Emergent Parafermionic Zero Modes in Fermionic Systems

Parafermionic bound states, Z_n-symmetric generalizations of Majorana zero modes, can emerge as edge states in strongly correlated systems displaying fractionalized excitations. The non-trivial fractional nature of Z₃ parafermions, in particular, can be used to produce Fibonacci anyons, a key ingredient in a universal topological quantum computer.

In this talk, I will summarize some of the efforts in our group investigating possible paths toward *realizing* and *detecting* emergent parafermions in strongly interacting electronic systems. In particular, we introduce a representation of Z₃ parafermions in terms of purely fermionic operators. From there, we establish the equivalency of a family of lattice fermionic models written on the basis of the t−J model with a Kitaev-like chain supporting free Z₃ parafermionic modes at its ends. By using density matrix renormalization group (DMRG) calculations, we are able to characterize the topological phase transition and study the effect of local operators (doping and magnetic fields) on the spatial localization of the parafermionic modes and their stability.

We also propose a way to detect parafermionic zero modes using a quantum dot tunnel coupled to the edge of a system hosting Z₄ parafermions. We show that the dot's zero-energy spectral function and average occupation numbers can be used to distinguish between different phases of the system (trivial, Z₄, and 2 x Z₂). This opens the prospect of using quantum dots as detection tools to probe nontrivial topological phases in strongly correlated systems.