Multi-terminal transport through a quantum dot in the Coulomb blockade regime

– Three terminal tunnelling experiments on quantum dots in the Coulomb-blockade regime allow a quantitative determination of the coupling strength of individual quantum states to the leads. Exploiting this insight we have observed independent fluctuations of the coupling strengths as a function of electron number and magnetic field due to changes in the shape of the wave function in the dot. Such a detailed understanding and control of the dot-lead coupling can be extended to more complex systems such as coupled dots, and is essential for building functional quantum electronic systems. In a standard two-terminal experiment with a single quantum dot in the Coulomb blockade regime [1], the current in a conductance resonance is determined by the average coupling of the electron wave function in the dot with the corresponding wave functions in both leads. In the linear regime, such an experiment does not allow to determine the individual coupling of the wave function in the dot to each terminal. Here we demonstrate that in the single-level tunnelling regime of the Coulomb blockade it is possible to deduce the individual coupling strengths from the dot to the leads if three or more terminals are connected to the dot. It is possible to determine the conductance matrix of the quantum dot, and to calculate the individual tunnelling rates from the dot to each lead. For weak coupling, the magnitude of the tunnelling rates of a given terminal is found to vary independently of the two other tunnelling rates when the number of electrons in the dot is changed. This result can be related to the chaotic nature of the wave function in the dot. The fluctuations of the shape of the wave function in the dot due to quantum interference is directly observed via the magnetic field dependence of the coupling strengths. Finally, level broadening beyond thermal effects becomes visible as the coupling strength of a single lead increases. This set-up allows then to tune the tunnelling rates from the dot into the three terminals individually. The sample has been fabricated on an AlGaAs-GaAs heterostructure containing a twodimensional electron gas (2DEG) 34 nm below the sample surface. A back gate situated 1.4 μm below the 2DEG allows to tune the electron density. All measurements presented here were performed at a back gate voltage of -1.4 V, giving a 2DEG density of 3.7×10 cm and (∗) E-mail: [email protected]