Conductance Plateaus at Quantum Hall Integer Filling Factors in Germanium Quantum Point Contacts

Abstract

Constricting transport through a one-dimensional quantum point contact in the quantum Hall regime enables gate-tunable selection of the edge modes propagating between voltage probe electrodes. Here we investigate the quantum Hall effect in a quantum point contact fabricated on low disorder strained germanium quantum wells. For increasing magnetic field, we observe Zeeman spin-split 1D ballistic hole transport evolving to integer quantum Hall states, with well-defined quantised conductance increasing in multiples of $e^2/h$ down to the first integer filling factor $ν=1$. These results establish strained germanium as a viable platform for complex experiments probing many-body states and quantum phase transitions.

Figures (3)

• Figure 1: (a) Scanning electron micrograph of a nominally identical quantum point contact (QPC) device and schematic of the circuit. An ac-voltage signal $V_{\mathrm{sd}}$ is applied across the QPC, and $I_{\mathrm{sd}}$, $V_{\mathrm{xx}}$, and $V^*_{\mathrm{xy}}$ are measured. (b) Conductance $G$ as a function of split-gate voltage $V_{\mathrm{sg}}$. Plateaus form at integer multiples of $2e^2/h$ indicating ballistic 1D conductance inside the QPC constriction. The trace has beencorrected for a series resistance $R_{\mathrm{s}}=2.4kΩ$). The grey arrow indicates the $0.7\times 2e^2/h$ anomaly. (c) Colour map of source-drain bias transconductance $\partial G/\partial V_{\mathrm{sg}}$ (a.u.) plotted against $V_{\mathrm{dc}}$ and $V_{\mathrm{sg}}$. Light blue regions correspond to risers in 1D conductance and dark blue regions correspond to plateaus. The white overlaid traces indicate the dc voltage drop across the QPC. (d) 1D subband spacing $\Delta E_{n,n+1}$ as a function of subband index $n$ extracted from source-drain bias spectroscopy in panel (c).
• Figure 2: (a) Colour map of longitudinal resistivity $R_{\mathrm{xx}}$ as a function of split gate voltage $V_{\mathrm{sg}}$ and out-of-plane magnetic field $B_{\perp}$. The bottom of the map is the region of QPC pinch off; the 1D subband occupation of the QPC approaches the 2D definition point near the top of the map. The integer Landau filling factors are labelled. (b) Colour map of diagonal resistivity $R^*_{\mathrm{xy}}$ as a function of split gate voltage $V_{\mathrm{sg}}$ and out-of-plane magnetic field $B_{\perp}$.
• Figure 3: Transverse (Hall) conductance $G^*_{\mathrm{xy}}$ as a function of split gate voltage $V_{\mathrm{sg}}$ at Landau filling factors $\nu = 1,2,3,4$, taken at $B =$5T, 3.2T, 2.2T, 1.7T respectively. Each trace has been corrected for a fixed series resistance of $R_{\mathrm{s}} = 5.6kΩ, 3.3kΩ, 4.9kΩ, 6.7kΩ$, respectively. Traces have been offset in $V_{\mathrm{sg}}$ for clarity.