, 6]. In the nanoscale quantum systems, the electrical transport is ballistic, while the phase coherence of the electrons is preserved. Especially, the quantum interference effects in an AB ring including a quantum dot have been reported . The results showed that Fano effect with asymmetric parameters was a good probe to quantum interference effects in the nanoscale systems. The transport properties of a quantum ring consisting of two parallel-coupled quantum dots sandwiched between two metallic electrodes have been also studied theoretically and experimentally in the last few decades [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. For example, an AB interferometer including two coupled quantum dots with each quantum dot inserted in each arm was presented, and an oscillating electric current was detected experimentally [8, 9]. Such a double-quantum-dot model consisting of the parallel-coupled double-dot system has been studied extensively in some previous theoretical works [13, 14, 15, 16, 17, 18]. When the interdot coupling is considered, a bonding molecular state and an antibonding molecular state are developed. A swap effect can be found in the quantum system by tuning the magnetic flux threading the quantum ring, which may be used in the future quantum computations .
Recently, the transport properties of multi-parallel-coupled quantum dots have attracted considerable attention due to their potential applications and abounding physics [23, 24, 25, 26, 27, 28, 29, 30, 31]. Zeng et al. studied the AB effects in a quantum ring consisting of four quantum dots sandwiched between two metallic electrodes, and a Fano dip is developed when the energy levels of quantum dots in two arms are mismatched . Guevara et al. offered a quantum model describing multi-parallel-coupled quantum-dot molecule, and Fano effects in the quantum system were studied in detail . More recently, Li et al. studied the electrical transport through a triple-arm AB interferometer consisting of three parallel quantum dots with electron-electron interactions under an applied electric field .
Model and Methods
Results and Discussion
In this section, the dependence of the linear conductance σ on system parameters is discussed numerically and analytically. The coupling strength between the quantum dots and the metallic electrodes Open image in new window is taken as the energy unit. Through this paper, all energy levels in quantum dots, tunneling couplings and Fermi energy are measured by Open image in new window.
Without Magnetic Flux
From the above equation, we see clearly σ = 0 for Open image in new window or Open image in new window. The linear conductance spectrum has mirror symmetry around ε3 in the case of ε3 = 0. With increasing ε3, the mirror symmetry is broken. The left Fano peak is suppressed, while the right Fano peak is firstly suppressed, then it is enhanced.
With Magnetic Flux
where δ1 and δ2 represent two small quantities. Equation (26) shows two narrower conductance peaks are centered at Open image in new window as shown in Fig. 6. When ϕ = n π(n is odd number), the linear conductance disappears everywhere for any value of EF.
In summary, the transport properties and quantum interference effects in a double-AB interferometer in series consisting of five quantum dots in the case of symmetric dot-electrode tunneling couplings are studied by using Green’s function equation of motion method. The energy levels of all quantum dots can be tuned by the voltages applied on the quantum dots in experiments. The linear conductance can be effectively modified by the intermediate quantum dot 3. As the energy level in the quantum dot 3 changes, a three-peak structure in the linear conductance spectrum evolves into a two-peak structure. When the quantum-dot levels in arms are not aligned with one another, two Fano resonances with different Fano factors may appear in the quantum device. The AB oscillation for the magnetic flux in the double-AB interferometer is also studied in this work. The results show that the AB oscillating behavior depends strongly on the difference between the magnetic fluxes threading the left and right quantum rings. An AB oscillation with π-period for the magnetic flux threading the left quantum ring is developed when the difference between the two magnetic fluxes is (2n + 1)π(n = 0, 1, 2,…).
The authors thank the supports of the National Natural Science Foundation of China (NSFC) under Grant No. 10947130 and the Science Foundation of the Education Committee of Jiangsu Province under Grant No. 09KJB140001. The authors also thank the supports of the Foundations of Changshu Institute of Technology.
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