Correlated Double-Electron Additions at the Edge of a Two-Dimensional Electronic System

We create laterally large and low-disorder GaAs quantum-well-based quantum dots that act as small two-dimensional electron systems. We monitor tunneling of single electrons to the dots by means of capacitance measurements and identify single-electron capacitance peaks in the addition spectrum from occupancies of one up to thousands of electrons. The data show two remarkable phenomena in the Landau level filling factor range $\nu =2$ to $\nu =5$ in selective probing of the edge states of the dot: (i) Coulomb blockade peaks arise from the entrance of two electrons rather than one; (ii) at and near $\nu =5/2$ and at fixed gate voltage, these double-height peaks appear uniformly in a magnetic field with a flux periodicity of $h/2e$, but they group into pairs at other filling factors.

Figure 1

Electron additions in a small 2D quantum dot. (a) The quantum dot is confined between two electrodes, one of which (tunneling electrode) is tunnel coupled to the dot. The carrier concentration can be tuned by the gate electrode. (b) Schematic of the sample design with a small metallic island (dot) that is tunnel coupled to a reservoir and capacitively coupled to the bottom electrode. (c) Isolated electron additions as a function of the gate voltage. The spacing between successive capacitance peaks largely reflects the additional energy required to overcome the Coulomb repulsion of the electrons already in the dot. The heights of the single-electron capacitance peaks in this trace are typical of those measured throughout the experiment. (d) Single-electron capacitance peaks (bright curves) in a small quantum dot as a function of the external magnetic field and gate voltage.

Figure 2

Electron additions in a large quantum dot. Brighter regions correspond to higher capacitance. (a) Under a perpendicular magnetic field, the 2DES forms Landau levels, producing dips in the capacitance corresponding to each integer filling factor. There are roughly 2000 electron additions in the voltage range shown. (b) States with negative slope, corresponding to edge states, near $\nu =5/2$. The broad horizontal lines may correspond to states under the gate region but outside of the dot itself. (c) Localized states in the Landau gap follow the underlying filling factor. States in the center and the top left of the figure track $\nu =1$ and $\nu =2$, respectively. The states that are nearly parallel to the field axis are the first few electrons added to the dot in isolated localized states, as in Ref. [26]. (d) Capacitance peaks of the first few electrons added to the dot as a function of the magnetic field.

Figure 3

Electron addition spectra in the $N=0$ versus the $N=1$ Landau level. (a) Capacitance data taken as a function of the gate voltage and magnetic field in the ${\mathrm{\Phi }}_0=h/e$ regime. The filling factor is near $\nu =3/2$. (b) When the gate voltage is tuned to near filling factor $\nu =5/2$, the periodicity in the magnetic field is halved. (c) Corresponding Fourier transforms of two different regions as a function of ${\mathrm{\Phi }}_0/\mathrm{\Delta }B$. The blue and red curves are the Fourier transforms near $\nu =3/2$ and $\nu =5/2$, respectively.

Figure 4

Double-height peaks in the $N=1$ Landau level and bunching of paired peaks away from filling factor $\nu =5/2$. (a) Electron charge comparison between the first electrons and the paired electrons. The blue curve (first electrons) is centered at a bias voltage of $-0.0795\mathrm{V}$ and the red curve (paired electrons) at 0.3655 V. (b) High magnetic field resolution measurement showing bunched pairs. The ac excitation is $100\mu \mathrm{V}\mathrm{rms}$. The filling factor ranges from $\nu =2.9$ at 6.25 T to $\nu =2.83$ at 6.40 T. As this scan is close to $\nu =3$, notice that two localized states appear with positive slope. However, the localized states do not appear to interact with the edge states at all.