Shell Filling and Trigonal Warping in Graphene Quantum Dots

Abstract

Transport measurements through a few-electron circular quantum dot in bilayer graphene display bunching of the conductance resonances in groups of four, eight and twelve. This is in accordance with the spin and valley degeneracies in bilayer graphene and an additional threefold 'minivalley degeneracy' caused by trigonal warping. For small electron numbers, implying a small dot size and a small displacement field, a two-dimensional s- and then a p-shell are successively filled with four and eight electrons, respectively. For electron numbers larger than twelve, as the dot size and the displacement field increase, the single-particle ground state evolves into a three-fold degenerate minivalley ground state. A transition between these regimes is observed in our measurements and can be described by band-structure calculations. Measurements in magnetic field confirm Hund's second rule for spin filling of the quantum dot levels, emphasizing the importance of exchange interaction effects.

arXiv comment10 pages, 7 figures

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• Gate-Controlled Quantum Dots Based on Two-Dimensional Materials
• Theory of tunneling spectra for a few-electron bilayer graphene quantum dot
• Counting Statistics of Single Electron Transport in Bilayer Graphene Quantum Dots
• Valley current generation using biased bilayer graphene dots
• Spin-valley locked excited states spectroscopy in a one-particle bilayer graphene quantum dot
• Gate-tunable regular and chaotic electron dynamics in ballistic bilayer graphene cavities
• Pauli blockade catalogue and three- and four-particle Kondo effect in bilayer graphene quantum dots
• Extended Hubbard model describing small multi-dot arrays in bilayer graphene
• Impact of competing energy scales on the shell-filling sequence in elliptic bilayer graphene quantum dots
• Switching spin filling sequence in a bilayer graphene quantum dot through trigonal warping
• Tunable p-n junction barriers in few-electron bilayer graphene quantum dots
• Electric-field independent spin-orbit coupling gap in hBN-encapsulated bilayer graphene
• Three-carrier spin blockade and coupling in bilayer graphene double quantum dots
• Electrically-tunable graphene nanomechanical resonators
• Tuning confined states and valley g-factors by quantum dot design in bilayer graphene
• Optical Properties of Gated Bilayer Graphene Quantum Dots with Trigonal Warping
• Ultra-Fast All-Electrical Universal Nano-Qubits
• The role of antisymmetric orbitals and electron-electron interactions on the two-particle spin and valley blockade in graphene double quantum dots
• Electronic and Spin-Orbit Properties of hBN Encapsulated Bilayer Graphene
• Electrically tunable MoSe${}_2$/WSe${}_2$ heterostructure-based quantum dot