Interplay of ferromagnetism, nematicity and Fermi surface nesting in kagome flat band

TL;DR

This work analyzes interaction-driven phases in partially filled kagome flat bands using self-consistent Hartree-Fock with on-site $U$ and inter-sublattice $V_1,V_2$ interactions. It identifies a robust competition between ferromagnetism and nematic order, with inter-sublattice repulsion favoring nematicity over a wide range of fillings and coupling strengths, while translational-symmetry breaking can arise near a van Hove singularity. Phase diagrams reveal that nematic order is a generic outcome of flat-band physics, particularly away from half-filling, and that nesting-induced density waves are fragile in the flat-band regime and can be suppressed by out-of-plane hopping. The results provide a minimal framework for understanding correlated flat-band phases in kagome systems and offer a lens to interpret nematic features observed in CoSn-based materials.

Abstract

Recent experiment on Fe-doped CoSn has uncovered a series of correlated phases upon hole doping of the kagome flat bands. Among the phases observed, a nematic phase with a six- to two-fold rotation symmetry breaking is found to prevail over a wide doping and temperature range. Motivated by these observations, we investigate the interaction-driven phases realized in a kagome model with partially filled, weakly dispersing flat bands. Density-density interactions up to second-nearest neighbors are considered. We identify a close competition between ferromagnetic and nematic phases in our self-consistent Hartree-Fock calculations: while on-site interaction favors ferromagnetism, the sizable inter-sublattice interactions stabilize nematicity over a wide doping window. Competition from translational-symmetry-breaking phases is also considered. Overall, our results show that nematicity is a generic outcome of partially filled kagome flat bands and establish a minimal framework for understanding correlated flat-band phases.

Figures (6)

• Figure 1: (a) Kagome lattice with blue, yellow and pink dots representing sites from sublattice A, B and C respectively. The red circle in the center of hexagon indicates the density distribution of hexagon states. The first Brillouin zone is attached as inset. (b) band structure of ${\hat{H}}_{o}$, where $\mu=2$, $t_{1}=1$, $t_{2}=-0.025$. The upper panel shows the overall dispersion which is approximately $6t_1$. The lower panel shows the zoomed-in FB dispersion around 0.15$t_1$. Accompanying the band structure is the Fermi surface for with parallel and curved edges respectively. (c)(d) Sublattice weights over the whole BZ for toy model and realistic 48-band Wannier model of CoSn with on-site SOCchen2024CoSn_experiment respectively, where from the left to right, the graph is for sublattice A, B and C correspondingly. (e) From left to right, $\chi_{{\textbf{0}}}(t_z)/\chi_{{\textbf{0}}}(0)$ and $\chi_{{\textbf{m}}}(t_z)/\chi_{{\textbf{m}}}(0)$ against the out-of-plane hopping $t_z$.
• Figure 2: (a)(b) phase diagram for interaction strength over filling with fixed ratio $V_1=V_2=U/2$ for translation invariant and broken cases respectively. Universal cutoff $\delta=0.01$ is employed to classify symmetry breaking. The colormap captures nematicity: how much the six-fold symmetry is broken, where ${\langle{\Delta\hat{C}_{6}}\rangle}<\delta$ is marked as symmetric by blue. The size of inner circle scales with the energy difference from the referenced state, while the outer ring thickness scales with the maximum magnetic moment $\textrm{max}|{\langle{\hat{m}_{i}}\rangle}|$. The different shapes of inner marker indicates translation symmetry, where circle, stripe and cross stand for translation invariant (TI), stripe and $2\times2$ phases accordingly. The brown/grey outer rings represent FM/ferrimagnetic and AFM (AFi) phase. (c)The upper panel is $\chi_{{\textbf{0}}}/\chi_{{\textbf{m}}}$ with horizontal dashed red line indicating where $\chi_{{\textbf{0}}}/\chi_{{\textbf{m}}}$=1. The lower panel is for bare $\chi_{{\textbf{0}}}$ and $\chi_{{\textbf{m}}}$ values respectively, where they both acquire log divergence at filling 0.4.
• Figure 3: (a)(c)(e) Band structure for nematic FM, FM and nematic phases at $U=2V_1=2V_2=5W$ at filling 1/4, 1/2 and 3/4 respectively. The grey(blue) line is the original(SCHF) band. Dashed green(red) horizontal line is the original(SCHF) Fermi level. (b)(d)(f)Sublattice distribution per sublattice per spin over $1^{st}$ BZ for corresponding filling 1/4, 1/2 and 3/4 respectively.
• Figure 4: SCHF phase diagram at specific fillings. (a)-(c) $U$ versus $V_1=V_2$ phase diagram at filling $1/4$, $1/2$ and $3/4$. (d)-(f) $U=5W$, $V_1$ versus $V_2$ plot at filling $1/4$, $1/2$ and $3/4$. All plots share the same upper and lower bound of energy and magnetic moment scaling.
• Figure 5: phase diagram for (a)$U$ versus $V_1=V_2$ and (b)$V_2$ versus $V_1$ with $U=5W$ at filling of VHS.