Strongly Anisotropic Ballistic Magnetoresistance in Compact Three-Dimensional Semiconducting Nanoarchitectures

We establish theoretically that in nonmagnetic semiconducting bilayer or multilayer thin film systems rolled up into compact quasi-one-dimensional nanoarchitectures, the ballistic magnetoresistance is very anisotropic: conductances depend strongly on the direction of an externally applied magnetic field. This phenomenon originates from the curved open geometry of rolled-up nanotubes, which leads to a tunability of the number of quasi-one-dimensional magnetic subbands crossing the Fermi energy. The experimental significance of this phenomenon is illustrated by a sizable anisotropy that scales with the inverse of the winding number, and persists up to a critical temperature that can be strongly enhanced by increasing the strength of the external magnetic field or the characteristic radius of curvature, and can reach room temperature.

Figure 1

(a) Cross section of a rolled-up nanotube with 1.1 windings perpendicular to the tube axis. $R_{\text{in}}$, $R_{\text{out}}$ indicate the inner and outer radii of curvature. The black line indicates the 2DEG embedded in a bilayer stack. (b) Cartoon representation of the magnetic states for a 2DEG on a nanotube with periodic boundary conditions. (c) Same for open boundary conditions.

Figure 2

(a) Magnetic spectrum for a nanotube with $R_{\text{in}}=32\pi \mathrm{nm}$ subject to a 1.65 T transversal magnetic field assuming periodic boundary conditions (BCs). $k_z$ is the momentum along the tube axis. (b) Same for a single wound RUNT with open boundary conditions and magnetic field oriented along the edge axis ($\theta \equiv 0$). The green and orange lines explicitly show the dispersive edge states that are absent assuming periodic boundary conditions. (c) and (d) show the evolution of the magnetic spectrum of panel (b) varying the magnetic field direction to $\theta =\pi /4$ and $\theta =\pi /2$ respectively.

Figure 3

(a) Low-temperature magnetoconductance measured in $2e^2/h$ units as a function of the inverse of the 2DEG Fermi wavelength for a magnetic field oriented parallel to the edge axis (blue line) and perpendicular to it (purple line). (b) Maximum value of the anisotropy BAMR(0) for temperatures up to room temperature.

Figure 4

(a) Angular dependence of the BAMR at $T=20\mathrm{K}$ and Fermi wavelength ${\lambda }_F\simeq 46\mathrm{nm}$. The solid lines correspond to a fit obtained using Eq. (3). (b) Scaling of the BAMR effect as a function of the number of windings of the nanotube for different values of the Fermi wavelength.