0.7 Structure and Zero Bias Anomaly in Ballistic Hole Quantum Wires

We study the anomalous conductance plateau around $G=0.7(2e^2/h)$ and the zero bias anomaly in ballistic hole quantum wires with respect to in-plane magnetic fields applied parallel $B_{\parallel }$ and perpendicular $B_{\perp }$ to the quantum wire. As seen in electron quantum wires, the magnetic fields shift the 0.7 structure down to $G=0.5(2e^2/h)$ and simultaneously quench the zero bias anomaly. However, these effects are strongly dependent on the orientation of the magnetic field, owing to the highly anisotropic effective Landé $g$-factor $g^{*}$ in hole quantum wires. Our results highlight the fundamental role that spin plays in both the 0.7 structure and zero bias anomaly.

Figure 1

(a) $G$ of the quantum wire versus side-gate voltage $V_{\mathrm{SG}}$, for $T=20$, 200, 320, 550, and 650 mK; Each curve is shifted to sit on top of the 20 mK curve; (b) $G$ versus source-drain bias $V_{\mathrm{SD}}$ for different $V_{\mathrm{SG}}$ at $T=20\mathrm{mK}$; (c) $G$ versus $V_{\mathrm{SD}}$ for different $V_{\mathrm{SG}}$ at $T=320\mathrm{mK}$; data are taken for back and middle gates fixed at 2.5 and $-0.225\mathrm{V}$ respectively. No magnetic field is applied to the system; (a), (b) and (c) are data taken from the same cool down.

Figure 2

(a) $G$ of the quantum wire versus side-gate voltage $V_{\mathrm{SG}}$ for different in-plane magnetic fields parallel to the wire ($B_{\parallel }$) from 0 T (i.e., when 1D subbands are degenerate), to 3.6 T (i.e., when 1D subbands are completely spin-resolved), in increments of 0.2 T (from left to right). $T=20\mathrm{mK}$, back and middle gates are at 2.5 and $-0.225\mathrm{V}$, respectively. All curves are offset for clarity. (b) gray scale of the transconductance as a function of $B_{\parallel }$ up to 8.8 T and $G$. White regions correspond to low transconductance (conductance plateaus). (c) gray scale of the transconductance as a function of versus $B_{\perp }$ and $G$, with similar experimental conditions.

Figure 3

(a) and (b): $G$ versus $V_{\mathrm{SD}}$ for different $V_{\mathrm{SG}}$ of the same quantum wire at (a) $B_{\parallel }=0\mathrm{T}$ and (b) $B_{\parallel }=3.6\mathrm{T}$, $T=20\mathrm{mK}$, back and middle gates are at 2.5 and $-0.225\mathrm{V}$, respectively, [(a) and (b) are taken at the same cool down]. (c), (d), and (e): $G$ versus $V_{\mathrm{SD}}$, for different $V_{\mathrm{SG}}$, for $B_{\perp }=0$, 3.6 and 10 T, in similar experimental conditions [(c), (d) and (e) are taken at the same cool down; (c) and Fig. 1b are the same data]: the ZBA is clearly observed at $B_{\perp }=0$ and 3.6 T. At $B_{\perp }=10\mathrm{T}$, the ZBA vanishes at low conductance.