Geometric blockade in a quantum dot coupled to two-dimensional and three dimensional electron gases

Abstract

We fabricated a quantum dot coupled laterally to a two-dimensional electron gas and vertically to a three-dimensional electron gas in order to investigate the eigenstate dependence of tunneling rate to these gases. We observed a bias-dependent ``geometric" current blockade. By tunneling via the asymmetric couplings, population inversion is induced and a dark metastable triplet state is revealed. The metastable state stops the current transport process, suppresses the current and asymmetrically widens the Coulomb diamond. By analyzing the current as a function of source-drain and gate voltage and the magnetic field, we concluded that this effect is due to the geometric shape of the electronic states in the dot and the current is limited by the tunneling rate due to the eigenstates, that is, artificial $σ$-coupling and $π$-coupling.

Figures (6)

• Figure 1: (Color online)(a) Schematic drawing of single artificial atom rectifier. The colors yellow (light gray), orange (light gray), blue (dark gray) and magenta (dark gray) indicate the metal for the electrode, the metal for the gate, n-doped GaAs, and AlGaAs for the tunnel barrier, respectively.(b) SEM image of single artificial atom rectifier. (c) Schematic diagram of cross section where the red (gray) line in (a) indicates the area. The quantum dot is vertically confined in the quantum well fabricated from the AlGaAs(7 nm)/InGaAs(12 nm)/AlGaAs(50 nm) heterostructure. The measured dot is located in the 300 x 300 nm$^{2}$ mesa. Slant lines indicate depletion layers. At the negative bias $V_{SD}<0$, electrons are injected laterally from the 2DEG via the barrier modulated by the split gate to the dot and escape vertically to the 3DEG via the AlGaAs barrier. The current does not flow through the lower thick AlGaAs barrier. The side gate controls the number of electrons in the dot.
• Figure 2: (Color online) Schematic of principal single-particle eigenstates in dot. The vertical connections of all states to the 3DEG are approximately the same. However, tunneling to the 2DEG from the $1s$ or $2p_{y}$ state is suppressed by the geometry. The degeneracy of $2p_{x}$ and $2p_{y}$ is broken by the elliptical nature of the potential Austing99. The widths of arrows indicate the intensities of couplings. The lateral tunnelings from the 2DEG to the $1s$ and $2p_{y}$ orbitals, are weaker than the tunnelings from 2DEG to a $2p_{x}$ orbital because of a longer effective tunneling distance. The intensity of the vertical tunneling coupling does not depend on the form of the wave function.
• Figure 3: (a) $N=2$ Coulomb diamond showing current on color scale versus source-drain and gate voltages. (b) Schematic of (a). For $V_{SD}<0$, injection is from the 2DEG. The blockade at C is due to the dark $1s2p_x$ state, which is stable on the left side of cotunneling line $\Delta (2,2^*)$ and above the "escape" chemical potential line $\mu (2^*,1)$. (c) $dI/dV$ plots of (a). The onset of cotunneling (vertical black lines)is remarkably observed.
• Figure 4: (Color online) Current vs voltage plots at $V_{G}$= -1.85, -1.64 and -1.66 (V). The markers A - F indicate the same regions in Fig. \ref{['fig:diamond']}. The arrow indicates the suppression due to the geometric blockade.
• Figure 5: (Color online) Schematic of states $1s^2$, $1s2p_x$, $1s^22p_x$, $1s2p_x2p_y$ and $1s2p_x^2$ showing strong (filled arrows) and weak (hollow arrows) connections due to single electron tunneling from the 2DEG lead. Note: the diagram is only for the reverse bias ( injection from 2DEG ) case. For example, $1s2p_x\rightarrow 1s2p_x2p_y$ is weak because tunneling from the 2DEG to the $2p_{y}$ level is weak owing to its orientation. However, $1s^22p_x\rightarrow 1s2p_x$ is strong because it is an ejection event to the 3DEG. Thus, when $1s2p_x^2$ is energetically inaccessible at the diamond border, the $1s2p_x$ population strongly increases. Hollow gray arrows denote (weak) relaxation processes, at constant $N$, requiring spin flips.