[Paper Review] Valley-Polarized Quantum Anomalous Hall Phase in Bilayer Graphene with Layer-Dependent Proximity Effects

Marc Vila, José H. García+1 more|arXiv (Cornell University)|Jun 30, 2021

Graphene research and applications105 references38 citations

TL;DR

This paper proposes a valley-polarized quantum anomalous Hall effect (VP-QAHE) in bilayer graphene by applying spin-orbit coupling and magnetic exchange interactions separately to different layers via proximity effects. The resulting topological gap opens only at one Dirac cone, enabling a robust, gate-tunable, and switchable chiral edge state with Chern number C = ±1, controllable by reversing the exchange field or electric field to toggle between valleys.

ABSTRACT

Realizations of some topological phases in two-dimensional systems rely on the challenge of jointly incorporating spin-orbit and magnetic exchange interactions. Here, we predict the formation and control of a fully valley-polarized quantum anomalous Hall effect in bilayer graphene, by separately imprinting spin-orbit and magnetic proximity effects in different layers. This results in varying spin splittings for the conduction and valence bands, which gives rise to a topological gap at a single Dirac cone. The topological phase can be controlled by a gate voltage and switched between valleys by reversing the sign of the exchange interaction. By performing quantum transport calculations in disordered systems, the chirality and resilience of the valley-polarized edge state are demonstrated. Our findings provide a promising route to engineer a topological phase that could enable low-power electronic devices and valleytronic applications.

Motivation & Objective

• To realize a fully valley-polarized quantum anomalous Hall phase in bilayer graphene, a topological state with quantized Hall conductivity and chiral edge states at zero magnetic field.
• To overcome the challenge of simultaneously inducing strong spin-orbit coupling and magnetic exchange interaction in graphene, which are typically weak or incompatible in conventional heterostructures.
• To exploit layer-dependent wavefunction localization in bilayer graphene to selectively apply spin-orbit coupling and magnetism to different layers, enabling independent control of band splittings.
• To demonstrate that the resulting topological phase is robust against disorder and can be switched between valleys via gate voltage or exchange field reversal.
• To propose a feasible experimental route using van der Waals heterostructures with common 2D materials (e.g., transition metal dichalcogenides and ferromagnetic insulators) to realize the VP-QAHE.

Proposed method

• Construct a tight-binding Hamiltonian for Bernal-stacked bilayer graphene encapsulated between a ferromagnetic insulator (FMI) and a strong spin-orbit coupling (SOC) material, with separate proximity effects on each layer.
• Model the spin-orbit coupling via Rashba and intrinsic (Kane-Mele-like) terms, with the valley-Zeeman component (λVZ) responsible for valley-dependent spin splitting.
• Include magnetic proximity effect via an exchange term Hex = M ∑ c†_is [m·s]_ss' cis', with m = ẑ, to induce layer-specific spin splitting.
• Use the interlayer potential U (tunable via perpendicular electric field) to control band hybridization and reverse layer localization of conduction and valence bands.
• Compute the Chern number C = (1/2π) ∫ Ω(k) d²k to confirm topological character, and perform Landauer-Büttiker transport calculations in disordered nanoribbon geometries.
• Employ the Kwant software package to simulate quantum transport and extract Hall conductance and edge state chiralities under various disorder and field configurations.

Experimental results

Research questions

• RQ1 Can a fully valley-polarized quantum anomalous Hall effect be realized in bilayer graphene by applying spin-orbit and magnetic proximity effects separately to different layers?
• RQ2 How does layer-dependent wavefunction localization enable selective control of spin splitting in conduction and valence bands?
• RQ3 Can the topological phase be switched between valleys by reversing the sign of the exchange interaction or tuning the interlayer potential?
• RQ4 How robust are the chiral edge states to bulk and edge disorder in realistic disordered systems?
• RQ5 What are the minimal experimental requirements (materials, parameters) for observing the VP-QAHE with current technology?

Key findings

• A topological gap opens only at a single Dirac cone (K or K') due to asymmetric spin splitting between conduction and valence bands, resulting in a valley-polarized quantum anomalous Hall state with Chern number C = ±1.
• The edge states are chiral and robust against both bulk and edge disorders, as confirmed by quantum transport simulations in nonlocal geometries.
• The valley polarization and edge state chirality can be reversed by flipping the sign of the exchange interaction (M), enabling electrical switching between valleys.
• The topological phase can be tuned by an external electric field that reverses the layer localization of the wavefunctions, thereby swapping the roles of conduction and valence band spin splittings.
• The VP-QAHE is realizable with currently available materials, such as transition metal dichalcogenides (for SOC) and 2D magnets (for exchange), in van der Waals heterostructures.
• The predicted topological gap is robust even with realistic parameter values, and the system exhibits quantized Hall conductance σxy = e²/h, confirming the topological nature of the phase.