Imaging magnetic focusing of coherent electron waves

The coherent flow of electrons through a two-dimensional electron gas1,2,3,4,5,6,7,8 (2DEG) offers promising approaches for spintronics8,9,10 and quantum information processing11,12. Cryogenic scanning probe microscopes (SPMs) are a valuable tool for imaging electron motion13,14,15,16,17,18,19,20,21,22,23,24,25, but have been limited by their inability to follow such motion through an open structure under an applied magnetic field. Here we report a way to visualize the flow of electron waves from one point to another by using the SPM tip to create a lens in the 2DEG below. The lens deflects electrons and casts a shadow downstream. We use this technique to image magnetic focusing in a GaAs 2DEG. Magnetic focusing occurs when electrons flowing from one quantum point contact (QPC) rejoin at a second QPC a number of cyclotron diameters away3,4,9,26,27. Our images show semicircular trajectories as the electrons bounce along the boundary, as well as fringes created by the interference of multiple paths, demonstrating that the flow is coherent18,19,28. Remarkable agreement between experiment and theory demonstrates our ability to visualize electron trajectories in a magnetic field, and to make a new type of imaging electron interferometer.