Tunable Fano and Dicke effects in quantum transport in double quantum dots sandwiched between topological insulators

We study the quantum transport in double quantum dots (DQD) sandwiched between surfaces of topological insulator (TI) ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$, which possess strong spin-orbit coupling (SOC) and ${}^{d}{\mathrm{C}}_{3v}$ double group symmetry. Different from the spin-conserved case with two-dimensional electron gas (2DEG) electrodes, the conductance displays a universal scaling relation for different Fermi energy associated with the topological nature/linear dispersion of topological surface states. The interplay between direct interdot tunneling and surface state mediated interaction leads to tunable Dicke and Fano effects with changing the interdot distance. We propose nano-rulers with different measurement range and resolution based on the Fano $q$-factor. Furthermore, when applying an in-plane Zeeman field, a crossover from a double-peak shape to a quad-peak shape in conductance curve appears. Moreover, the rotational symmetry of the system could also be revealed from the conductance pattern. Our findings contribute to a better understanding of the quantum transport in the presence of electrode's SOC topological states.