Interaction-Driven Surface Chern Insulator in Nodal Line Semimetals

Abstract

Nodal line semimetals are characterized by nontrivial bulk-band crossings, giving rise to almost flat drumhead-like 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 non-magnetic, 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 C = −1. We show that this phenomenology is robust against chiral-symmetry breaking, that gives a finite dispersion to the DSS. Our results show that nodal line semimetals are a promising platform to implement surface Chern insulators and dissipation-less electron transport by exploiting enhanced interaction effects of the DSS.Topological electronic states have motivated large research efforts due to their gapped bulk coexisting with protected gapless surface modes [1][2][3][4][5][6][7]. In particular, chiral edge states are especially attractive as they would yield unidirectional channels lacking electric loss, representing a cornerstone in low consumption electronics. Natural compounds for Chern insulator have been proven to be rather elusive, motivating several proposals for its realization [8][9][10][11], yet the most successful implementation requires a building block that is also very rare in nature: magnetically doped topological insulators [3, 13, 14]. Thus, a key question is whether if Chern insulators can be engineered by means of a family of materials more common in nature, which would open new possibilities in condensed matter research, apart from applications in low consumption electronics.During the last years, the classification of topological insulators has been extended to so-called topological semimetals [15, 16], i.e., systems that are gapless in the bulk and simultaneously host topologically protected surface states. The topological band crossing may occur at discrete points or along closed loops in reciprocal space. The former case corresponds to Weyl/Dirac semimetals [17][18][19][20], whereas the latter is referred as nodal line semimetals (NLSMs) [8, 9,[21][22][23][24][25][26][27][28][29][30][31][32][33][36][37][38][39][40][41][42][43][44][45][46][47]. The nodal line carries a π Berry flux [21], resulting in drumhead-like surface states (DSS) [26]. In the presence of chiral symmetry, such DSS are perfectly flat, so that any residual electronic interaction would overcome the surface kinetic energy, providing a perfect platform to realize strongly correlated and symmetry-broken surface states [2,48,[50][51][52]. Very recently, the spontaneous magnetization in the flat band of zigzag graphene nanoribbon was observed [53][54][55][56], indicating that the same physics may exist in the DSS, a higher-dimensional analogy of the 1D flat band in graphene nanoribbon [11].In this Lette...

Second-order topological phases protected by chiral symmetry

“…The gap opens at the point nodes because the symmetry protection is absent. Hence, we can discuss a surface Chern insulator due to massive Dirac cones 33,34,37,49 . In the specific case, we can easily diagnose existence of the gapless hinge states (see the Appendix B).…”

Topological nodal line semimetals in graphene network structures

“…For example, Kopnin et al [80] have proposed to realize hightemperature superconductor by introducing pairing interaction into these flat bands. Chen et al [101] proposed that if electron-electron interaction is taken into account, the surface flat bands will lead to Stoner ferromagnetic instability and even 2D Chern insulator at the surface. These expectation seems to be very promising since the recent remarkable experimental observation of Mott insulator and superconductor in twisted bilayer graphene.…”

Z2 characterization for three-dimensional multiband Hubbard models

“…We attribute this to the strong spin-orbit coupling in our system which curves the flat bands and thus decreases the surface density of states. A recent study found an inversion of the Berry curvature of one K point driven by spin-orbit coupling and two-particle interactions in the Haldane model, which leads to a surface Chern insulator [59]. Bulk antiferromagnetism in NLSMs was investigated in Ref.…”