Nematic quantum criticality in three-dimensional Fermi system with quadratic band touching

Understand

We construct and discuss the field theory for tensorial nematic order parameter coupled to gapless four-component fermions at the quadratic band touching point in three (spatial) dimensions.

• Within a properly formulated epsilon-expansion this theory is found to have a quantum critical point, which describes the (presumably continuous) transition from the semimetal into a (nematic) Mott insulator.
• The latter phase breaks the rotational, but not the time-reversal symmetry, and may be relevant to materials such as gray tin or mercury telluride at low temperatures.
• The critical point represents a simple quantum analogue of the familiar classical isotropic-to-nematic transition in liquid crystals.