Figure 5 : Calculation of the electron density and estimation of the Wigner crystal size.

From: Wigner and Kondo physics in quantum point contacts revealed by scanning gate microscopy

Figure 5

(a) Geometry of the metallic gates and SGM tip defined in the Comsol simulation software and example of electrostatic potential map computed for a given gate voltage and tip position. The Fermi energy EF is 8 meV in the 2DEG. (b) Map of the two-dimensional electron density n2D in the 2DEG computed classically but self-consistently with the potential, when the tip is at 1 μm from the QPC. (c) One-dimensional electron density n1D obtained by integration of n2D along the y axis, when the tip is at 1 μm and 400 nm from the QPC. Choosing a critical density determines the expected size Lcrystal of the 1D Wigner crystal. (d) Computed size of the Wigner crystal as a function of tip position in an horizontal plane 30 nm above the surface (Vgate=−1 V). The region in red corresponds to a closed contact (the electron density is zero at the QPC center for these tip positions). Black lines indicate tip positions for which Lcrystal is enlarged by , corresponding at first order to the addition of one charge to the crystal. (e) Computed size of the Wigner crystal for tip positions in a vertical plane (above line X1 at 35° from QPC axis).