Possible triplet $p+ip$ superconductivity in graphene at low filling

We study the Hubbard model on the honeycomb lattice with nearest-neighbor hopping $\left(t>0\right)$ and next-nearest-neighbor hopping $\left(t^{\prime }<0\right)$. When $t^{\prime }<-t/6$, the single-particle spectrum is featured by the continuously distributed Van Hove saddle points at the band bottom, where the density of states diverges in a power law. We investigate possible unconventional superconductivity in such systems with the Fermi level close to the band bottom by employing both random-phase-approximation and determinant quantum Monte Carlo approaches. Our study reveals a possible triplet $p+ip$ superconductivity in this system with appropriate interactions. Our results might provide a possible route to look for triplet superconductivity with relatively high transition temperature in low-filled graphene and other similar systems.

Figure 1

(a) The energy band along the high-symmetry line in the first Brillouin zone. (b) The DOS as a function of energy with $t^{\prime }=-0.2t$. (c) The Fermi surface at filling $n=0.2$.

Figure 2

Largest eigenvalues of the susceptibility matrix in noninteracting limit in the first Brillouin zone.

Figure 3

Panels (a) and (b) show the $p_x$ and $p_y$ pairing symmetries in $k$ space and panel (c) shows the phase of the $p+ip$ pairing symmetry on the honeycomb lattice in real space.

Figure 4

Panel (a) shows the $f$ pairing in $k$ space and panel (b) shows the phase of the $f$ pairing symmetries in real space.

Figure 5

Panels (a) and (b) show the $d_{xy}$ and $d_{x^2-y^2}$ pairing symmetries in $k$ space and panel (c) shows the phase of the $d+id$ pairing symmetries in real space.

Figure 6

The lattice geometries for the (a) $2\times 108$, (b) $2\times 75$, and (c) $2\times 48$ honeycomb lattices.

Figure 7

Pairing susceptibility $P_{\alpha }$ as a function of temperature for different pairing symmetries with $U=3t$ at (a) $n=0.2$ and (b) $n=0.1$ on a $2\times 75$ lattice (solid line). The $P_{p+ip}$ at $n=0.2$ on a $2\times 48$ lattice (dashed red line) and a $2\times 108$ lattice are also shown (dotted red line) in panel (a). Here the units of temperature are $t$.

Figure 8

Pairing susceptibility $P_{p+ip}$ as a function of temperature with $U=3t$ and $n=0.2$ for (a) a $2\times 75$ lattice and (b) a $2\times 12$ lattice (solid line). The fits are shown as dashed lines.

Figure 9

The intrinsic pairing interaction $P_{p+ip}-{\tilde{P}}_{p+ip}$ as a function of temperature for (a) different $U$ and (b) different $n$ on a $2\times 75$ lattice.