Theoretical calculation for the small dot - big dot system

by Mr. Yuval Dahan

Physics department, BGU

at Condensed Matter Seminar

Mon, 13 Jan 2025, 11:10
Sacta-Rashi Building for Physics (54), room 207

Abstract

In this thesis, we provide analytical and numerical calculations for measuring the entropy of a quantum
dot (QD). We continue the work of T. Child and J. Folk et. al where a method for measuring the entropy
is demonstrated, based on the Maxwell relation ∂S/∂μ = ∂N/∂T . Experimentally, the derivative ∂N/∂T is obtained by
measuring the occupation numbers N(T + ΔT) and N(T) and computing the difference. According to the
authors of the mentioned paper, this measurement is valid when Γ/T ≲ 25. This constraint arises because, for
Γ ≫ T, the occupation function N(ϵ) becomes dominated by Γ, leading to a negligible difference N(T +ΔT)−
N(T). As a result, this limitation prevents exploration of the Kondo regime, where strong coupling between
the quantum dot and the reservoir is required. To circumvent this limitation, Folk proposed an innovative approach: partitioning the system into two
components — one to inhabit the Kondo effect and the other to contribute electrons and determine the shape
of the occupation curve. This approach is implemented using the Oreg and Goldhaber-Gordon setup, which
consists of a small dot, a large dot, and two leads. The small dot is weakly coupled to the lead, with ΓL ≪ T,
ensuring that the transition width of electrons between the lead and the dot is governed by T. Meanwhile,
the Kondo effect takes place between the small dot and the large dot, where a stronger coupling ΓB can be
employed.
This thesis provides the theoretical calculations to support the mentioned solution. We do so by exploring the system’s parameters space, using Numerical Renormalization Group (NRG), which eventually will help us understand how to tune the (physical) system to implement that solution.

Created on 12-01-2025 by Naamneh, Muntaser (mnaamneh)
Updaded on 12-01-2025 by Naamneh, Muntaser (mnaamneh)