Abstract
We consider a setup consisting of two coupled sheets of bilayer graphene in the regime of strong spin-orbit interaction, where electrostatic confinement is used to create an array of effective quantum wires. We show that for suitable interwire couplings the system supports a topological insulator phase exhibiting Kramers partners of gapless helical edge states, while the additional presence of a small in-plane magnetic field and weak proximity-induced superconductivity leads to the emergence of zero-energy Majorana corner states at all four corners of a rectangular sample, indicating the transition to a second-order topological superconducting phase. The presence of strong electron-electron interactions is shown to promote the above phases to their exotic fractional counterparts. In particular, we find that the system supports a fractional topological insulator phase exhibiting fractionally charged gapless edge states and a fractional second-order topological superconducting phase exhibiting zero-energy $\mathbb{Z}_{2m}$ parafermion corner states, where $m$ is an odd integer determined by the position of the chemical potential.
Highlights
Over the past few decades, topological phases of quantum matter have been the subject of extensive studies, both in theory and in experiments
We show that suitable interactions can drive the system into a fractional phase exhibiting zeroenergy Z2m parafermion corner states for an odd integer m, placing our model in the class of fractional second-order topological superconductors (TSCs)
We have considered a model based on two coupled sheets of bilayer graphene in the strong spinorbit interaction (SOI) regime
Summary
Over the past few decades, topological phases of quantum matter have been the subject of extensive studies, both in theory and in experiments. In order to access a regime with stronger SOI and avoid the need for curvature, we consider a van der Waals heterostructure combining layers of graphene and a TMD [45,46,47,48,49,50,51,52,53,54,55,56] In this case, the proximity-induced SOI is of the form Hso = αλzσz + αR(λzγxσy − γyσx ), where σi for i ∈ {x, y, z} is a Pauli matrix acting in spin space [47,50]. Our analysis can be extended to the nonperturbative regime, confirming that the found topological properties persist as long as the bulk gap is not closed
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