Finite-size effects on transverse magnetoresistance of ${\mathrm{NbSe}}_3$

A charge-density-wave material ${\mathrm{NbSe}}_3$ with thickness less than 1 μm shows a distinct peak in the low temperature transverse magnetoresistance when the magnetic field is applied along the $c$ axis. The resistance peak is less pronounced as the field is tilted away from the $c$ axis to the $a^{*}$ axis. The peak height also decreases as the temperature increases, although the magnetic field at the peak shows no appreciable dependence on temperature. The resistance peak is attributed to surface diffuse scattering of normal carriers which remain even below the lower charge-density-wave transition temperature.

Figure 1

The magnetoresistance of a ${\mathrm{NbSe}}_3$ crystal with 0.49 μm thickness (sample 1) at several temperatures; $T=16.00\mathrm{K}$, 12.00 K, 10.00 K, 8.00 K, 6.00 K, 4.00 K, and 0.28 K from the top curve to the bottom one. Inset: An enlargement of the low-magnetic-field region. $T=8.00\mathrm{K}$, 6.00 K, 4.00 K, and 0.28 K from top to bottom. The arrows indicate the magnetic fields $B=0.55\hslash \sqrt{S_{a\ast b}∕\pi }∕e{d}_{a*}$ and $2.0\hslash \sqrt{S_{a\ast b}∕\pi }∕e{d}_{a*}$.

Figure 2

The magnetoresistance of (a) thick (3) and (b) thin (4) crystals, measured at 0.28 K for the field orientations $\theta =0°$, 30°, 60°, 90°, 120°, and 150°. The $c$ axis corresponds to $\theta =98°$ for sample 3 and $\theta =36°$ for sample 4. The arrows indicate the magnetic fields $B=0.55\hslash \sqrt{S_{a\ast b}∕\pi }∕e{d}_{a*}$ and $2.0\hslash \sqrt{S_{a\ast b}∕\pi }∕e{d}_{a*}$.

Figure 3

The magnetic fields $B_{\max }$ and $B_{\min }$, where the magnetoresistance curves show a maximum and a minimum, plotted as a function of $\hslash \sqrt{S_{a\ast b}∕\pi }∕e{d}_{a*}$. The closed and open circles show $B_{\max }$ and $B_{\min }$, respectively. The solid lines have slopes of 0.55 and 2.0.

Figure 4

The magnetoresistance of sample 6 at $T=1.72\mathrm{K}$. This sample has the narrowest width along the $c$ axis. The upward arrows indicate the magnetic fields $B=0.55\hslash \sqrt{S_{a\ast b}∕\pi }∕e{d}_{a*}$ and $2.0\hslash \sqrt{S_{a\ast b}∕\pi }∕e{d}_{a*}$, while the downward arrows indicate $B=0.55\hslash \sqrt{S_{bc}∕\pi }∕e{d}_c$ and $2.0\hslash \sqrt{S_{bc}∕\pi }∕e{d}_c$.