Incoming electrons

Choose coordinates xx and yy on a horizontal 2-d graphene sheet. We will inject electrons into the sheet from the origin OO such that they enter the upper half-plane (y>0y>0) but the direction is otherwise totally random. The speed of electrons in graphene is vFv_F, and the mass of each electron is mm.

We now put an electron detector along the xx-axis (y=0y=0) and apply an external magnetic field B0B_0 perpendicular to the plane (parallel with the zz-axis). At what value of xx in meters will the detector receive the greatest signal?

Assume that every electron that goes to the lower half plane (y<0y<0) will disappear (for example, the lower half plane is made of a special material which absorbs electrons).

Details and assumptions

To make the problem numerically simpler, use the following values for your calculation:

  • vF=1 m/sv_F=1~\mbox{m/s}

  • m=1 kgm=1~\mbox{kg}

  • B0=1 TB_0=1~\mbox{T}

  • The electron charge is e=1 Ce=1~\mbox{C}.

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