# Exotic odd-even parity effects in transmission phase, (Andreev) conductance, and shot noise of a dimer atomic chain by topology

## TL;DR

This paper explores how topologically nontrivial dimer chains exhibit unique odd-even parity effects in transmission, conductance, noise, and phase, driven by zero-energy edge states, with implications for hybrid normal-superconductor junctions.

## Contribution

It reveals the topological origin of odd-even parity effects in transport properties and the role of zero-energy edge states in hybrid junctions, a novel insight into topological quantum transport.

## Key findings

- Opposite odd-even parity in conductance and noise for topological chains
- Zero-energy edge states influence Andreev bound states and conductance anomalies
- Distinct $2 ext{ extpi}$ phase variation at zero-energy resonance

## Abstract

We investigate the transport properties through a finite dimer chain connected to two normal leads or one normal and one superconductor (SC) leads. The dimer chain is described by the Su-Schrieffer-Hegger model and can be tuned into a topologically nontrivial phase with a pair of zero-energy edge states (ZEESs). We find that if the dimer chain is of nontrivial topology, (1) it will show apparent but opposite odd-even parity of the number of sites, in comparison with the topologically trivial and plain chains, in the (Andreev) transmission probability at the Fermi energy (i.e. the conductance and the Andreev conductance), the noise Fano factor in the zero bias limit, and even the transmission phase due to the coupled ZEESs; (2) the ZEES can determine appearance of the Andreev bound states at the site connected to the SC lead, and thereby induces a nonzero-bias-anomaly in the Andreev differential conductance of the hybrid junction; (3) the transmission phase of the normal junction has a unique $2\pi$ continuous phase variation at the zero-energy resonant peak that is also different from the usual phase shift in resonant point in usual systems.