Quantum anomalous Hall insulator phase in asymmetrically functionalized germanene

Using first-principles computations, we discuss topological properties of germanene in buckled as well as planar honeycombs with asymmetric passivation via hydrogen and nitrogen (GeHN) atoms. GeHN in the planar structure is found to harbor a quantum anomalous Hall (QAH) insulator phase. Our analysis indicates that the buckled GeHN also possesses a QAH phase under tensile strain. We computed the associated Chern numbers and edge states to confirm the presence of the QAH state. In particular, chiral edge bands connecting conduction and valence bands were found at the edges of a planar zigzag GeHN nanoribbon. By considering a range of buckling distances, we demonstrate how the system undergoes the transition from the trivial to the QAH phase between the buckled and planar structures. Finally, we show CdTe(111) to be a suitable substrate for supporting buckled germanene in the QAH phase. Our results suggest that functionalized germanene could provide a robust QAH-based platform for spintronics applications.

Figure 1

Crystal structures of germanene honeycombs passivated with hydrogen and nitrogen. (a) Top view with the primitive cell marked (red line). (b) and (c) Side views of different GeHN films. Hydrogen and nitrogen decoration of germanene with a planar (b) and buckled (c) germanene honeycomb. (d) Total energy per unit cell as a function of the lattice constant. Various phases assumed by the planar (black squares) and buckled (red circles) GeHN films are identified.

Figure 2

Band structures of a planar GeHN film at the optimized lattice constant $a=4.40\AA$. (a) Non-spin-polarized without SOC. (b) Spin polarized without SOC. (c) Spin polarized with SOC. Red and blue lines in (b) denote spin-up and spin-down states, and red and blue circles in (c) denote $+mz$ and $-mz$, respectively. Inset in (c) shows the first Brillouin zone in which the high symmetry points are marked. Band structures of a planar GeHN film at $a=4.08\AA$. (d) Non-spin-polarized without SOC. (e) Spin polarized without SOC. (f) Spin polarized with SOC. Filled orange (olive) circles refer to $s$ ($p$) orbitals where sizes of circles are proportional to the amplitude of the orbital contribution.

Figure 3

(a) The first-principles band structure (black lines) is compared with the corresponding results obtained from a Wannier90-based tight-binding fit (red dotted lines) for $a=4.08\AA$. (b) Berry curvature computed using the tight-binding Hamiltonian. (c) Band structure of a GeHN nanoribbon with zigzag edge. The sizes of blue and red circles are proportional to the contribution from the left- and right-hand side edges, respectively.

Figure 4

Topological phase transition in a buckled GeHN film from a QAH insulator to a trivial insulator phase as the buckling distance ($d_B$) increases at a lattice constant of 4.08 Å. The $s$-orbital contribution is labeled by red circles.

Figure 5

Band structures of a buckled GeHN film at $a=4.68\AA$. (a) Spin polarized without SOC. (b) Spin polarized with SOC. (c) Spin-polarized band structure of N-adsorbed germanene on Te-terminated surface of CdTe(111) substrate without SOC. The red and blue lines represent the spin-up and spin- down states, and the circles are the contributions from the N and Ge atoms. (d) The first-principles band structure with SOC (black lines) is compared with the corresponding results obtained from a Wannier90-based tight-binding fit (red dotted lines). (e) Crystal structure of N-adsorbed germanene on the Te-terminated surface of CdTe(111) substrate. (f) Band structure of a nanoribbon with zigzag edge. The sizes of blue and red circles in (f) are proportional to the contributions from the left- and right-hand side edges, respectively.