Row coupling in an interacting quasi-one-dimensional quantum wire investigated using transport measurements

We study electron transport in quasi-one-dimensional wires at relatively weak electrostatic confinements, where the Coulomb interaction distorts the ground state, leading to the bifurcation of the electronic system into two rows. Evidence of finite coupling between the rows, resulting in bonding and antibonding states, is observed. At high dc source-drain bias, a structure is observed at $0.5\left(2e^2/h\right)$ due to parallel double-row transport, along with a structure at $0.25\left(2e^2/h\right)$, providing further evidence of coupling between the two rows.

Figure 1

(Color online) (a) Evolution of conductance plateaus with 1D confinement at $B=16\text{T}$; the magnetic field was applied in the plane of the 2DEG, perpendicular to the 1D channel. Conductance $G\left(V_{tg}\right)$ was measured as $V_{tg}$ was swept at fixed $V_{sg}$, with a constant offset of 2 V between the split gates. $V_{sg}$ was incremented between traces in steps of $-50\text{mV}$ (left to right) from $-2.6,-0.6\text{V}$ to $-4.5,-2.5\text{V}$ (voltages on both split gates given). The device layout is shown in the inset. The arrow indicates the region in which a double row forms. (b) Grayscale plot of transconductance $dG/d{V}_{tg}$ as a function of $V_{tg}$ and $V_{sg}$ at 16 T, with white representing regions of high transconductance. “$\ast$” marks the disappearance of the first plateau and the anticrossing of energy levels. The dashed lines mark typical “cuts” through each region of confinement; some of the plateau heights at these cuts are marked. (c) Energy level diagrams showing the spin splitting of 1D subbands with magnetic field at points corresponding to (i), (ii), and (iii) on (b). Descending (solid) and ascending (dashed) branches represent spin-down $(\downarrow )$ and spin-up $(\uparrow )$ states, respectively, as illustrated in (c) (iii). The vertical dashed lines correspond to $B=16\text{T}$.

Figure 2

(Color online) (a) Conductance traces at 0 T, sweeping $V_{tg}$ at fixed $V_{sg}$ (sample A). $V_{sg}$ is incremented from $-2.6,-0.6\text{V}$ (left) to $-3.7,-1.7\text{V}$ (right). (b) Grayscale $dG/d{V}_{tg}$ plot of (a) as a function of $V_{tg}$ and $V_{sg}$. The first bonding (1) and antibonding $\left(1^{\ast }\right)$ states are shown in the inset. (c) Grayscale $dG/d{V}_{mid}$ plot for sample B as a function of $V_{mid}$ and $V_{sg}$. The first bonding (1) and antibonding $\left(1^{\ast }\right)$ states are shown in the inset; the first three bonding and antibonding states are marked on the grayscale.

Figure 3

(Color online) (a) and (b) Conductance traces sweeping $V_{tg}$ at $V_{sg}=-2.59,-0.77\text{V}$ $\left(B=0\text{T}\right)$ and $-2.79,-0.79\text{V}$ $\left(B=16\text{T}\right)$, respectively. $V_{sd}$ is incremented from zero on the left to $-3\text{mV}$ on the right, in steps of 0.25 mV; traces are offset for clarity. (c) Conductance traces at $B=0\text{T}$, sweeping $V_{sg}$, for an uncoupled double row of electrons (data from another quantum wire). $V_{sd}$ is incremented from left to right in steps of 0.5 mV from zero to $-5\text{mV}$; traces are offset for clarity. The arrows indicate the 0.5 feature at finite bias. The grayscale plots of $dG/d{V}_{tg}$ corresponding to (a) and (b) are shown in (d) and (e), respectively, as a function of $V_{tg}$ and $V_{sd}$. (f) Grayscale shows the characteristic single row behavior, in strong confinement, at 0 T. Certain conductance plateaus are marked on the grayscales in units of $2e^2/h$.