Metal-Insulator Transition

In 1d there is always a bound state, no matter how shallow the potential well:

In 3d, screening of potential wells can eliminate bound states.

The critical spacing between hydrogen-like atoms (4a*) for the emergence of metallic behavior is observed for a wide range of systems:

From Marder's textbook “Condensed Matter Physics”. The y-axis is the effective Bohr radius in the host material (depends on effective mass and dielectric constant). The solid line shows n_crit = (4 a*)^(1/3)

Original reference: Accnt Chem. Res. 15 97-93 (1982)

In class we approach the transistion using semiclassical physics. The lattice constant a can be tuning to a critical value. Big a, little a…

Topological phenomena

We could morph this chip into different geometries, while still keeping the essential physical phenomena of the ac-Josephsen effect that makes it a voltage standard.

Aharonov-Bohm Effect

One of the seven wonders of the quantum world.

Penny says to Leonard: “Recently I’ve been thinking that given the parameters of your experiment, the transport of electrons through the aperture the nano-fabricated metal rings is qualitatively no different than the experiment already conducted in the Netherlands. Their observed phase shift in the diffusing electrons inside the metal ring already conclusively demonstrated the electric analogue of the Aharonov-Bohm quantum-interference effect.”