Ferromagnetism in Quantum Dot Plaquettes

Abstract

Following the recent claimed obsevation of Nagaoka ferromagnetism in finite size quantum dot plaquettes, a general theoretical analysis is warranted in order to ascertain in rather generic terms which arrangements of a small number of quantum dots can produce saturated ferromagnetic ground states and under which constraints on interaction and inter-dot tunneling in the plaquette. This is particularly necessary since Nagaoka ferromagnetism is fragile and arises only under rather special conditions. We test the robustness of ground state ferromagnetism in the presence of a long-range Coulomb interaction and long-range as well as short-range interdot hopping by modeling a wide range of different plaquette geometries accessible by arranging a few (~4) quantum dots in a controlled manner. We find that ferromagnetism is robust to the presence of long range Coulomb interactions, and we develop conditions constraining the tunneling strength such that the ground state is ferromagnetic. Additionally, we predict the presence of a partially spin-polarized ferromagnetic state for 4 electrons in a Y-shaped 4-quantum dot plaquette. Finally, we consider 4 electrons in a ring of 5 dots. This does not satisfy the Nagaoka condition, however, we show that the ground state is spin one for strong, but not infinite, onsite interaction. Thus, even though Nagaoka's theorem does not apply, the ground state for the finite system with one hole in a ring of 5 dots is partially ferromagnetic. We provide detailed fully analytical results for the existence or not of ferromagnetic ground states in several quantum dot geometries which can be studied in currently available coupled quantum dot systems.

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Cited by in corpus (16)

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• Studying many-body localization in exchange-coupled electron spin qubits using spin-spin correlations
• Engineering the Kitaev spin liquid in a quantum dot system
• Onset of ferromagnetism for strongly correlated electrons in one-dimensional chains
• Exact analytical treatment of multiqubit noisy dynamics in exchange-coupled semiconductor spin qubits
• Certain exact many-body results for Hubbard model ground states testable in small quantum dot arrays
• Collective ground states in small lattices of coupled quantum dots
• Stable and Metastable Kinetic Ferromagnetism on a Ring
• Quantum entanglement in a pure state of strongly correlated quantum impurity systems
• Extended quasiparticle Padé approximation for non-Fermi liquids
• Quantum permutation puzzles with indistinguishable particles
• Kondo effect in Lieb's ferrimagnetic system on the T-shaped bipartite lattice
• Spin-polarized transport in quadruple quantum dots attached to ferromagnetic leads
• Shaping Magnetic Order by Local Frustration for Itinerant Fermions on a Graph
• Optimal array geometries for kinetic magnetism and Nagaoka polarons
• Itinerant magnetism in Hubbard models with long-range interactions