Correlations and topology in hybrid graphene-based devices

• Autor(a) principal: Manesco, Antonio Lucas Rigotti
• Data de Publicação: 2021
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: https://www.teses.usp.br/teses/disponiveis/97/97134/tde-04052022-112041/
• topic: Andreev reflections; correlações eletrônicas; electronic correlations; fases topológicas; grafeno; graphene; reflexões de Andreev; superconductivity; supercondutividade; topological phases

Graphene is a two-dimensional carbon allotrope with a honeycomb crystal structure in which electronic excitations behave as massless Dirac particles. The absence of an effective mass makes graphene a gapless material with outstanding electronic properties. Paradigmatic works, such as Haldane and Kane-Mele models, show that certain mass terms in honeycomb materials lead to topologically non-trivial phases. However this masses are inexistent or nearly negligible in free-standing graphene. In this thesis, we follow a diferente approach: we investigate topological phases in graphene driven by electronic correations. In the first part, we explore the emergence of Majorana zero modes when superconductivity is induced by proximity effect at the canted-antiferromagnetic quantum Hall edge states.We derive a low-energy theory for the Majorana end states combining bundary conditions for normal and Andreev reflections. The two-band nature of this system motivated us to extend the classification of one-dimensional topological superconductors to multiband systems. We finally investigate the current status of state-of-art experiments on proximitized quantum Hall graphene and explore possible mechanisms for the propagation of Andreev edge states at the normal/superconductor interface. Or results show that the recently reported interference of chiral Andreev edge states is due to disorder at the interface. Furthermore, we point out necessary improvements to achieve the topological regime. The second part of this thesis is devoted to study electronic correlations in buckled graphene superlattices reported in a recent experiment. The buckling transition occurs when the structure relaxes under in-plane strain. From the low-energy perspective, electrons experience strain similarly to a pseudo-magnetic field. This field leads to the formation of pseudo-Landau levels, resulting in a bandwidth quench and an increase of the density of states at half-filling. Thus, the effects of electron-electron interactions are enhanced, and correlated phases take place. We prove the existence of a modulated ferrimagnetic superlattice from Hubbard calculations and show the possibility of electric tunability of correlations. Moreover, we develop a low-energy theory for this system and explore the effects of long-range interactions, showing the existance of a competing charge density wave phase. Finally, we show that both correlated phases present quantum valley Hall insulator regimes, proposing buckled graphene superlattices as a platform for correlation-driven valley topology.