Incipient Formation of an Electron Lattice in a Weakly Confined Quantum Wire

We study the low-temperature transport properties of 1D quantum wires as the confinement strength $V_{\mathrm{conf}}$ and the carrier density $n_{1\mathrm{D}}$ are varied using a combination of split gates and a top gate in $\mathrm{GaAs}/\mathrm{AlGaAs}$ heterostructures. At intermediate $V_{\mathrm{conf}}$ and $n_{1\mathrm{D}}$, we observe a jump in conductance to $4e^2/h$, suggesting a double wire. On further reducing $n_{1\mathrm{D}}$, plateau at $2e^2/h$ returns. Our results show beginnings of the formation of an electron lattice in an interacting quasi-1D quantum wire. In the presence of an in-plane magnetic field, mixing of spin-aligned levels of the two wires gives rise to more complex states.

Figure 1

(a) Conductance traces of sample A measured by sweeping the $V_{\mathrm{tg}}$ at various fixed $V_{\mathrm{sg}}$. Moving right to left, $V_{\mathrm{sg}}$ is incremented from $-2$ to $-0.52\mathrm{V}$ in steps of 20 mV, corresponding to a widening of the quantum wire or a weakening of the confining potential. (b) A schematic diagram of the device (not to scale) showing the split gates (sg) and top gate (tg) separated by a dielectric layer (PMMA). (c) Conductance characteristics of a sample B showing the suppression and disappearance of the plateau at $2e^2/h$ with weakening confinement. All other measurements described in this Letter are from sample A.

Figure 2

Gray-scale plots of transconductance $dG/d{V}_{\mathrm{tg}}$ as a function of $V_{\mathrm{tg}}$ and $B$ for the last few subbands in sample A. Each panel corresponds to a given $V_{\mathrm{sg}}$, and therefore wire width, which decreases from left to right. Dark and light areas correspond to regions of small and large gradients, respectively, in $dG/d{V}_{\mathrm{tg}}$ with respect to $V_{\mathrm{tg}}$. The white lines therefore represent the risers between conductance plateaus, i.e., subband edges, while the dark areas represent the plateaus themselves. The reentrant $2e^2/h$ plateau at far left of Fig. 1a is represented as a thin dark line at $V_{\mathrm{tg}}\sim -1.34\mathrm{V}$ in the low-field region of panel 1.

Figure 3

(a) Conductance traces as in Fig. 1a, but in an in-plane magnetic field $B=7\mathrm{T}$ perpendicular to the transport direction. Well-defined plateaus quantized in multiples of $e^2/h$ are present on the right. The first quantized plateau at $e^2/h$ disappears in the intermediate $V_{\mathrm{tg}}$ regime, coincident with the suppression of $2e^2/h$ plateau. It should be noted that, were it a noninteracting single-mode wire, this would not be possible. The oscillation superimposed on the suppressed plateau can be shown to be due to a mixing of two spin-aligned rows from the corresponding gray scale of this plot. (b) A repeat of the measurement shown in (a), but with $B=16\mathrm{T}$. The onset of the oscillations coincides with the incursion of a descending plateau coming from $2e^2/h$, as indicated by the blue arrow.

Figure 4

(a) Conductance traces taken at $V_{\mathrm{sg}}=-1\mathrm{V}$ showing the evolution of the declining $2e^2/h$ plateau with increasing temperature. From left to right, $T_{\mathrm{lattice}}=0.05,0.1,0.2,0.3,0.4,0.5,0.6,0.8,1.0,1.2,1.45,1.95,2.65,3.5,4.5\mathrm{K}$. (Traces have been offset from the 50 mK trace for clarity.) (b) A single trace from Fig. 3b showing the behavior of the oscillatory structure as the channel is shifted laterally by differentially biasing the split gates. (Successive traces are offset, the bold trace corresponding to equal bias on the split gates.)