Nonlocality of local Andreev conductances as a probe for topological Majorana wires
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2023
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| author | Dourado, Rodrigo A. Penteado, Poliana H. Egues, J. Carlos |
| author_facet | Dourado, Rodrigo A. Penteado, Poliana H. Egues, J. Carlos |
| contents | We propose a protocol based only on local conductance measurements for distinguishing trivial from topological phases in realistic three-terminal superconducting nanowires coupled to normal leads, capable of hosting Majorana zero modes (MZMs). By using Green functions and the scattering matrix approach, we calculate the conductance matrix and the local density of states (LDOS) as functions of the asymmetry in the couplings to the left ($Γ_L$) and right ($Γ_R$) leads. In the trivial phase, we find that the zero-bias local conductances are distinctively affected by variations in $Γ_R$ (for fixed $Γ_L$): while $G_{LL}$ is mostly constant, $G_{RR}$ decays exponentially as $Γ_R$ is decreased. In the topological phase, surprisingly, $G_{LL}$ and $G_{RR}$ are both suppressed with $G_{LL} \sim G_{RR}$. This \textit{nonlocal} suppression of $G_{LL}$ with $Γ_R$ scales with the MZM hybridization energy $\varepsilon_m$ and arises from the emergence of a dip in the LDOS near zero energy at the left end of the wire, which affects the local Andreev reflection. We further exploit this nonlocality of the local Andreev processes and the gate-controlled suppression of the LDOS by proposing a Majorana-based transistor. Our results hold for zero and low electron temperatures $T<20$ mK. For $T = 30, 40$ mK, $G_{LL}$ and $G_{RR}$ become less correlated. As an additional nonlocal fingerprint of the topological phase at higher $T$'s, we predict modulations in our \textit{asymmetric} conductance deviation $δG^{asym}_{LL}= G_{LL}^{Γ_R = Γ_L} - G_{LL}^{Γ_R \ll Γ_L}$ that remains commensurate with the Majorana oscillations in $\varepsilon_m$ over the range $30<T< 150~\rm{mK}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2303_01867 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Nonlocality of local Andreev conductances as a probe for topological Majorana wires Dourado, Rodrigo A. Penteado, Poliana H. Egues, J. Carlos Mesoscale and Nanoscale Physics Quantum Physics We propose a protocol based only on local conductance measurements for distinguishing trivial from topological phases in realistic three-terminal superconducting nanowires coupled to normal leads, capable of hosting Majorana zero modes (MZMs). By using Green functions and the scattering matrix approach, we calculate the conductance matrix and the local density of states (LDOS) as functions of the asymmetry in the couplings to the left ($Γ_L$) and right ($Γ_R$) leads. In the trivial phase, we find that the zero-bias local conductances are distinctively affected by variations in $Γ_R$ (for fixed $Γ_L$): while $G_{LL}$ is mostly constant, $G_{RR}$ decays exponentially as $Γ_R$ is decreased. In the topological phase, surprisingly, $G_{LL}$ and $G_{RR}$ are both suppressed with $G_{LL} \sim G_{RR}$. This \textit{nonlocal} suppression of $G_{LL}$ with $Γ_R$ scales with the MZM hybridization energy $\varepsilon_m$ and arises from the emergence of a dip in the LDOS near zero energy at the left end of the wire, which affects the local Andreev reflection. We further exploit this nonlocality of the local Andreev processes and the gate-controlled suppression of the LDOS by proposing a Majorana-based transistor. Our results hold for zero and low electron temperatures $T<20$ mK. For $T = 30, 40$ mK, $G_{LL}$ and $G_{RR}$ become less correlated. As an additional nonlocal fingerprint of the topological phase at higher $T$'s, we predict modulations in our \textit{asymmetric} conductance deviation $δG^{asym}_{LL}= G_{LL}^{Γ_R = Γ_L} - G_{LL}^{Γ_R \ll Γ_L}$ that remains commensurate with the Majorana oscillations in $\varepsilon_m$ over the range $30<T< 150~\rm{mK}$. |
| title | Nonlocality of local Andreev conductances as a probe for topological Majorana wires |
| topic | Mesoscale and Nanoscale Physics Quantum Physics |
| url | https://arxiv.org/abs/2303.01867 |