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Homework #3
PH 671 - Spring 2016, Due 5pm on Friday, Week 3
Under construction
1D Subbands (5 pts)
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.
Quantum of conductance at finite temperature (5 pts)
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 » kBT). 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).
Journal reading (5 pts)
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