Topological zero-reflection points in multi-terminal quantum wire junctions

arXiv:2606.31586v3 Announce Type: replace-cross Abstract: We study scattering in noninteracting multi-terminal quantum wire junctions and show that junctions with dihedral symmetry can exhibit exact zero-reflection points for $N \ge 4$ terminals. By analyzing the scattering matrix, we identify these reflectionless points in the $(E,t')$ parameter space, where $E$ is the incident particle energy and $t'$ is the junction hopping amplitude. These points exhibit an even-odd dependence on $N$ and converge asymptotically to a common limiting value in the large-$N$ limit. We show that the reflectionless points are characterized by an integer winding number associated with the phase of the reflection amplitude, providing a topological description for their stability against weak on-site disorder. We also consider junctions with broken time-reversal symmetry and find that a magnetic flux can induce additional reflectionless points, including for the $N = 3$ case. For a four-terminal junction threaded by a $\pi$-flux, we identify a unique parameter regime in which the reflection amplitude vanishes over the entire energy band. Finally, we discuss experimental signatures through the behavior of Friedel oscillations and examine the stability of these reflectionless points in the presence of weak interactions.

Abstract:We study scattering in noninteracting multi-terminal quantum wire junctions and show that junctions with dihedral symmetry can exhibit exact zero-reflection points for $N \ge 4$ terminals. By analyzing the scattering matrix, we identify these reflectionless points in the $(E,t')$ parameter space, where $E$ is the incident particle energy and $t'$ is the junction hopping amplitude. These points exhibit an even-odd dependence on $N$ and converge asymptotically to a common limiting value in the large-$N$ limit. We show that the reflectionless points are characterized by an integer winding number associated with the phase of the reflection amplitude, providing a topological description for their stability against weak on-site disorder. We also consider junctions with broken time-reversal symmetry and find that a magnetic flux can induce additional reflectionless points, including for the $N = 3$ case. For a four-terminal junction threaded by a $\pi$-flux, we identify a unique parameter regime in which the reflection amplitude vanishes over the entire energy band. Finally, we discuss experimental signatures through the behavior of Friedel oscillations and examine the stability of these reflectionless points in the presence of weak interactions.

16 pages, 1 table, 8 captioned figures. Revised version

Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Physics (quant-ph)

arXiv:2606.31586 [cond-mat.mes-hall]

(or arXiv:2606.31586v3 [cond-mat.mes-hall] for this version)

https://doi.org/10.48550/arXiv.2606.31586 Focus to learn more arXiv-issued DOI via DataCite

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Topological zero-reflection points in multi-terminal quantum wire junctions

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