Magnetotransport in a spatially modulated magnetic field

Abstract

We h a ve measured the Shubnikov de Haas SdH oscillations of a nonplanar two-dimensional electron gas 2DEG fabricated by o vergrowth of a GaAs AlGaAs heterojunction on a pre-patterned substrate. When placed in a uniform external magnetic eld B, the eld normal to the nonplanar 2DEG is spatially modulated, and electrons experience a nonuniform magnetic eld. In a tilted magnetic eld, the SdH oscillations are much more strongly damped than in a eld perpendicular to the substrate. We consider several mechanisms and conclude that the electron scattering by the magnetic eld spatial uctuations plays a main role in the transport properties of a nonplanar 2DEG at low magnetic eld.Recently, new regrowth techniques have been reported to produce a two-dimensional electron gas 2DEG on nonplanar pre-patterned GaAs substrates 1,2 . The interest in fabricating such systems is generated by the possibility t o i n vestigate the physics of electron motion in a nonuniform magnetic eld. Since a 2DEG is sensitive to only the normal component of the magnetic eld B, electrons con ned to a nonplanar heterojunction experience nonuniform magnetic eld varying with position, depending of the surface shape, if an uniform B is applied to such nonplanar surface.This letter reports on the fabrication of 2DEG on a nonplanar stripe-shaped surface with small heights of the stripes. The 2DEG has the mobility of 250-400 10 3 cm 2 Vs at a carrier density o f 5 . 4 10 11 cm ,2 . We studied the electron transport properties of nonplanar 2D electrons in a magnetic eld. Fig. 1a shows the pro le of the surface in the direction along the stripes x direction and across the stripes y direction measured by atomic force microscopy. Along the x direction we can see both irregular and periodical components in the surface corrugation. The average periodicity is coincident with the antidot lattice periodicity before overgrowth. The corrugation height h v aries between 20 and 65 A. Fig. 1a shows also a irregular surface pro le along the y direction with smaller corrugation height and larger average periodicity than along the x direction. The origin of these irregularities in not understood. The patterned area was 140 140 m 2 . After regrowth, the HEMT structure was processed into Hall bars, and the nonplanar surface was situated on the one side of Hall bar see insert of g 2 . As was mentioned before, since 2DEG is sensitive only to the normal component o f B , measuring the resistance for di erent angles between the eld and the normal to the substrate surface allows us to vary the magnitude of the magnetic eld uctuations. If magnetic eld is tilted away from the normal to the substrate, the normal component o f B c a n b e expressed as B N x; y; z= B5f = j 5f j ; 1 where gradient 5f df dx, df dy, df dz is de ned for the surface f x; y; z = 0. In realistic samples we h a ve df=dy h=d 1. Therefore, if the external magnetic eld is tilted in the y direction, the expression 1 can