Wigner crystals of two-dimensional electrons

5 problems

• Critical density for Wigner crystallization of the clean 2D electron gas

  Open

  Computer simulations predict the electron sheet crystallizes once repulsion exceeds kinetic energy by a factor of roughly 30 to 40, but the exact threshold and whether the change is abrupt are not pinned down.

• How does the field-induced Wigner crystal melt into quantum Hall liquids?

  Open

  A strong perpendicular magnetic field shrinks electron orbits and favors a crystal at low filling, but fractional quantum Hall liquids compete with it. How the system passes between the two, and whether unusual intermediate states appear, is open.

• Are there intermediate phases between the Wigner crystal and Fermi liquid?

  Contested

  Theory argues that with long-range Coulomb repulsion a sharp switch from liquid to crystal is impossible in two dimensions, so mixed phases of crystal bubbles or stripes should appear in between. Whether these microemulsion phases exist is disputed.

• Is the low-density insulator in silicon devices a pinned Wigner solid?

  Open

  Below the critical density, clean silicon electron sheets stop conducting, and their current-voltage curves look like those of a solid held in place by impurities that slides when pushed hard enough. Whether this insulator is a pinned electron crystal or a disordered glass of trapped electrons is unsettled.

• Magnetic ground state of the 2D Wigner crystal near melting

  Open

  Electrons in the crystal can swap places by quantum tunneling, which couples their spins. Which spin arrangement results near the melting density, possibly a spin liquid (a state with no magnetic order even at zero temperature), is unknown.