Unconventional High-Temperature Superconductivity from Repulsive Interactions: Theoretical Constraints

Unconventional symmetries of the order parameter allowed some researchers to maintain that a purely repulsive interaction between electrons provides superconductivity without phonons in a number of high-temperature superconductors. It is shown that the Cooper pairing in $p$ and $d$ states is not possible with the realistic Coulomb repulsion between fermions at relevant temperatures in any dimension.

Figure 1

Angular momentum of the order parameter as the function of the dimensionless repulsion $s=e^2/\pi \hslash v_F$ in the 3D Coulomb gas. The inset shows the first-order (a) and the second-order (b)–(e) contributions to the two-particle vertex.

Figure 2

The absolute value of the coupling constant for the 2D Hubbard model with the nearest-neighbor hopping as the function of the chemical potential for four unconventional symmetries of the order parameter. The inset shows the angular dependence of the $d_{x^2-y^2}$ state similar to that found in Ref. 8.

Figure 3

$U-\mu$ phase diagram of 2D electrons on the square lattice showing no $d$- or $p$-wave symmetry of the ground state for weak repulsion $U$. There is a critical value of $U$ at any doping below which the ground state is not superconducting (NSC).

Figure 4

The absolute value of the coupling as the function of the chemical potential for two unconventional order parameters.