Abstract
We suggest the tried approach of impurity band engineering to produce flat bands and additional nodes in Dirac materials. We show that surface impurities give rise to nearly flat impurity bands close to the Dirac point. The hybridization of the Dirac nodal state induces the splitting of the surface Dirac nodes and the appearance of new nodes at high-symmetry points of the Brillouin zone. The results are robust and not model dependent: our tight-binding calculations are supported by a low-energy effective model of a topological insulator surface state hybridized with an impurity band. Finally, we address the effects of electron-electron interactions between localized electrons on the impurity site. We confirm that the correlation effects, while producing band hybridization and the Kondo effect, keep the hybridized band flat. Our findings open up prospects for impurity band engineering of nodal structures and flat-band correlated phases in doped Dirac materials.
Highlights
Impurity band engineering is at the core of the modern semiconducting industry because impurity bands enable the functionality of a semiconductor
The presence of surface impurities leads to impurity resonance states that appear as nearly flat bands in the spectral function of the doped surface [Fig. 1(b)], while the undoped surface exhibits unperturbed Dirac states
We find that for J > Jc, strong interaction physics within a localized f band nominally located below the Fermi level results in a renormalization of the f -electron energy, pushing it up to just above the chemical potential, where the f band can effectively hybridize with the Dirac c band and yield the nearly flat bands discussed previously
Summary
Impurity band engineering is at the core of the modern semiconducting industry because impurity bands enable the functionality of a semiconductor. A well-known example of such manipulation is the quantum anomalous Hall effect (QAHE) [2,3], which is a new quantum state of matter observed in magnetically doped three-dimensional (3D) topological insulators (TIs). It occurs as a result of a gap opening at the Dirac node of TIs due to broken time-reversal symmetry. It is known that impurities give rise to low-energy resonant states near Dirac nodes [4,5,6]. Microscopic tight-binding model calculations are accompanied by low-energy continuum model calculations for a TI surface state hybridized with a doubly degenerate impurity band
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