We demonstrate ballistic transport in a cross junction in a high-mobility,
two-dimensional electron gas, which is rolled up as a tube. The
distinctiveness of our structure is, that the electron mean free
path is as large as the radius of the tube, r = 20 μm.
As a result we observe negative bend resistances at zero magnetic
field indicating that part of the electron trajectories move
ballistically along the periphery of the tube. They bend in space by
about 60 ° while still being confined in the curved quantum
well. In magnetic fields which are perpendicular at the center of
the cross junction, the bend resistance is symmetric with respect to
the field orientation.
In contrast, we observe a dramatically different behavior, when the magnetic
field is tilted away from the surface normal at the center of the
cross junction arc by an angle φ. In this case electrons follow trochoid-like
trajectories due to reflection at magnetic barriers. Electrons on such trajectories move in an opposite direction as compared to the direction of conventional guided electrons. An analysis with the Landauer-Büttiker formalism shows, that the bend resistance becomes strongly asymmetric with respect to the orientation of the magnetic field.
At high magnetic fields, the conductance is completely determined by one-dimensional channels (1DC), related to Landau states, that are bent away from the sample edge into the conducting layer due to the magnetic field gradient.
We show, that narrowing of two 1DC with opposite electron velocities will enhance the interaction, which determines the bend resistance at transitions from one filling factor to another. This is the same scheme as for the non-zero bend resistances due to trochoid-like trajectories at low fields, which therefore may be regarded as a
precursor for the 1DC at high magnetic fields. We also discuss the case with the magnetic field being oriented tangentially along to the curved surface, when the magnetic field is of opposite directions in different regions of the sample. Investigations on systems like this open the way to study motion of electrons on nontrivial curved surfaces and the global topology effects on quantum-mechanical wave functions. |