Study on Disorder and Branched Electron Flow 8 |

ABSTRACT:

The effects ofa magnetic afield are somewhat intuitive, but are nonetheless interesting tonote. First, let us consider the effect of a magnetic field on the electron uxitself. In a system with a bat potential, the effect of the field would be tobend all electron trajectories to curves with some known cyclotron radius. Withdisorder present, however, the dynamics will favor some paths over others(hence the branched nature of the own). The competition between these dynamicsfor electrons in the magnetic field results in a \ratcheting" of thebranches as the field strength is increased, rather than a continuous sweeping.Though this is difficult to convey without a continuous set of ux images. Theshifting of branches has greater implications for the experimental situation,since the accessible conductance measurement depends on scattering. We canunderstand the correlation between the measured conductance and electron ux byconsidering classical trajectories. To decrease the conductance of the system,a trajectory needs to be scattered by the AFM tip and return to the QPC. In theabsence Here we see two sets of electron ux density data, taken with the samedisordered potential but at two differentmagnetic field values. For the topimage B = 0, and for the bottom image B = 25 mT. Both data sets cover an areatwo microns long by one micron high. We see that, when the field is increased,the branches do not bend continuously. Rather, the branches are the same out tosome distance, at which point the electrons take clearly distinct paths. Weunderstand this as the effect of the magnetic field accumulating until it issuffcient to cause trajectories to jump from one dynamically favored branch toanother. This ratcheting effect continues as the ux increases, resulting in acumulative net bending of trajectories. We also notethat ux density has shifted within the branches present, another effect thataccomplishes the net bending caused by the magnetic field.this means that thetrajectory should impinge on the AFM tip Potential at a right angle to theclassical turning point and be scattered back along itself.