Anomalous spin-dependent behavior of one-dimensional subbands

We report an electron interaction effect in $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ quantum wires. Using dc-bias spectroscopy, we show that large and abrupt changes occur to the energies of spin-down (lower energy) states as they populate. The effect is not observed for spin-up energy states. At $B=0$, interactions have a pronounced effect, in the form of the well-known 0.7 structure. However, our results show that interactions strongly affect the energy spectrum at all magnetic fields, from $0\text{to}16\mathrm{T}$, not just in the vicinity of the 0.7 structure.

Figure 1

(Color online) (a) Gray scale of $dG∕d{V}_{\mathrm{g}}$ data at $5\mathrm{T}$ as a function of $V_{\mathrm{ds}}$ and $V_{\mathrm{g}}$. Upper panel: $dG∕d{V}_{\mathrm{g}}$ at $5\mathrm{T}$ from $V_{\mathrm{ds}}=0$ (top trace) to $V_{\mathrm{ds}}=0.12\mathrm{mV}$ (bottom trace). (b) Closeup of features in (a) between $V_{\mathrm{g}}=-1.18\mathrm{V}$ and $V_{\mathrm{g}}=-1.215\mathrm{V}$. Conductances of the plateau regions are marked in units of $2e^2∕h$. (c) As (b) but annotated. (d) Configuration of energy levels at the points marked in (c).

Figure 2

(Color online) (a) A typical example of $V_{\mathrm{ds}}$ data for the first subband at $B=0$. (b) $dG∕d{V}_{\mathrm{g}}$ data used in (a), from $V_{\mathrm{ds}}=0$ to $0.24\mathrm{mV}$ in steps of $0.03\mathrm{mV}$, for the first three subbands. The pinch-off voltages have been aligned for clarity, and the peaks labeled with their corresponding subbands. (c)–(f) $V_{\mathrm{ds}}$ data for 2↓ at $B=5$, 9, 11, and $14\mathrm{T}$. V-shaped splitting begins at $0.07\mathrm{mV}$, $0.09\mathrm{mV}$, $0.12\mathrm{mV}$, and $0.15\mathrm{mV}$, respectively. The white lines are a guide to the eye. (g) Plot of the biases at which splitting begins, as a function of $B$, for 1↓ and 2↓ (open or closed symbols) of three samples (circles, squares or triangles). The onset of splitting is found by marking the $dG∕d{V}_{\mathrm{g}}$ peak trajectories by hand and finding their intersection. (h) $V_{\mathrm{ds}}$ data from another sample at $16\mathrm{T}$. V-shaped splitting on the first two subbands clearly begins at $V_{\mathrm{ds}}>0$.