Quantum Spin Hall Effect and Su-Schrieffer-Heeger Model Implementation in Novel C3N-based Dumbbell Morphologies

TL;DR

This work analyzes topological phases in dumbbell-like carbon nitride DB C3NX (X = C, Si, Ge) using first-principles calculations, tight-binding theory, and transport analyses. It shows that DB C3NSi and DB C3NGe host quantum spin Hall states arising from SOC, with an external transverse electric field driving a transition to a normal insulator; Wannier charge centers and Berry curvature confirm a $Z_2=1$ in the nontrivial phase. The authors map the quasi-1D nanoribbons to SSH-like chains, uncovering topology controlled by intra- and inter-unit-cell hopping and predicting robust edge modes. Real-space decimation and Green's function transport connect bulk topology to spectral and conductance signatures, revealing multiple conduction channels and field-tunable edge transport. Overall, the study provides a pathway to electrically control topological phases in light-element 2D materials and highlights SSH-like physics in nanoribbon geometries.

Abstract

Two-dimensional carbon nitride materials have been the center of attention for their diverse usage in energy harvesting, environmental remediation and nanoelectronic applications. A broad range of utilities with decent synthetic plausibility have made this family a sweet spot to dive into, whereas the underlying analytical aspects are yet to have prominence. Recently, using the machinaries of first principles, we reported a family of six different structures C3NX with a unique dumbbell-shaped morphology, functionalizing the recently synthesized monolayer of C3N. Here we have critically explored the non-trivial topological phases of the semimetallic Dumbbell C3NX sheets and nanoribbons. Spin-orbit coupling induced gap across the Fermi level, its subsequent tuning via an external electric field, portrayal of band inversion from the Berry curvature distribution and the evaluation of topological index using the Wannier charge center (WCC) firmly establishes the traces of topological footprint. The real space decimation scheme and Green function technique evaluate the underlying spectral information with corresponding transport characteristics. Fascinating features of these quasi-1D systems are observed utilizing the Su-Schrieffer-Heeger (SSH) model where different twisted phases reveal distinct topological signatures even in a low atomic mass system like DB C4N.

Figures (17)

• Figure 1: Relaxed unit cell of the family of semi-metallic dumbbell C$_3$NX system. Here figure (a) shows the side view, (b) the top view and (c) the adatoms responsible for dumbbell formation. Figure-(d) shows the full 2D sheet which is periodic in both x and y directions. The C (brown), N (grey) and X (blue) are the carbon, nitrogen and adatoms (C, Si and Ge) respectively.
• Figure 2: Phonon dispersion curve and ab-initio molecular dynamics (AIMD) plot for semi-metallic dumbbell C$_4$N and C$_3$NGe. Here figures (a) and (c) show the phonon dispersion and the AIMD plot for DB C$_4$N whereas figures (b) and (d) are for DB C$_3$NGe. The AIMD plots for these materials are examined and found in the canonical ensemble (NVT) while exposed to a 500 K and 300 K heat bath respectively for 2000 fs (with a time step of 1 fs) without any structural breakage.
• Figure 3: Electronic structure of the family of semi-metallic dumbbell C$_3$NX system. Here figure (a), (b) and (c) shows the existence of the Dirac cone in all three DB C$_4$N, C$_3$NSi and C$_3$NGe at high symmetry 'K' point. Figure-(d,e,f) shows the atom- (and corresponding orbital) resolved density of states for all three dumbbell formations respectively.
• Figure 4: The electrical tunability of the band gap and the indication of a possible topological phase transition in C$_3$NX systems (in this case, X=Si) is done through the TB model. The band gap exhibits a linear variation with the electric field, decreasing before reaching a critical value. Beyond this value, the band gap increases. At the critical electric field strength, the system behaves as a semimetal with zero band gap value.
• Figure 5: Variation of band gap of DB C$_3$NGe system with transverse electric field. Here (a) E$<$ E$_c$ (b) E $\approx$ E$_c$, and (c) E $>$ E$_c$ is computed using DFT. The band gap first decreases with the electric field which causes a topological phase transition and then increases again to a normal insulating phase.