Prediction of the Capacitance Line Shape in Two-Channel Quantum Dots

We propose a setup to realize two-channel Kondo physics using quantum dots. We discuss how the charge fluctuations on a small dot can be accessed by using a system of two single-electron transistors arranged in parallel. We derive a microscopic Hamiltonian description of the setup that allows us to make the connection with the two-channel Anderson model (of extended use in the context of heavy-fermion systems) and in turn make detailed predictions for the differential capacitance of the dot. Its line shape, which we determined precisely, shows a robust behavior that should be experimentally verifiable.

Figure 1

Cartoon micrograph of the proposed setup: a small quantum dot (dot) is connected to two larger dots (grains) that once the tuning is done are isolated from the 2DEGs at right and left. On the top defining gates of the dot a system of two SETs is built in. A set of gates controls the occupancy of dots and grains ($V_g$ and $V_{gL,R}$), their intercoupling ($V_{t_{L,R}}$), and their coupling to the 2DEGs ($V_{pL,R}$).

Figure 2

Charge susceptibility of the quantum dot as a function of energy splitting. The open circles indicate the vanishing-temperature TBA result. The solid line corresponds to a Lorentzian fit, while the dashed line is the fit to the derivative of a Fermi-Dirac distribution. With the same symbols as before, the overlay shows the excess charge on the dot as a function of energy splitting.

Figure 3

Low-temperature charge susceptibility of the quantum dot as a function of its excess charge. The open circles are the results of the TBA analysis and the solid and dashed lines are the translation of the Lorentzian and Fermi-Dirac fit in Fig. 2. The dash-dotted line is a fit to the functional form appropriate for a different setup with a single grain. The dotted lines are finite-temperature TBA results for two different $k_{\mathrm{B}}T\gg \Delta$.