Commensurability oscillations by snake-orbit magnetotransport in two-dimensional electron gases

Commensurate magnetoresistance periodic oscillations generated by transversal electron snake orbits are found experimentally. A two-dimensional electron gas is exposed to a magnetic field that changes sign along the current longitudinal direction and is homogeneous in the transverse direction. The change in sign of the magnetic field directs the electron flow along the transversal direction, in snake orbits. This generates resistance oscillations with a predictable periodicity that is commensurate with the width of the electron gas. Numerical simulations are used to reveal the character of the oscillations.

Figure 1

(a) Top-view scheme of the sample layout. The Dy film is magnetized in the transport direction, creating a localized magnetic field profile under the edges. The homogeneous Cr/Au gate that covers the whole structure is not shown. (b) Sketch of the sample orientation with respect to the magnetic field ${\vec{B}}_{\mathrm{ext}}$ generated by the superconducting magnet. (c) Longitudinal resistance of the magnetic barrier as a function of $B_{\parallel }$ for parallel alignment of the sample. Arrows indicate the sweep direction. (d) The barrier's Hall resistance (blue) and the extracted magnetization trace of the Dy film (red).

Figure 2

$R_{23}\left(B_{\perp }\right)$ for samples (a) A and (b) B for different electron densities, with the Dy film at saturation magnetization. The insets in (b) sketch $B_z\left(x\right)$ (red) for positive and negative $B_{\perp }$.

Figure 3

Experimental data from sample B in comparison with the semiclassical and the quantum simulations, for the electron density $n=3.5\times {10}^{15}{\mathrm{m}}^{-2}$. The dotted lines indicate the position of the oscillations that are visible in the experimental curve (corresponding to peaks 1, 2, and 3).

Figure 4

Local density of states at the maxima of resistance peaks (a) 2 and (b) 3 as well as at the minimum in between (c) for the experimentally implemented structure with a Hall bar width of $10\mu \mathrm{m}$, and (d) for the maximum of resistance peak 2 in a 5-$\mu \mathrm{m}$-wide Hall bar. In each case, the electron motion is exemplified by a corresponding classical trajectory (red lines with arrows). Also, the zero lines of the perpendicular magnetic field $B-z\left(x\right)$ are denoted by the semitransparent gray lines.