Inducing topological order in a honeycomb lattice

Abstract

We explore the possibility of inducing a topological insulator phase in a honeycomb lattice lacking spin-orbit interaction using a metallic (or Fermi gas) environment. The lattice and the metallic environment interact through a density-density interaction without particle tunneling, and integrating out the metallic environment produces a honeycomb sheet with in-plane oscillating long-ranged interactions. We find the ground state of the interacting system in a variational mean-field method and show that the Fermi wave vector k F of the metal determines which phase occurs in the honeycomb lattice sheet. This is analogous to the Ruderman-KittelKasuya-Yosida (RKKY) mechanism in which the metal's k F determines the interaction profile as a function of the distance. Tuning k F and the interaction strength may lead to a variety of ordered phases, including a topological insulator and anomalous quantum-Hall states with complex next-nearest-neighbor hopping, as in the Haldane and the Kane-Mele model. We estimate the required range of parameters needed for the topological state and find that the Fermi vector of the metallic gate should be of the order of 3π/8a (with a being the graphene lattice constant). The net coupling between the layers, which includes screening in the metal, should be of the order of the honeycomb lattice bandwidth. This configuration should be most easily realized in a cold-atoms setting with two interacting Fermionic species.

Giant Topological Insulator Gap in Graphene with5dAdatoms

“…Nevertheless, to realize their full potential systems more amenable to experimental investigations are highly desirable. In this regard the ability to design new 2D topological insulators from conventional, widely available materials would constitute a major step forward, and many proposals of this spirit now exist [19][20][21][22][23][24][25][26].…”

“…Nevertheless, to realize their full potential systems more amenable to experimental investigations are highly desirable. In this regard the ability to design new 2D topological insulators from conventional, widely available materials would constitute a major step forward, and many proposals of this spirit now exist [19][20][21][22][23][24][25][26].Following this strategy, here we introduce a new mechanism for engineering a topological insulator state in graphene-arguably now the most broadly accessible 2D electron system. Historically, graphene was the first material predicted to realize a topological insulator in seminal work by Kane and Mele [1], though unfortunately the gap is unobservably small due to carbon's exceedingly weak spin-orbit coupling [27][28][29][30][31].…”

Quantum anomalous Hall insulator stabilized by competing interactions

“…While some mean-field based analyses propose the presence of a QAH state at finite interaction strength in Dirac semimetals [10,[14][15][16], other analytical and numerical studies find charge ordered phases instead [17][18][19][20][21][22][23]. Although the QAH phase appears to be absent for linearly dispersing fermions on the honeycomb lattice, other routes for stabilizing a QAH state have been explored [24][25][26][27][28][29][30][31]. One such route utilizes the finite density of states at the Fermi level in two-dimensional semimetals with a quadratic band touching point (QBT) [11,12].…”

Topological Fermi Liquids from Coulomb Interactions in the Doped Honeycomb Lattice

“…More recent attempts explore the possibility of getting T broken phases from interactions in physical lattice models. There again previous examples involve next to nearest neighbor interactions, hoppings, or complicated lattice structures [14][15][16][17][18].…”