In one extreme, where the interactions
are sufficiently weak compared to the interactions, electrons form a “Fermi
liquid” – the state that accounts for the properties of simple metals. In the other extreme, where the interactions
are dominant, the electrons form various “Mott” insulating or “Wigner
crystalline” phases, often characterized by broken spatial and/or magnetic symmetries. Corresponding charge and/or magnetically
ordered insulating phases are common in nature.
Between these two extremes lie highly correlated electronic fluids, and
correspondingly a host of interesting and perplexing materials, including such
diverse systems as the cuprate and iron-based high temperature superconductors,
the failed metamagnet Sr3Ru2O7, and a variety
of quantum Hall fluids. Some insight
into electron fluids in this rich intermediate coupling regime can be obtained
from viewing them as partially melted electron solids, rather than as strongly
interacting gases. Here, analogies with
the liquid crystalline phases of complex classical fluids provide useful
guidance for a new approach to this key problem in condensed matter physics.