Abstract
Parafermionic zero modes, $\mathbb{Z}_n$-symmetric generalizations of the well-known $\mathbb{Z}_2$ Majorana zero modes, can emerge as edge states in topologically nontrivial strongly correlated systems displaying fractionalized excitations. In this paper, we investigate how signatures of parafermionic zero modes can be detected by its effects on the properties of a quantum dot tunnel-coupled to a system hosting such states. Concretely, we consider a strongly-correlated 1D fermionic model supporting $\mathbb{Z}_4$ parafermionic zero modes coupled to an interacting quantum dot at one of its ends. By using a combination of density matrix renormalization group calculations and analytical approaches, we show that the dot's zero-energy spectral function and average occupation numbers can be used to distinguish between trivial, $\mathbb{Z}_4$ and $2\times \mathbb{Z}_2$ phases of the system. The present work opens the prospect of using quantum dots as detection tools to probe non-trivial topological phases in strongly correlated systems.
Highlights
The production and detection of quasiparticles with statistics which are neither fermionic or bosonic is a fundamental quest in condensed matter physics
Several questions remain open, from possible realizations of different parafermions to their experimental signature. We address these questions by proposing the use of quantum dots (QD) as an experimental probe to detect the signature of parafermionic modes similar to zerobias peaks predicted in Majorana-quantum dot setups [28,29,30,31,32]
We propose that quantum dots can be useful tools to probe the presence of parafermionic zero modes in strongly correlated topological systems
Summary
The production and detection of quasiparticles with statistics which are neither fermionic or bosonic is a fundamental quest in condensed matter physics. Parafermions have been subjected to renewed interest [16,17,18,19,20], as parallels of parafermionic- and MZM-hosting systems were suggested [14,21] Due to their unusual nature, proposals for the experimental realization of parafermionic zero modes (PZMs) usually rely on finding Zn-symmetric ground states of effective. Recently a Kitaev-type lattice model hosting free PZMs was mapped into a strongly interacting model of (spinful) fermionic particles in a onedimensional (1D) lattice [26,27] These models might look somewhat unrealistic due to the presence of rather exotic three-body interaction terms, they offer a concrete path to realizations of parafermions in electronic systems, similar to the role the Kitaev chain played for the Majorana zero modes almost 20 years ago [8].
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