[Paper Review] Unconventional topological superconductivity and phase diagram for a two-orbital model of twisted bilayer graphene

Maciej Fidrysiak, M. Zegrodnik+1 more|arXiv (Cornell University)|May 3, 2018

Graphene research and applicationsMaterials Science4 citations

TL;DR

This paper proposes a two-orbital model of twisted bilayer graphene that explains unconventional topological superconductivity via strong electronic correlations, inducing spin-triplet $d_{x^2-y^2} + id_{xy}$ pairing. It constructs a phase diagram showing Mott-insulating and superconducting phases as functions of electron concentration, with topological edge states emerging in the superconducting regime, consistent with experimental observations in a semi-quantitative manner.

ABSTRACT

We consider the superconducting and Mott-insulating states for the twisted bilayer graphene, modeled by two narrow bands of electrons or holes with appreciable intraatomic Coulomb inter- actions. The interaction induces the kinetic exchange which leads to the real-space, either triplet- or singlet-spin pairing, in direct analogy to heavy-fermions and high-temperature superconductors. We construct explicitly the phase diagram as a function of electron concentration for the spin- triplet $d_{x^2-y^2} + id_{xy}$ paired case, as well as determine the topological edge states. The model reproduces principal features observed experimentally in a semi-quantitative manner. The essential role of electronic correlations in driving both the Mott-insulating and superconducting transitions is emphasized.

Motivation & Objective

• To understand the origin of unconventional superconductivity in twisted bilayer graphene, particularly the role of electronic correlations.
• To model the interplay between Mott-insulating and superconducting phases in a two-orbital electronic system.
• To determine the topological nature of the superconducting state and its edge states.
• To reproduce key experimental features of twisted bilayer graphene in a semi-quantitative manner.
• To establish a phase diagram as a function of electron concentration for spin-triplet paired states.

Proposed method

• Formulating a two-orbital model for twisted bilayer graphene with narrow bands and strong intraatomic Coulomb interactions.
• Deriving the kinetic exchange interaction from electron correlations, leading to real-space spin-triplet or singlet pairing.
• Constructing the superconducting phase diagram for the $d_{x^2-y^2} + id_{xy}$ pairing channel as a function of electron concentration.
• Analyzing topological properties via the calculation of edge states in the superconducting phase.
• Using effective Hamiltonian techniques to map the correlated electron system to a superconducting state with non-trivial topology.
• Comparing theoretical predictions with experimental observations in twisted bilayer graphene.

Experimental results

Research questions

• RQ1 How do electronic correlations drive both Mott-insulating and superconducting transitions in twisted bilayer graphene?
• RQ2 What is the nature of the superconducting pairing symmetry in the two-orbital model of twisted bilayer graphene?
• RQ3 How does the phase diagram of superconducting and Mott-insulating states evolve with electron concentration?
• RQ4 What topological edge states emerge in the superconducting phase, and how are they related to the pairing symmetry?
• RQ5 To what extent can the model semi-quantitatively reproduce experimentally observed features in twisted bilayer graphene?

Key findings

• The model reproduces the coexistence of Mott-insulating and superconducting phases in twisted bilayer graphene, with electron concentration as a key tuning parameter.
• Spin-triplet $d_{x^2-y^2} + id_{xy}$ pairing is induced by kinetic exchange from strong electronic correlations, analogous to heavy-fermion and high-temperature superconductors.
• A well-defined phase diagram is constructed showing the emergence of superconductivity and Mott insulating states across different electron fillings.
• Topological edge states are identified in the superconducting phase, confirming the topological nature of the $d_{x^2-y^2} + id_{xy}$ paired state.
• The theoretical results show semi-quantitative agreement with experimental observations in twisted bilayer graphene.
• The essential role of electronic correlations is confirmed in driving both the Mott transition and the unconventional superconducting pairing.