Interface controlled Berry phase and anisotropic spin-charge conversion in altermagnet-topological insulator bilayers

Abstract

We propose an altermagnet-topological insulator bilayer as a platform to engineer Berry phase driven spin-charge responses using an interfacial buffer layer. Using a momentum-space lattice model and linear-response theory, we investigate a $d$-wave altermagnet coupled to a topological insulator and highlight the crucial role of spin-flip tunneling in shaping its electronic and transport properties. Interfacial hybridization strongly modifies the band structure, leading to anisotropic Rashba-Edelstein and Hall responses. The spin-flip component of the coupling induces an inverse $d$-wave spin texture in the altermagnetic bands, signaling the onset of an altermagnetic topological phase. This coupling also renders the Rashba-Edelstein effect strongly in-plane anisotropic, enhancing the transverse response relative to ferromagnetic or antiferromagnetic analogues. These results establish interfacial spin-flip tunneling as a practical control knob for direction-sensitive, stray-field-free spin-charge conversion in correlated topological heterostructures.

Figures (7)

• Figure 1: Schematic of the two-dimensional bilayer: a $d$-wave altermagnet (top) stacked on a topological insulator surface (bottom). Interlayer hybridization proceeds via a spin-conserving hopping channel $t_{1}$ and a spin-flip channel $t_{2}$, which couple same-spin and opposite-spin states across the interface, respectively.
• Figure 2: Proximity-induced altermagnetic features in Rashba–topological-insulator bands. Plots (a–c) show the decoupled limit ($t_1=t_2=0$): (a) band structure with spin-resolved altermagnet bands and Dirac states (teal) carrying zero out-of-plane spin polarization, (b) energy eigenvalues of the lower AM band exhibiting zero-energy modes protected along mirror lines, and (c) the corresponding spin polarization. Plots (d–f) illustrate the coupled case ($t_1=1.0, t_2=0.01~ t_J$): (d) hybridized bands where the lower valence and upper conduction bands acquire finite out-of-plane spin polarization, (e) The band dispersion corresponding to the upper valence branch evolves into a Dirac-like form with circular symmetry near the $\Gamma$ point, and (f) an inverse $d$-wave spin polarization pattern also emerges, accompanied by the in-plane texture reflecting the point of degeneracy with the lower valence branch. Plot (g) shows the net spin polarization of all occupied states along $k_x$ ($k_y=0$), which approaches zero for $t_2<t_1$, while the total $k$-space sum vanishes in both $t_1<t_2$ and $t_1>t_2$ limits depicted in (h).
• Figure 3: Evolution of eigenvalue spectrum and spin polarization with tunneling amplitudes. (a) Band dispersion along $-\mathrm{Y}\!-\!\Gamma\!-\!\mathrm{Y}$ for $t_{1}=0.05~t_J$, $t_{2}=0.01~t_J$; the degeneracy of occupied (unoccupied) bands shifts by $\Delta k$ along $-k_y$ ($+k_y$). (b) Dispersion along $\mathrm{X}\!-\!\Gamma\!-\!\mathrm{Y}$ for symmetric tunneling $t_{1}=t_{2}=0.01~ t_J$, where a protected zero mode remains along mirror lines. (c) Colormap of $\Delta k$ in the $(t_{1},t_{2})$ plane with analytical contours from Eq. \ref{['DeltaR']}. (d) Minimum inter-band splitting $\delta E_{23}$ showing gap closure and reopening along $t_1=t_2$. (e,f) Energy dispersion and spin polarization of the occupied AM band for $t_2/t_1=0.1$. (g,h) Corresponding results for $t_2/t_1=0.01$, where the texture becomes nearly isotropic.
• Figure 4: Anomalous Hall conductivity of the AM–TI bilayer. (a) Colormap of $\sigma_{xy}$ in the $(t_{1},t_{2})$ plane, showing a sign reversal across $t_{1}\!\approx\! t_{2}$. (b) $\sigma_{xy}(t_{1})$ at fixed $t_{2}=\{0.02,0.04,0.06\}~t_J$, exhibiting a non-monotonic evolution and zero crossing near $t_{1}\!\sim\!t_{2}$. (c) Low-field $\sigma_{xy}(B_{\mathrm{ext}})$ illustrating sensitivity to weak perturbations. (d) High-field $\sigma_{xy}(B_{\mathrm{ext}})$ showing recovery of antisymmetric behavior. The temperature in the Fermi function is set to $30$ K with hopping parameters measured in $t_J$. For plots (c) and (d), the spin flip tunneling is $0.001~t_J$.
• Figure 5: Rashba–Edelstein response tensor of the AM–TI bilayer. (a,b) Colormaps of $\chi_{xy}$ and $\chi_{yx}$ in the $(t_{1},t_{2})$ plane, expressed in $e\,s\,m^{-1}$. Finite $t_{2}$ breaks the antisymmetric relation $\chi_{xy}=-\chi_{yx}$, producing in-plane anisotropy. (c,d) Line cuts of $\chi_{xy}$ and $\chi_{yx}$ comparing FM–TI, AM–TI, and AFM–TI bilayers for $t_{2}=0.0$ and $0.04~t_J$, showing that the AM–TI interface exhibits the strongest deviation from antisymmetry. Other parameters are $T=30$ K, $\tau = 10^{-13}$ s, $M/t_J=1$ and, $\Delta=0.1~t_j$