Only a magnetic field is present. Run and we see in the right display both simple CCW "electron" orbits near the origin and rather strange orbits near the Fermi surface. At any particular time between the discontinuous jumps from one place on the zone boundary to another, these seem to be circulating CCW. If we watch the empty states, i.e. the hole representation at the left with the different segments of the Brillouin zone appropriately shifted, we see well behaved nearly circular orbits with a CW sense of circulation.
Add an electric field of 2x10^6 V/m in the x-direction and initialize the program. Show graph to see a plot of the x- and y-components of the average hole velocity. What is the sign of the y-component of the average electron velocity? What does this imply for the sign of the Hall effect? Note the signs of the x- and y-components of the average hole velocities. You may display these on a graph with the show graph toggle. Change the Fermi energy to 3 eV and turn off the show holes toggle so that the graph displays the electron velocities. Explain the signs here relative to those for the hole picture. Why are the y-components of the velocities the same, even though the charges of the carriers are opposite?