Effective action and interaction energy of coupled quantum dots.pdf

Effective action and interaction energy of coupled quantum dots Sourin Das and Sumathi Rao Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211019, India (February 1, 2008) 3 0 0 We obtain the effective action of tunnel-coupled quantum dots, by modeling the system as a Lut- 2 tinger liquid with multiple barriers. For a double dot system, we find that the resonance conditions y for perfect conductance form a hexagon in the plane of the two gate voltages controlling the density a of electrons in each dot. We also explicitly obtain the functional dependence of the interaction en- M ergy and peak-splitting on the gate voltage controlling tunneling between the dots and their charging energies. Our results are in good agreement with recent experimental results, from which we obtain 7 the Luttinger interaction parameter K = 0.74. 2 ] l PACS number: 71.10.Pm, 73.23.Hk, 73.63.Kv l a h - Coulomb blockade CB [1] in quantum dots has gained action exactly, by integrating out Gaussian degrees of s e in importance in recent years, due to its potential for freedom. Hence our results give the interaction energy m application as single electron transistors. Recent exper- directly in terms of the microscopic variables and ap- . iments [2–4] on coupled quantum dots have revealed a plied voltages. We find that in the weak tunneling limit, t a variety of features, the most salient of which is the con- the peak splitting is proportional to the square-root of m ductance peak splitting controlled by inter-dot tunneli