Robust topological superconductivity in spin-orbit coupled systems at higher-order van Hove filling

Abstract

Van Hove singularities (VHSs) in proximity to the Fermi level promote electronic interactions and generate diverse competing instabilities. It is also known that a nontrivial Berry phase derived from spin-orbit coupling (SOC) can introduce an intriguing decoration into the interactions and thus alter correlated phenomena. However, it is unclear how and what type of new physics can emerge in a system featured by the interplay between VHSs and the Berry phase. Here, based on a general Rashba model on the square lattice, we comprehensively explore such an interplay and its significant influence on the competing electronic instabilities by performing a parquet renormalization group analysis. Despite the existence of a variety of comparable fluctuations in the particle-particle and particle-hole channels associated with higher-order VHSs, we find that the chiral $p \pm ip$ pairings emerge as two stable fixed trajectories within the generic interaction parameter space, namely the system becomes a robust topological superconductor. The chiral pairings stem from the hopping interaction induced by the nontrivial Berry phase. The possible experimental realization and implications are discussed. Our work sheds new light on the correlated states in quantum materials with strong SOC and offers fresh insights into the exploration of topological superconductivity.

Figures (4)

• Figure 1: (a) Energy dispersion of the two Rashba-split bands and their density of states. The positive/negative helicity band is denoted by red/green line. Four higher-order VHSs are located at the Fermi level (blue dashed line) and the adopted parameters are $\lambda_R=t_1, ~t_2=-t_1/2,~t_3=-\lambda_R/8,~\mu_0=-t_1$. (b) Fermi surface of the positive-helicity band hosting higher-order VHSs and its spin texture which is denoted by different colors based on their directions. (c) 2D dispersion around the higher-order saddle point with $E(\mathbf{k})=A(-k_x^4+k_y^2)$.
• Figure 2: (a) Low-energy patch model on the square lattice. The green arrow denotes the spin texture in each patch from the Dirac monopole (red sphere) at the center. (b--d) Three allowed interactions from the momentum conservation and fermionic nature and the pairing hopping process ($\gamma_3$) obtains a nontrivial Berry phase.
• Figure 3: Susceptibilities (a, c) as functions of $\log(T/t_1)$ and RG flows (b, d) with initial repulsive interaction $\gamma_{1,2}(0)=0.02$ and $\tilde{\gamma}_3(0)=0.04$. Inset figures show the critical interactions $\Gamma_i$ as functions of $d^{\text{ph}}_{\mathbf{Q}_1}$ with $\tilde{\Gamma}_3=-i\Gamma_3$. The upper and bottom panels denote the cases of the higher-order VH dispersion with $\epsilon^e_{\alpha}(\mathbf{k})$ and $\epsilon^o_{\alpha}(\mathbf{k})$, respectively. In (a) $\Pi_{0}^{\text{pp,ph}}$ and $\Pi_{{\bf Q}_1}^{\text{pp,ph}}$ manifest power-law diverging, while $\Pi_{{\bf Q}_2}^{\text{pp,ph}}$ diverge as the logarithmic behavior. In (c) all particle-particle and particle-hole fluctuations behaves as a power-law diverging. In (b), we take nesting parameters as $d_{{\bf 0},{\bf Q}_1}^{\text{pp}}=1$, $d^{\text{ph}}_{{\bf 0},{\bf Q}_1}=1/4$ and $d_{{\bf Q}_2}^{\text{ph,pp}}=0$. In (d), we take $d_{{\bf 0},{\bf Q}_1}^{\text{pp}}=1$, $d^{\text{ph}}_{{\bf 0}}=d^{\text{pp}}_{{\bf Q}_1}=1/3$ and $d_{{\bf Q}_2}^{\text{ph,pp}}\simeq 0.39$.
• Figure 4: RG flow diagrams of the reduced RG equation \ref{['rRG:eq1']} in the parameter space $(\gamma_2/\gamma_1,\tilde{\gamma}_3/\gamma_1)$ for the $\epsilon_{\alpha}^e({\bf k})$ (a) and $\epsilon^o_{\alpha}({\bf k})$ (b), with $\gamma_1<0$. Phase diagrams for the higher-order VHSs with $\epsilon_{\alpha}^e({\bf k})$ (c) and $\epsilon^o_{\alpha}({\bf k})$ (d) for the initial interaction $\gamma_1(0)=0.1$. The color map represents the critical RG scale $\text{log}(y_c)$ and the red region, namely too large $y_c$, denotes that there is no instability. In (a,c), we take nesting parameters as $d_{{\bf 0},{\bf Q}_1}^{\text{pp}}=1$, $d^{\text{ph}}_{{\bf 0},{\bf Q}_1}=1/4$ and $d_{{\bf Q}_2}^{\text{ph,pp}}=0$. In (b,d), we take $d_{{\bf 0},{\bf Q}_1}^{\text{pp}}=1$, $d^{\text{ph}}_{{\bf 0}}=d^{\text{pp}}_{{\bf Q}_1}=1/3$ and $d_{{\bf Q}_2}^{\text{ph,pp}}\simeq 0.39$.