Majorana representation for topological edge states of massless Dirac fermion with non-quantized Berry phase
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909231625535488 |
|---|---|
| author | Pratama, F. R. Nakanishi, Takeshi |
| author_facet | Pratama, F. R. Nakanishi, Takeshi |
| contents | We study the bulk-boundary correspondences for zigzag ribbons (ZRs) of massless Dirac fermion in two-dimensional $α$-${T}_3$ lattice. By tuning the hopping parameter $α\in[0,1]$, the $α$-${T}_3$ lattice interpolates between pseudospin $S=1/2$ (graphene) and $S=1$ (${T}_3$ or dice lattice), for $α=0$ and $1$, respectively, which is followed by continuous change of the Berry phase from $π$ to $0$. The range of existence for edge states in the momentum space is determined by solving tight-binding equations at the boundaries of the ZRs. We find that the transitions of in-gap bands from bulk to edge states in the momentum space do not only occur at the positions of the Dirac cones but also at additional points depending on $α\notin \{0,1\}$. The $α$-${T}_3$ ZRs are mapped into stub Su-Schrieffer-Heeger chains by performing unitary transforms of the bulk Hamiltonian. The non-trivial topology of the bulk bands is revealed by the Majorana representation of the eigenstates, where the $\mathbb{Z}_2$ topological invariant is manifested by the winding numbers on the complex plane and the Bloch sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17919 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Majorana representation for topological edge states of massless Dirac fermion with non-quantized Berry phase Pratama, F. R. Nakanishi, Takeshi Mesoscale and Nanoscale Physics We study the bulk-boundary correspondences for zigzag ribbons (ZRs) of massless Dirac fermion in two-dimensional $α$-${T}_3$ lattice. By tuning the hopping parameter $α\in[0,1]$, the $α$-${T}_3$ lattice interpolates between pseudospin $S=1/2$ (graphene) and $S=1$ (${T}_3$ or dice lattice), for $α=0$ and $1$, respectively, which is followed by continuous change of the Berry phase from $π$ to $0$. The range of existence for edge states in the momentum space is determined by solving tight-binding equations at the boundaries of the ZRs. We find that the transitions of in-gap bands from bulk to edge states in the momentum space do not only occur at the positions of the Dirac cones but also at additional points depending on $α\notin \{0,1\}$. The $α$-${T}_3$ ZRs are mapped into stub Su-Schrieffer-Heeger chains by performing unitary transforms of the bulk Hamiltonian. The non-trivial topology of the bulk bands is revealed by the Majorana representation of the eigenstates, where the $\mathbb{Z}_2$ topological invariant is manifested by the winding numbers on the complex plane and the Bloch sphere. |
| title | Majorana representation for topological edge states of massless Dirac fermion with non-quantized Berry phase |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2406.17919 |