Quantized conductance of one-dimensional strongly correlated electrons in an oxide heterostructure

Oxide heterostructures are versatile platforms with which to research and create novel functional nanostructures. We successfully develop one-dimensional (1D) quantum-wire devices using quantum point contacts on MgZnO/ZnO heterostructures and observe ballistic electron transport with conductance quantized in units of $2e^2/h$. Using dc-bias and in-plane field measurements, we find that the $g$ factor is enhanced to around 6.8, more than three times the value in bulk ZnO. We show that the effective mass $m^{*}$ increases as the electron density decreases, resulting from the strong electron-electron interactions. In this strongly interacting 1D system we study features matching the “0.7” conductance anomalies up to the fifth subband. This Rapid Communication demonstrates that high-mobility oxide heterostructures such as this can provide good alternatives to conventional III-V semiconductors in spintronics and quantum computing as they do not have their unavoidable dephasing from nuclear spins. This paves a way for the development of qubits benefiting from the low defects of an undoped heterostructure together with the long spin lifetimes achievable in silicon.

Figure 1

(a) Scanning electron micrograph of a QPC (source S and drain D), and schematic diagram of the device cross section across the channel. The 2DEG forms at the MgZnO/ZnO interface (red line). Ti/Au gates are patterned using electron-beam lithography and deposited on parylene-$C$ insulator. (b) Conductance $G$ as a function of split-gate voltage $V_{\mathrm{SG}}$ (devices A and B), showing plateaus at multiples of $2e^2/h$. Inset: $G$ over the full $V_{\mathrm{SG}}$ range. The drop corresponds to depletion of electrons beneath the gates leaving a quasi-1D wire in the gap. (c) Transconductance $dG/d{V}_{\mathrm{SG}}$ vs bias $V_{\mathrm{dc}}$ and $V_{\mathrm{SG}}$ (devices A and B). Dark (bright) regions correspond to plateaus (risers) in conductance. The energy difference between the third and fourth 1D subbands is $e\mathrm{\Delta }{V}_{\mathrm{dc}}$, which is measured from the crossing point of adjacent subbands as indicated in the plot. The numbers indicate heights of conductance plateaus (units $e^2/h)$.

Figure 2

The differential conductance $dG/d{V}_{\mathrm{SG}}$ (units $2e^2/h/V)$ vs $V_{\mathrm{SG}}$ at different (a) $B_{\parallel }$, and (b) and (c) $B_{\perp }$ for devices as labeled. $\mathrm{\Delta }B$ indicates the required $B_{\parallel }$ for the crossing of subbands $2_{\uparrow }$ and $3_{\downarrow }$. Ellipses in (b) indicate positions of subband crossings. The calculated electron energy spectrum vs $B_{\perp }$ with (d) constant and (e) increasing $m^{*}$. The numbers indicate the heights of conductance plateaus (units $e^2/h)$, and blue dots mark positions of crossings.

Figure 3

Transconductance $dG/d{V}_{\mathrm{SG}}$ as a function of $V_{\mathrm{SG}}$ and $V_{\mathrm{dc}}$ for (a) device A at $B_{\perp }=1\mathrm{T}$, and (b) device C at $B_{\perp }=2\mathrm{T}$. In device C, the high electron density and thick MgZnO $\left(500\mathrm{nm}\right)$ require strong negative voltages to define the 1D wire. The plateau conductances are indicated (units $e^2/h)$. (c) $m^{*}$ measured vs $G$ in both devices, compared with the bulk value for ZnO.

Figure 4

Conductance $G$ vs $V_{\mathrm{SG}}$ at different $B_{\parallel }$ from 0 to $1\mathrm{T}$ in steps of $0.02\mathrm{T}$. Each trace is shifted to the right by $0.01\mathrm{V}$ relative to the previous trace for clarity. Red dots illustrate how the shoulder features resembling the 0.7 anomaly evolve with $B_{\parallel }$ [same measurement data and labels as in Fig. 2]. An estimated series resistance of around $110\mathrm{\Omega }$ has been subtracted.