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Topological states in normal and superconducting $p$-wave chains
Superconductivity · Submitted 16 May 2014
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim However, we show by mapping the $s$- and $p$- fermions to two copies of Majoranas, that the excitations in the ends of a finite $sp$ chain are indeed conventional fermions though endowed with protected topological properties.
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We study a two-band model of fermions in a 1d chain with an antisymmetric hybridization that breaks inversion symmetry. We find that for certain values of its parameters, the $sp$-chain maps formally into a $p$-wave superconducting chain, the archetypical 1d system exhibiting Majorana fermions. The eigenspectra, including the existence of zero energy modes in the topological phase, agree for both models. The end states too share several similarities in both models, such as the behavior of the localization length, the non-trivial topological index and robustness to disorder. However, we show by mapping the $s$- and $p$- fermions to two copies of Majoranas, that the excitations in the ends of a finite $sp$ chain are indeed conventional fermions though endowed with protected topological properties. Our results are obtained by a scattering approach in a semi-infinite chain with an edge defect treated within the $T$-matrix approximation. We augment the analytical results with exact numerical diagonalization that allow us to extend our results to arbitrary parameters and also to disordered systems.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study a two-band model of fermions in a 1d chain with an antisymmetric hybridization that breaks inversion symmetry. | contribution 0.85 | 0.77 | 0.03 | asserted 0.94 |
| s1 | We find that for certain values of its parameters, the $sp$-chain maps formally into a $p$-wave superconducting chain, the archetypical 1d system exhibiting Majorana fermions. | result 0.94 | 0.92 | 0.19 | asserted 0.99 |
| s2 | The eigenspectra, including the existence of zero energy modes in the topological phase, agree for both models. | result 1.00 | 0.85 | 0.11 | asserted 1.00 |
| s3 | The end states too share several similarities in both models, such as the behavior of the localization length, the non-trivial topological index and robustness to disorder. | result 1.00 | 0.84 | 0.09 | asserted 1.00 |
| s4 | However, we show by mapping the $s$- and $p$- fermions to two copies of Majoranas, that the excitations in the ends of a finite $sp$ chain are indeed conventional fermions though endowed with protected topological properties. | result 0.91 | 0.95 | 0.73 | asserted 1.00 |
| s5 | Our results are obtained by a scattering approach in a semi-infinite chain with an edge defect treated within the $T$-matrix approximation. | method 1.00 | 0.91 | 0.02 | asserted 0.99 |
| s6 | We augment the analytical results with exact numerical diagonalization that allow us to extend our results to arbitrary parameters and also to disordered systems. | method 0.99 | 0.96 | 0.04 | asserted 1.00 |
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Original abstract
We study a two-band model of fermions in a 1d chain with an antisymmetric hybridization that breaks inversion symmetry. We find that for certain values of its parameters, the $sp$-chain maps formally into a $p$-wave superconducting chain, the archetypical 1d system exhibiting Majorana fermions. The eigenspectra, including the existence of zero energy modes in the topological phase, agree for both models. The end states too share several similarities in both models, such as the behavior of the localization length, the non-trivial topological index and robustness to disorder. However, we show by mapping the $s$- and $p$- fermions to two copies of Majoranas, that the excitations in the ends of a finite $sp$ chain are indeed conventional fermions though endowed with protected topological properties. Our results are obtained by a scattering approach in a semi-infinite chain with an edge defect treated within the $T$-matrix approximation. We augment the analytical results with exact numerical diagonalization that allow us to extend our results to arbitrary parameters and also to disordered systems.
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What it cites · 7 sentences without a confident label
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The topological nature of the insulating phases of the $sp$-chain for the symmetric case $t_s= t_p=t$ and $ϵ^0_s=-ϵ^0_p=ϵ$ can be established by calculating the winding number of these phases [ref] .
New directions in the pursuit of Majorana fermions in solid state systems · End modes: Majoranas or conventional fermions? · 0.82
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Notice that, if we take $t_s= t_p=t$ and $ϵ^0_s=-ϵ^0_p=μ$, with $t$ and $μ$ referring to parameters of Kitaev's $p$-wave model, the results above translate directly into known results for this model [ref] .
New directions in the pursuit of Majorana fermions in solid state systems · End modes: Majoranas or conventional fermions? · 0.84
Cites as background 1 paper
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Also a one dimensional Kondo lattice has been considered [ref] .
End states in a 1-D topological Kondo insulator · Introduction · 0.97
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