Investigation of Charge and Spin Persistent Current Characteristics and Topological Aspects of Pseudospin-1 𝜶-T3 Lattice Systems

Abstract

We study prototype of a pseudospin-1 fermionic α-T3 model, which smoothly interpolates between graphene (α = 0) and a dice lattice (α = 1). For α [0, 1], the band structure features ∈ a flat band at zero energy separating two linearly dispersive Dirac cones. We explore persistent charge and spin transport in an α-T3 quantum ring (QR) analytically in presence of a magnetic field, and systematically examine how different spin-orbit couplings (SOC) (both Haldane and Rashba types) impact Aharonov-Bohm oscillations and persistent currents in the spin and charge sectors. We also include (topological) defects to assess spintronic applications of our ring setup. We broaden our perspectives and examine an α-T 3 system as an electron pump, a gedanken experiment contemplated by Laughlin to demonstrate quantum Hall effect. Interestingly, the Fano factor reveals distinct transport regimes, demonstrating ballistic, Poissonian and diffusive behaviour for different values of α. Next, to shed light on the topological properties, we consider phases and phase transitions therein solely impacted by the electron-phonon coupling in the spin-orbit coupled α-T3 bulk and ribbon systems. Our model demonstrates multiple topological phase transitions shown via the presence (or absence) of chiral and helical edge modes in semi-infinite ribbon geometries which are further evidenced by computing the Z and Z2 invariants.