Interaction-Driven Surface Chern Insulator in Nodal Line Semimetals

Nodal line semimetals are characterized by nontrivial bulk-band crossings, giving rise to almost flat drumheadlike surface states (DSS), which provide an attractive playground where interaction can induce symmetry-broken states and potential emergent phases. Here, we show that electronic interaction drives a Stoner ferromagnetic instability in the DSS while the bulk remains nonmagnetic, which together with spin-orbit coupling drive the surface states into a 2D Chern insulator. We show that each piece of DSS carries a half-integer topological charge, which for systems containing two pieces of DSS yield a net Chern number $\mathcal{C}=-1$. We show that this phenomenology is robust against chiral-symmetry breaking, which gives a finite dispersion to the DSS. Our results show that nodal line semimetals are a promising platform to implement surface Chern insulators and dissipationless electron transport by exploiting enhanced interaction effects of the DSS.

Figure 1

(a) Nodal lines around $\mathit{K}$, ${\mathit{K}}^{\prime }$ points and corresponding DSS (light-orange disks) enclosed by their projection onto the surface Brillouin zone. (b) Spin-orbit coupling (SOC) introduces opposite mass terms to the DSS around $\mathit{K}$, ${\mathit{K}}^{\prime }$. Electronic interaction ($e\text{−}e$) inverts one of the bands. (c) Two pieces of DSS each carries a meron spin texture with a half-integer topological charge and together constitute a Skyrmion and result in a Chern number $\mathcal{C}=-1$. (d) Spin polarized surface states and chiral hinge current. Inset: diamond lattice with an open surface.

Figure 2

(a) Band structure of a slab of a NLSM showing the surface flat bands. (b) Density of states (DOS) in the bulk and on the surface. (c) Band structure with only SOC. (d) Spin texture of the surface states. (e) Band structure with only interaction effect. (f) Band structure with both SOC and interaction effects. The slab consists of 600 layers and we took $t^{\prime }=0.8t$, $\lambda =0.01t$, and $U=2t$.

Figure 3

(a) Real space distribution of the magnetization, where $z=0$ corresponds to the surface. (b) Energy gap as a function of the mean-field order parameter. Phase diagram associated with (c) surface magnetization and (d) energy gap in terms of SOC strength $\lambda$ and interaction $U$. (e) Band structure including the second-neighbor hopping $t_2=0.03t$, in the absence of $U$ and $\lambda$. (f) Phase diagram containing chiral-symmetry breaking. We took $t^{\prime }=0.8t$, $\lambda =0.01t$, and $U=2t$ for (a),(b), 200 layers for (a),(b),(c),(d),(f) and 600 layers for (e).

Figure 4

(a) Sketch of the interfacial states in a magnetic domain wall on the surface of the NLSM. (b) Surface spectral function of the magnetic domain wall depicted in (a), showing two copropagating states along the domain wall.