A path to high temperature superconductivity via strong short range repulsion in spin polarized band

TL;DR

The paper addresses whether purely repulsive interactions in a spin-polarized 2D metal can induce superconductivity with a controlled expansion and potentially high $T_c$. It exploits a screening plane with distance $d\\ll a$ and lattice-point-group symmetry to suppress the leading repulsion in an odd-parity channel, enabling second-order attraction in select $f$-wave channels; two concrete triangular-lattice models are analyzed: an extended Hubbard model and an orbital Wannier model. The extended-Hubbard analysis shows a $B_2$ $f$-wave channel evades first-order repulsion, but the second-order attraction is weak and yields only small $T_c$, while the orbital model—with large Wannier radius $r_0\\sim a$ and suppressed umklapps—achieves an order-unity pairing strength in $f$-wave channels near a controlled boundary $g_{\\rm eff}\\sim 1$, pointing to a pathway toward higher $T_c$. The results suggest a practical route to high-$T_c$ superconductivity in spin-polarized, screened systems (for example, layered or moiré materials near a screening plane), where the energy scale is electronic and tunable via $d$ and $r_0$.

Abstract

We consider a two dimensional metal that is spin polarized and with strongly repulsive interaction. The interaction is short-ranged and controlled by a screening plane located a distance $d$ away. We consider the case where $d$ is less than the unit cell spacing $a$. We show that due to Pauli exclusion, a controlled expansion is possible despite the strong repulsion, and in many cases results in pairing. We demonstrate this for a tight-binding model on a triangular lattice with nearest neighbor repulsion. We also treat a second model on the triangular lattice with Wannier orbitals with size comparable to $a$. In this case we find $f$-wave pairing with order unity pairing strength, potentially leading to high $T_c$.

Figures (3)

• Figure 1: The inset shows the geometry we propose: a screening plane is placed at a distance $d$ from a spin-polarized 2D system, which can be either a triangular crystal or a moire superlattice formed by two layers with unit cell size $a$. We consider the regime $d\ll a$. The main figure illustrates the momentum dependence of interaction $V(q)$. The difference between $V(q)$ and constant is the effective interaction $V_{\rm eff}(q)$ which is $\sim -q^2$ for $q\ll 1/d$ and much smaller than $V(0)$ at $q=1/a$. We predict a high-$T_c$ SC in the regime of $d\ll a$ when the Wannier orbital radius $r_0$ is comparable to $a$.
• Figure 2: The strength of superconductivity in nearest-neighbor Hubbard model. In the x axis, $U_1$ represents the nearest-neighbor repulsion. The quantity $W=9t$ is the bandwidth. The color code represent the strength of the leading pairing channel ${\rm max}(g_p^{\Gamma_i})$, which is the $B_2$ channel. The region where the perturbation theory is controlled lies to the left of the blue line where the expansion condition $V_0\nu_0<1$ is valid regardless of the density, and below the red line when the addition condition $V_0\nu_0(k_F a)^2/2 < 1$ is required. (Here $V_0$ represents $V(q=0)$, which is related to $U_1$ through $V_0 = 6A_{\rm uc} U_1$, where $A_{\rm uc}$ is the area of a unit cell.) We can see the numerically the attraction is very weak in this region.
• Figure 3: The strength of superconductivity in orbital model with gaussian interaction for $d=\frac{a}{3}$, $r_0 = \frac{a}{2}$. In the x axis, $U_0$ represents the onsite repulsion, defined through $U(r) = U_0 e^{-r^2/d^2}$. The quantity $W=9t$ is the bandwidth. The color code represents the strength of the leading pairing channel ${\rm max}(g_p^{\Gamma_i})$, which is one of $B_1$ and $B_2$ channels. The boundary of the controlled regime lies below the red line. It is determined by the condition $g_{\rm eff} = 1$, where $g_{\rm eff}$ is the dimensionless effective interaction, defined in Eq. \ref{['eq:geff']}. Note that strong attractive channels with strength of order unity are allowed.