Unusual spin-triplet superconductivity in monolayer graphene

TL;DR

This work proposes a mechanism for spin-triplet superconductivity in monolayer graphene driven by phonon-mediated interactions in the presence of an external gate and Hubbard-U correlations. By discretizing near-Fermi ${\\bf q}$-excitations and integrating out phonons, the authors derive a self-consistent framework in Nambu space that yields a triplet pairing gap $\\Delta^{\\rm sc}$ and reveals high transition temperatures at half-filling ($\\kappa=0.5$), with $T_{C1} \\approx 121.7$ K and $T_{C2} \\approx 236.2$ K for strong coupling, albeit within a narrow region of the effective coupling $\\lambda_{\\rm eff}$. The results show that gate potential $V$ and on-site repulsion $U$ strongly influence the SC domain and charge imbalance, while Dirac-point band gaps and phonon-induced flat bands support the condensate. If experimentally realized, these findings could point to a route toward room-temperature spin-triplet superconductivity in graphene and guide spectroscopic probes (e.g., NRIXS) to detect the predicted gap structures and flat-band features.

Abstract

In this paper we consider the phonons in monolayer graphene and we show the possibility for the spin-triplet superconducting excitations states by discretizing the single-particle excitations near Fermi wave vector. The molonayer graphene was supposed to be exposed under the influence of the external gate-potential and the local Coulomb interaction effects have been taken into account at each lattice site position in the monolayer. A sufficiently large temperature domain was found, where the superconducting order parameter is not vanishing. Corresponding to this, at the surprisingly high temperature limit, we obtain a narrow domain of the electron-phonon coupling parameter $λ_{\rm eff}$, emphasizing the superconducting state. We discuss the localizing role of Hubbard-$U$ interaction and the effects external gate potential on the calculated physical parameters in the system. We explain the importance of the chemical potential in the formation of the superconducting state. We show the existence of a large superconducting band-gap in the system even in the case of the absence of the applied electric field potential.

Figures (13)

• Figure 1: (Color online) The monolayer graphene exposed to the influence of the external electric field potential $V$. The green arrow shows the external excitation wave with the given wave vector ${\bf{Q}}$ and energy $\varepsilon_{{\bf{Q}}}=\hbar\Omega_{Q}$. We suppose that the voltage drop at the sublattice site $a$ is $V_{a}=+V/2$ and at the sublattice site $b$ is $V_{b}=-V/2$.
• Figure 2: (Color online) Single-particle ${\bf{q}}$-excitation above Fermi surface with a wave vector ${\bf{q}}$, along Fermi vector ${\bf{k}}_{\rm F}$.
• Figure 3: (Color online) Single-particle ${\bf{q}}$-excitation discretization above and below Fermi surface with a wave vector ${\bf{q}}/2$, according to discussion in Eq.(\ref{['Equation_8']}).
• Figure 4: The superconducting order parameter $\Delta^{\rm sc}$ (see in panel (a)), the chemical potential $\mu$ (see in panel (b)), calculated from Eq.(\ref{['Equation_55']}), as a function of temperature. The effective electron-phonon interaction parameter has been fixed at $\lambda_{\rm eff}=0.21\gamma_0=0.63$ eV and different values of the inverse filling coefficient $\kappa$ have been considered in the calculations.
• Figure 5: (Color online) The superconducting order parameter $\Delta^{\rm sc}$, calculated from Eq.(\ref{['Equation_55']}), as a function of temperature. The effective electron-phonon interaction parameter has been set at the value $\lambda_{\rm eff}=0.21\gamma_0=0.63$ eV, and different values of the external gate voltage $V$ have been considered in the calculations.