Physics of Low Dimensional Systems

Mentor:Natalia Kaputkina

Course Summary

The course “Physics of low-dimensional systems” is fundamental and has a theoretical orientation. At the same time it is theoretical base for working out of devices and optoelectronics devices, nanoelectronics, information systems of new generation. Low-dimensional systems are considered: quasi-two-dimensional structures- quantum wells, quasi-one-dimensional ones — quantum wires and quasi-zero-dimensional ones — quantum dots. The quantum-mechanical phenomena in such systems is discussed and effects of external electric and magnetic fields are considered. Theoretical and experimental methods of investigation of low-dimensional systems are considered. By first-principles methods and by computer simulations, following parameters of low-dimensional systems are obtained: resonant frequencies, energy and wave function spectra for electronic and excitonic systems with carriers in the coupled quantum wells and in the coupled quantum dots; evolution of a spectrum and spin rearrangement in the molecules consisted of horizontally and vertically coupled quantum dots. The estimation of characteristic dimensional parameters of systems for the account of internal interaction and interaction with an external electromagnetic field is considered.

Course Format

Hours of lectureHours of discussionHours of independent studyHours total

Please note that students are expected to study outside of class for three hours for every hour in class.

Course Content

The plan is to work through the following topics:

  1. Dimensional quantization
    • Observation conditions of quantum-dimensional system
    • Structures with low-dimensional electronic gas
    • Superlattices
  2. Manufacturing of low-dimensional systems technology
    • Molecular beam epitaxy
    • Gas epitaxy from metall-organics
    • Nanolithography
    • Self-organization of quantum dots and quantum wires.
  3. Charge carriers in low-dimensional systems
    • Density of energy states in low-dimensional electronic systems
    • Statistics of charge carriers in low-dimensional systems
    • Evolution from the discrete to the continuous spectra in quantization direction for low-dimensional systems for different dimensions
    • Quasi-lowdimensional systems
    • 2D and 3D shielding
    • Hydrogen-like atom, excitons in 1,2,3 d
  4. Quantum wells
    • Optical properties of quantum wells
    • Kinetic effects in 2d systems
  5. Quantum wires
    • Ballistic transport
    • Ballistic conductance of quantum wires
    • Quantum Hall effect and conductance of quantum wires
  6. Quantum dots
    • Energy spectra and wave functions. Effects of external fields
    • Systems of coupled quantum wells and quantum dots
    • Horizontal and vertical molecules of quantum dots
  7. Arrays of quantum dots
    • Tunnel effects
    • Periodic and aperiodic arrays of quantum dots
  8. Single and coupled quantum wells and quantum dots in microcavity
    • Formation of exciton-polaritons
    • Kostelitz-Thouless transition
    • Superfluidity and Bose-condensation of exciton polaritons
    • Effect of external fields
  9. Industrial applications of quantum-dimensional systems
    • Lasers on quantum wells and quantum dots
    • Optical modulators
    • Photodetector on quantum wells
    • High-mobility transistors
    • Ballistic-transport devices
    • One-electron transistors.


Primary textbooks:

  1. L. Pitaevskii and S. Stringari. Bose-Einstein Condensation. Oxford University Press, Oxford ; New York, June 2003.
  2. Hilda A. Cerdeira, Bernhard Kramer, and Gerd Schön. Quantum Dynamics of Submicron Structures. number 291 in NATO ASI. Springer, 1995. URL:

Additional textbooks:

  1. E. L. Albuquerque and M. G. Cottam. Theory of elementary excitations in quasiperiodic structures. Physics Reports, 376(4—5):225—337, March 2003. URL:, doi:10.1016/S0370-1573(02)00559-8.

Problems and solutions:

  1. Keith Barnham and Dimitri Vvedensky. Low-Dimensional Semiconductor Structures: Fundamentals and Device Applications. Cambridge University Press, Cambridge, UK ; New York, August 2001.

Homework Assignments

Weekly, 15 problem sets in total, due at the beginning of the lecture. You may also submit via e-mail before the due date/time. It is of outmost importance that you invest your own effort into solving problems. Should you consult any sources, please provide references. Homework assignments should be typed. Legible handwritten assignments are acceptable.


Class participation10%
Homework assignments20%
Midterm exam20%
Final exam50%