Engineering stacking-induced topological phase transitions in bilayer heterostructures

TL;DR

The study addresses the challenge of realizing tunable two-dimensional topological insulators by leveraging architecture rather than intrinsic material topology. It demonstrates that stacking two topologically trivial Rashba monolayers into an inverted BiSb–SbBi bilayer induces a nontrivial $Z_2$ phase governed by the interplay of SOC and interlayer tunneling, tunable via interlayer distance, SOC strength, and an external electric field. The work reveals a critical distance $d_c=2.84$ Å for the trivial-to-nontrivial transition and identifies the scaling $g_{\mathrm{eff}} \sim \lambda_{SOC}^2/t$ together with a zeroth Landau level as key experimental signatures, while predicting a gate-tunable, large spin Hall conductivity (${\sim}178$ to ${\sim}367$ $(\hbar/e)$ S/cm). These findings establish a practical route to engineer tunable 2D topological phases in van der Waals heterostructures, with BiSb bilayers offering a realistic platform for spintronic and quantum technologies.

Abstract

Nonmagnetic topological insulators (TIs) are known for their robust metallic surface/edge states that are protected by time-reversal symmetry, making them promising candidates for next-generation spintronic and nanoelectronic devices. Traditional approaches to realizing TIs have focused on inducing band inversion via strong spin-orbit coupling (SOC), yet many materials with substantial SOC often remain topologically trivial. In this work, we present a materials-design strategy for engineering topologically non-trivial phases, e.g., quantum spin Hall phases, by vertically stacking topologically trivial Rashba monolayers in an inverted fashion. Using BiSb as a prototype system, we demonstrate that while the BiSb monolayer is topologically trivial (despite having significant SOC), an inverted BiSb-SbBi bilayer configuration realizes a non-trivial topological phase with enhanced spin Hall conductivity. We further reveal a delicate interplay between the SOC strength and the interlayer electron tunneling that governs the emergence of a nontrivial topological phase in the bilayer heterostructure. This phase can be systematically tuned using an external electric field, providing an experimentally accessible means of controlling the system's topology. Our magnetotransport studies further validate this interplay, by revealing $g$-factor suppression and the emergence a zeroth Landau level. Notably, the inverted bilayer heterostructure exhibits a robust and tunable spin Hall effect, with performance comparable to that of state-of-the-art materials. Thus, our findings unveil an alternative pathway for designing and engineering functional properties in 2D topological systems using topologically trivial constituent monolayers.

Figures (10)

• Figure 1: Optimized crystal structures of (a) BiSb monolayer and (b) BiSb-SbBi bilayer, where $d$ represents the interlayer distance between the two inverted monolayers and $t$ denotes the interlayer electron tunneling. (c) Schematic illustration of the proposed experimental design scheme for realizing the BiSb–SbBi bilayer structure by folding a BiSb monolayer. (d) Variation of the Z$_2$ topological invariant in the BiSb-SbBi bilayer with varying interlayer distance $d$. The light red region indicates the topologically nontrivial phase with Z$_2$ = 1, while the light blue region represents the topologically trivial phase with Z$_2$ = 0.
• Figure 2: Electronic band structure of the BiSb-SbBi bilayer with varying interlayer distance ($d$). Electronic band structures are computed along high-symmetry directions of the Brillouin zone for (a)-(b) the BiSb monolayer, (c)-(d) the bilayer at d = 2.1 Å (optimized), (e)-(f) the bilayer at d = 5 Å, and (g)-(h) the orbital-projected band structure at d = 2.1 Å (optimized). Horizontal dashed lines mark the Fermi level. The top panels show band structures without SOC (red), while the bottom panels include SOC (blue).
• Figure 3: The variation of the Z$_2$ topological invariant as a function of artificial SOC strength ($\lambda_\textrm{SOC}$) is shown for (a) $d = 2.1 \, \text{Å}$ and (b) $d = 4 \, \text{Å}$.
• Figure 4: 2D phase diagram illustrating the variation of the Z$_2$ topological invariant in the BiSb-sbbi bilayer as a function of interlayer distance ($d$) and applied electric field ($E$). The color bar represents the corresponding values of the Z$_2$ invariant.
• Figure 5: Landau levels computed for the BiSb-SbBi bilayer at (a) $d = 2.1 \, \text{Å}$ (topologically nontrivial case) and (b) $d = 4 \, \text{Å}$ (topologically trivial case). The variation of the effective $g$-factor is presented for (c) $d = 2.1 \, \text{Å}$ and (d) $d = 4 \, \text{Å}$. The effective $g$-factors are computed for the Landau levels highlighted by the blue shaded regions in (a) and (b).