Quantized conductance in an AlAs two-dimensional electron system quantum point contact

We report experimental results on a quantum point contact (QPC) device formed in a wide AlAs quantum well where the two-dimensional electrons occupy two in-plane valleys with elliptical Fermi contours. To probe the closely-spaced, one-dimensional electric subbands, we fabricated a point contact device defined by shallow etching and a top gate that covers the entire device. The conductance versus top gate bias trace shows a series of weak plateaus at integer multiples of $2e^2∕h$, indicating a broken valley degeneracy in the QPC and implying the potential use of QPC as a simple “valley filter” device. A model is presented to describe the quantized energy levels and the role of the in-plane valleys in the transport. We also observe a well-developed conductance plateau near $0.7\times 2e^2∕h$ which may reflect the strong electron-electron interaction in the system.

Figure 1

(a) Conductance vs gate voltage. The arrow indicates the “0.7 structure.” (b) The transconductance $dG∕d{V}_G$. The minima, nearly periodic in $2e^2∕h$ (except for the “0.7 structure”), indicate developing plateaus in the conductance trace.

Figure 2

(a) Device schematic of the shallow-etched QPC. The $k$-space orientation of the in-plane valleys labeled as $X$ and $Y$ is also shown. (b) Confinement potential along the dashed line in (a). The Fermi energy varies with the gate bias voltage. (c) Device cross section along the dashed line in (a).

Figure 3

(Color online) (a) Schematic drawing showing the potential landscape surrounding the QPC and the orientations of the two in-plane valleys $X$ and $Y$. (b) Potential cross section along the transport direction [dotted line in (a)]. (c) Dependence of the Fermi energy on to the gate voltage. The circles are the expected level crossings. Right inset: The conductance vs $V_G$ trace together with an idealized conductance step model to determine the level crossings (see text). Left inset: The QPC energy levels assuming a fixed channel width of $w=300\mathrm{nm}$. It is apparent that the energy levels do not fit the level crossings.

Figure 4

Magnetoresistance traces for the QPC device. Inset shows the contact geometry for these traces. The kink in the $R_{xx}$ magnetoresistance trace (marked by the arrow $B_K$) signals the field where the cyclotron orbit fits into the width of the QPC channel. For $V_G=0.6\mathrm{V}$, a Hall resistance $\left(R_{xy}\right)$ trace is also shown.

Figure 5

(a) Fourier transform (FT) spectrum of $R_{xx}$ representing density components in the 2D reservoir and the QPC. (b) Fourier transform spectrum of $d{R}_{xy}∕dB$ representing density components in the 2D reservoir alone. (c) Summary of the Fourier spectra peaks vs $V_G$.

Figure 6

QPC channel electrical width $\left(w\right)$, deduced from the kink in the magnetoresistance, for two possible cases where either valley $X$ or $Y$ is occupied; these cases are schematically illustrated on the right. Gray area denotes the error band for $w$ from the MR kink data. The open squares and solid line indicate $w$ determined from the QPC model (see text).

Figure 7

(Color online) (a) Potential landscape surrounding the QPC. (b) Potential cross section along the transport direction. A finite residual valley splitting $\left(\Delta E_V\right)$ in the 2D reservoir is shown. In the QPC this valley splitting is enough to completely depopulate the $X$ valley. (c) A revised QPC energy level model with variable channel width. The model fits the QPC energy levels to all observed level crossings.

Figure 8

(Color online) (a) Differential conductance $G=dI∕d{V}_{\mathit{SD}}$ traces measured at $T=0.3\mathrm{K}$. Each trace corresponds to incremental step of $2\mathrm{mV}$ in $V_G$ starting from $0.3\mathrm{V}$ at the bottom. (b) The transconductance $(dG∕d{V}_G)$ spectrum. The bluish (dark) regions correspond to developing plateaus. The numbers represent the plateaus indices.

Figure 9

(Color online) Full-width at half-maximum (FWHM) of the ZBA peak as a function of gate voltage. The color data points (plus signs) are associated with the conductance trace of the same color in the inset. For reference the conductance trace $G$ vs $V_G$ is replotted. Inset: Differential conductance $G=dI∕d{V}_{\mathit{SD}}$ at low conductance where the ZBA occurs.