Chiral finite-momentum superconductivity in the tetralayer graphene

Abstract

Motivated by the recent experimental discovery of superconductivity in rhombohedral tetralayer graphene, we investigate the pairing mechanism arising from the density-density interactions within the random-phase approximation. This approach successfully highlights the dominance of the chiral $p$-wave pairing between electrons with the same spin and valley index at low densities, while also predicting the superconducting range in agreement with experimental findings. Furthermore, we examine the characteristics of distinct superconducting regions: SC1 and SC2 exhibit chiral finite-momentum superconductivity with pronounced phase fluctuations, whereas SC4 displays zero-momentum superconductivity, with its transition temperature constrained by the pairing strength.

Figures (7)

• Figure 1: (a) Momentum dependence of the static charge susceptibility $\chi_{0,\bm{q}}$ and interaction $V_{\bm{q}}$ at a displacement field of $u=0.055$ eV and an electron density of $n=0.5\times 10^{12}$ cm$^{-2}$. (b) Momentum dependence of $\chi_{0,\bm{q}}$, $V_{\bm{q}}$ and $V_{0,\bm{q}}$ along the $q_x$ direction. (c) The corresponding Fermi surface. (d) Distribution of the average interaction strength $\langle V_{\bm{q}}\rangle_x$ along the $q_x$ direction across different displacement fields $u$ and electron densities $n$.
• Figure 2: (a) Momentum dependence of the pairing gap $\Delta_{\bm{k},\bm{Q}}$ at the electron density $n=0.5 ~(10^{-12}$ cm$^{-2}$) with the displacement field $u=0.055$ (eV) for its amplitude (Amp), angle (Arg), real (Re) and imaginary (Im) component. (b) Distribution of the average absolute value of gap $\langle|\Delta|\rangle$ over different values of $n$ and $u$. The black, green, and white hexagrams respectively indicate the possible SC1–SC3 regions. The dotted white line marks the trajectory plotted in Fig. \ref{['fig3']} and Fig. \ref{['fig4']}. (c) $\langle|\Delta|\rangle$ as a function of $n$ at different values of $u$. (d) Variation of $T_c$ with $n$ at different values of $u$. (e) The distribution of the constraint of $T_c$ (K) over different values of $u$ and $n$. We note that $\langle|\Delta|\rangle$ is evaluated at the low temperature of $T=0.001$ (K).
• Figure 3: (a) Dependence of the condensation energy $E_c$ on electron density for total pairing momenta $\bm{Q}=2\bm{K}$ and $\bm{Q}=0$ at $u=0.055$ (eV) and $T=0.001$ (K). For $\bm{Q}=2\bm{K}$, the pairing symmetries include $p_x$ or $p_y$, $p_x\pm p_y$ and $p_x\pm ip_y$. $\bm{Q}=0$ corresponds to the chiral intervalley pairing with parallel spins. (b) $E_c(2\bm{K}+\bm{q})$ as a function of $\bm{q}=(q_x,q_y)$, shown on the $\bm{q}$-plane for $u=0.055$ (eV) and $n=0.5$$(10^{12}$ cm$^{-2})$.
• Figure 4: (a) Temperature dependence of the superfluid density $\rho_{s,0}$ at various electron densities at fixed value of $u=0.055$ (eV). According to the Berezinskii-Kosterlitz-Thouless (BKT) theory, the cross points of curves with $\frac{\pi}{8}\rho_{s,0}=T_{\rm BKT}^0$ indicate the values of $T_{\rm BKT}^0$. (b) Extracted BKT transition temperature for the real and complex interaction $V_{\bm{k}'-\bm{k}},~V_{P,\bm{k}'-\bm{k}}$, respectively.
• Figure S1: (a) The energy dispersion at the displacement field $u=0.055$ eV, where the color represents the orbital weight of 1A and 4B. (b) The energy dispersion along the $k_x$ and $k_y$ direction at $u=0.055$ eV, where color indicates the orbital weight of 1A. (c) The distribution of density of state $N(E_F)$(meV$^{-1}$) across different dispalcement field $u$ and electron density $n$.