PH 671 - Spring 2016, Due 5pm on Friday, Week 3

Under construction

Show that the number of occupied 1d subbands in a metal wire is approximately equal to the number of atoms in the cross-section of the wire. Assume a free-electron Sommerfeld model when deciding which states will be occupied.

Show that the conductance of a ballistic (no scattering), one-dimensional wire is independent of temperature when the wire has sufficient charge carriers (μ and μ + eV » k_BT). Your answer should include a calculation of density of states D(E) in a one-dimensional system.

• Note: The Fermi-Dirac function f(E) can used to determine the occupancy of quantum state in the left and right reservoirs (chemical potentials μ + eV and μ respectively).

Write a one-paragraph summary (4 or 5 sentences) about an experimental or theoretical solid state physics paper from 2010 or later that contains one or more of the following:

• Measurement of current (or resistance) in a nanoscale system
• Measurements of current (or resistance) in a magnetic field
• Measurement of current (or resistance) near a phase transition (for example, normal metal to superconductor).
• An STM spectroscopy measurement

Include full bibliographic information (journal name, volume number, page number, article title). Please limit yourself to the following journals (this list can be augmented with class consensus; and you may need to request an interlibrary loan to access some):

• Science
• Nature
• Proceedings of the National Academy of Sciences (PNAS)
• Nature Physics
• Physical Review Letters
• Nano Letters
• Applied Physics Letters
• Physical Review X