An electronic nematic phase can be classified by a spontaneously broken
discrete rotational symmetry of a host lattice. In a square lattice, there are
two distinct nematic phases. The parallel nematic phase breaks x and y
symmetry, while the diagonal nematic phase breaks the diagonal (x+y) and
anti-diagonal (xβy) symmetry. We investigate the interplay between the
parallel and diagonal nematic orders using mean field theory. We found that the
nematic phases compete with each other, while they coexist in a finite window
of parameter space. The quantum critical point between the diagonal nematic and
isotropic phases exists, and its location in a phase diagram depends on the
topology of the Fermi surface. We discuss the implication of our results in the
context of neutron scattering and Raman spectroscopy measurements on
La2βxβSrxβCuO4β.Comment: 8 pages, 10 figure