Negative nonlocal vicinity resistance of viscous flow in a two-dimensional electron system

We perform a quantum transport study of Hall viscous liquid in multiterminal narrow Hallbar devices of a high-mobility two-dimensional electron system (2DES) in GaAs/AlGaAs heterostructure. In the nonlocal transport measurements of vicinity geometry under magnetic fields $\left(B\right)$, we observe that the absolute negative magnetoresistance $\left(R_{xx}\right)$ value $(R_{\text{min}}<0)$ and the corresponding magnetic field $\left(B_{\text{min}}\right)$ are both inversely proportional to the adjacent Hallbar arm distance $\left(L\right)$. The occurrence of negative resistance is dependent on the characteristic lengths of the devices and the electron flow direction under $B$-fields. The minimal resistance $R_{\text{min}}$ occurs when the cyclotron radius $R_C$ approximates $L$. Multiples of high-order ($n\mathrm{th}$-order) $R_{\text{min},n}$'s persist from low to high magnetic fields in a large sample size of $L=5\mu \mathrm{m}$. Our experimental study reveals the transport behaviors in the vicinity regime, where the negative resistances depict viscous electronic flows in the high-mobility 2DES. In addition, the negative and high-order minimal resistances expand to a magnetic field of several kGs.

Figure 1

(a) Longitudinal resistance (black dash-dotted curve) and Hall resistance (red solid curve) of S1 measured at 1.5 K. The insets show the configurations of $R_{xx}$ and $R_{xy}$ measurements, respectively. (b) Clockwise (black) and counterclockwise (red) $R_{xx}$ curves show mirror image features of each other with respect to the $B=0$ axis. (c) Clockwise (black) and counterclockwise (red) $R_{xx}$ curves show mirror image features of each other with respect to the $B=0$ axis.

Figure 2

(a) Temperature-dependent $R_{xx}$ of S1 at $T\sim 1.5-30$ K. The inset shows $R_{xx}$ (at $B\sim 0.96$ kG) vs $T$. (b) $T$-dependent $R_{xy}$ in the regime of $T\sim 1.5-30$ K.

Figure 3

(a) The Hallbar (S1, S2, and S3) size-dependent $I\text{−}V$ $\left(R_{xx}\right)$ under low $B$-fields at 1.5 K. The left inset shows the dimensions ($w$, $L$, and $d$) of the multiprobe Hallbar devices (S1, S2, and S3), which are consistent with the parameters in Table 1. The inset on the right exhibits the relations of the minimal $R_{xx}$ ($R_{\text{min}}$, left axis) vs $1/L$ and corresponding $B$-field ($B_{\text{min}}$, right axis) vs $1/L$. Both $R_{\text{min}}$ and $B_{\text{min}}$ are proportional to $1/L$. (b) The zoomed-in features of the negative nonlocal resistance of S1 at 1.5 K. Black, blue, and red dashed lines highlight the minimal features that are centered near $B=0.96$, 0.48, and 0.24 kG, respectively.

Figure 4

Longitudinal resistance and Hall resistivity in the $I\text{−}V$ measurements of structure S4 at 1.5 K. Top inset: zoomed-in $R_{xy}$ features at $-2<B<2$ kG (red curve), and the blue dots highlight the indication features of viscous electron fluids at $-1<B<1$ kG. The configurations of $R_{xx}$ and $R_{xy}$ in nonlocal $I\text{−}V$ measurements are displayed in the inset at the bottom-right corner and the bottom inset, respectively. In addition, the trajectory of the electron flows under magnetic fields with the relation of $2(n+\frac{1}{2})R_C=L$ is shown in the upper right inset, where the zeroth order ($n=0$) is displayed by the black solid curve and the integer $n\mathrm{th}$ order is exhibited by the red dashed curve.