Geometry, chirality, topology and electron–electron interactions in the quadruple quantum dot molecule

• Energy spectrum of quadruple quantum dot systems with different topologies.
• Extended Hubbard model applied on quadruple quantum dot molecule.
• Occurrence of chiral states and topological phase, effective gauge field.
• Total spin tuning of ground state without magnetic field.
• Occurrence of spin blockade with changing topology or electron–electron interactions.

We present a theory of electronic properties of a quadruple quantum dot molecule (QQD) which focuses on geometry, chirality, and electron–electron interactions. The QQD is described by the extended Hubbard model solved using exact diagonalization method in real and Fourier space. The energy spectrum of a QQD is analysed as a function of the number of electrons Ne, for ring, linear, or star geometry. We discuss the interplay of chirality, topology, and Fermi statistics for a half-filled ring QQD charged with either additional electron or hole. We show that the chirality leads to the appearance of a topological phase and an effective gauge field stabilizing the spin polarised state. The spin polarised state with extra electron (hole) and spin unpolarised state at half-filling lead to spin blockade in transport through the ring-like QQD but not through a linear nor star QQD molecule. We demonstrate that the ground state can be tuned between a total spin S=1/2 and S=3/2 by changing the strength of on-site interactions or tuning the tunnelling matrix element.