Spin-imbalance induced buried topological edge currents in Mott \& topological insulator heterostructures

TL;DR

This work analyzes a ferrimagnetic Mott insulator–topological insulator heterostructure on a Lieb lattice to understand buried topological edge modes under proximity effects. Using unrestricted Hartree-Fock and slave-rotor mean-field methods with self-consistent long-range Coulomb interactions, it shows that interface magnetization induces a spin imbalance in the buried edge modes while preserving their metallic, topologically protected character. This spin imbalance drives a finite charge current at the interface, effectively converting a spin Hall response into a charge Hall-like response that can be tuned by spin-orbit coupling and interface geometry. Slave-rotor results corroborate the Hartree-Fock findings, revealing robust edge states and mid-gap spectral features due to correlation effects, pointing to feasible paths for low-energy spintronic devices in correlated oxide heterostructures.

Abstract

We theoretically investigate the heterostructure between a ferrimagnetic Mott insulator and a time-reversal invariant topological band insulator on the two-dimensional Lieb lattice with periodic boundary conditions. Our Hartree-Fock and slave-rotor mean-field results incorporate long-range Coulomb interactions. We present charge and magnetic reconstructions at the two edges of the heterostructure and reveal how \textit{buried} topological edge modes adapt to these heterostructure edge reconstructions. In particular, we demonstrate that the interface magnetic field induces a spin imbalance in the edge modes while preserving their topological character and metallic nature. We show that this imbalance leads to topologically protected buried spin and charge currents. The inherent spin-momentum locking ensures that left and right movers contribute to the current at the two buried interfaces in opposite directions. We show that the magnitude of the spin-imbalance induced charge and spin current can be tuned by adjusting the spin-orbit coupling of the bulk topological insulator relative to the correlation strength of the bulk Mott insulator. Thus, our results demonstrate a controlled conversion of a spin Hall effect into an analog of a charge Hall effect driven by band topology and interaction effects. These topologically protected charge and spin currents pave the way for advances in low-energy electronics and spintronic devices.

Figures (5)

• Figure 1: Heterostructure schematic : We divide a periodically identified Lieb lattice into $U\neq 0$ and $\lambda\neq0$ parts along the x-direction. The resulting interfaces (vertical dashed lines) are parallel to the y-direction. Unit cells and sites of $\lambda_R-U_L$ interface ($I_1$) and $U_R-\lambda_L$ interface ($I_2$) are labeled as follows. The [ac] edge denotes that the (ac) sites on the $U_L$ edge hybridize with the (b) sites on the region labeled by $\lambda_R$. At the [b] edge, the (b) sites on the $U$ side interface with (ac) sites of the TI. The three-unit cell consists of sites labeled by 'a, 'b', and 'c.' The two heterostructure cases with interfaces [b]-[ac] and [b]-[b] are demarcated at the bottom with arrows. The three site unit cell is marked with 'I' and the vertical layers of (ac) sites and (b) sites demarcated by $\mathcal{L}=$1, 2 ,3 ... are also shown.
• Figure 2: Density of states & edge modes for [b]-[ac] heterostructure. (i) show the unit-cell projected DOS. The interface unit cell DOS (black) and (red), respectively, are for the [b] and [ac] interfaces, one unit cell on either side of the interface. (ii) and (iii) show the spin-resolved momentum ($k_y$)-dependent buried-interface modes at the two interfaces. The dispersions are computed, including contributions from one unit cell on the $U\neq0$ and three on the $\lambda\neq0$ side, for the [ac] (black) and [b] (red) interfaces respectively. The results are presented for $\lambda=0.3t$ and $U=7t$ on a Lieb lattice with 20 three-site unit cells along the x-direction, while translation symmetry is assumed along the y-direction.
• Figure 3: Magnetic & charge reconstructions: (i) and (iii) show the layer-dependent charge density $N(\mathcal{L})$ (black line) and magnetization $M(\mathcal{L})$ profile along the x-direction perpendicular to the interface respectively for the [b]-[ac] heterostructure. (ii) and (iv) show the corresponding results for the [b]-[b] heterostructure. In all the panels alternate layers are composed of (a-c) and (b) sites along x- axis as can be seen from Fig. \ref{['fig:1']}. The results are shown for $\lambda=0.3t$ and $U=7t$.
• Figure 4: Charge and spin currents for the [b]-[ac] hetereostructure: (i) shows the charge current $J_c=J\uparrow+J_\downarrow$ (red circles) and magnetization $M$ (green triangles) as a function of $\lambda$. The magnetization $M$ is averaged over unit cell magnetization $M_z$ of three edge unit cells on the $\lambda\neq 0$ region. The left (right) panel shows the results for the [b] ([ac]) edges for $U=7.0t$. The corresponding spin currents ($J_s=J_\uparrow-J_\downarrow$) at the two edges are shown in panels (iii) and (iv). Both $J_c$ and $J_s$ are also averaged over contributions of three edge unit cells on the TI side.
• Figure 5: Slave-rotor single-particle unit-cell resolved density of states for the [b]-[ac] heterostructure: We show the unit-cell projected SR DOS. The interface unit-cell DOS (black) and (red), respectively, are for the [b] and [ac] interfaces, one unit cell on either side of the interface. The results are presented for $\lambda=0.3t$ and $U=7t$ on a Lieb lattice with 20 three-site unit cells along the x-direction, while translation symmetry is assumed along the y-direction.