Theoretical Condensed Matter Physics

Graduate Program Orientation
Department of Physics & Astronomy

September 17, 2015

Presentation Slides: [PDF]

Introduction: Condensed matter physics is the field of study and inquiry into the fundamental properties of matter and radiation, and the physical phenomena that result from their interactions. Theoretical research in condensed matter physics involves the discovery of new concepts related to the collective behavior of enormous numbers of atomic constituents, combined with the application of statistical mechanics and quantum theory to describe and predict the behavior of macroscopic matter. The concept of ``spontaneous symmetry breaking'' was developed as an organizing principle in condensed matter physics from the theory of phase transitions and emergent physical properties of the lower symmetry phase of matter. The ideas and mathematics underlying the connections between symmetry, symmetry breaking, phase transitions, collective behavior and emergent properties of matter are so powerful and general that the conceptual framework of `spontaneous symmetry breaking' is a cornerstone of nearly every sub-field of physics and physical sciences - from the forces governing the `families' of sub-atomic particles to the regular structures observed in crystals or the patterns that evolve in non-equilibrium fluid motion.

Recent theoretical developments in condensed matter physics emphasize a new organizing principle based on topological invariants connected directly to the Hamiltonian governing the condensed matter system, as opposed to quantization rules that emerge from spontaneous symmetry breaking. This marriage between topology and condensed matter physics is at the heart of the quantum Hall effect2 - the quantization of the Hall conductance of a two-dimensional electron fluid confined in a semiconductor heterostructure, σxy = N (e2/h) - and has led to several remarkable predictions for new states of matter in semiconductors and insulators with strong spin-orbit interactions, a class of materials referred to as ``topological insulators''. The existence of topological quantization in condensed matter systems has also driven the theoretical research into the possibility of new solid-state devices for quantum information storage and quantum computation. The idea is to combine the topological quantization associated with electronic states that govern the low-energy physical properties of the topological condensed matter to ``protect'' quantum information encoded in these states from environmental de-coherence. There is a broad effort theoretically and experimentally to classify, predict, identify and characterize the physical properties of topological condensed matter systems.


  1. More is Different , P. W. Anderson, Science, Vol. 177, pp. 393-396 (1972) [DOI]
  2. Quantized Hall Conductance in a Two-Dimensional Periodic Potential , D Thouless, et al. Phys. Rev. Lett. Vol. 49, 405-409 (1982) [DOI]

Condensed Matter Theory NU Physics Department Northwestern University
Last update: September, 2015