[Paper Review] Electrically tunable stacking domains and ferroelectricity in moir\'e superlattices

Daniel Bennett, Benjamin Remez|arXiv (Cornell University)|Aug 24, 2021

Ferroelectric and Piezoelectric Materials55 references51 citations

TL;DR

This paper proposes a theoretical model showing that an external electric field induces asymmetric relaxation in moiré superlattice stacking domains, leading to a net polarization and ferroelectric-like response. The field softens the domain walls and tunes their width via dielectric screening, with critical fields for domain collapse predicted at ~2.47 V/Å for MoS2, providing a mechanism for electrically tunable ferroelectricity in 2D heterostructures.

ABSTRACT

It is well known that stacking domains form in moir\'e superlattices due to the competition between the interlayer van der Waals forces and intralayer elastic forces, which can be recognized as polar domains due to the local spontaneous polarization in bilayers without centrosymmetry. We propose a theoretical model which captures the effect of an applied electric field on the domain structure. The coupling between the spontaneous polarization and field leads to uneven relaxation of the domains, and a net polarization in the superlattice at nonzero fields, which is sensitive to the moir\'e period. We show that the dielectric response to the field reduces the stacking energy and leads to softer domains in all bilayers. We then discuss the recent observations of ferroelectricity in the context of our model.

Motivation & Objective

• To understand the origin of unconventional ferroelectricity observed in bilayer graphene and hBN, which are non-polar materials.
• To investigate how an applied electric field modifies the stacking domain structure in moiré superlattices through coupling with spontaneous polarization.
• To model the dielectric response of bilayer systems to electric fields and its impact on domain wall softness and stability.
• To explain recent experimental observations of field-dependent hysteresis and ferroelectric behavior in twisted 2D materials.

Proposed method

• Develops a continuum field theory model for moiré superlattices, including elastic energy, stacking energy, and electrostatic energy under an external field.
• Incorporates the full non-harmonic van der Waals potential for stacking energy, enabling accurate description of field-induced breakdown.
• Includes both the direct coupling of the electric field to the out-of-plane dipole moment and the dielectric response via polarizability expansion.
• Uses a 1D Frenkel-Kontorova (FK) model to analytically and numerically solve for domain wall profiles and width as a function of field and twist angle.
• Derives the domain wall width as a function of electric field and twist angle, showing divergence at a critical field E_crit ≈ 2.47 V/Å for MoS2.
• Validated with first-principles calculations and compares results across different twist angles and lattice mismatches.

Experimental results

Research questions

• RQ1 How does an applied electric field alter the equilibrium stacking domain structure in moiré superlattices?
• RQ2 What is the role of dielectric screening in modifying the effective stacking energy and domain wall softness?
• RQ3 Can the observed ferroelectric hysteresis in bilayer graphene and hBN be explained by field-dependent domain relaxation?
• RQ4 What is the critical electric field at which stacking domains become unstable or collapse?
• RQ5 How does the domain wall width depend on the twist angle and applied field in 2D heterostructures?

Key findings

• An external electric field induces asymmetric relaxation of stacking domains due to coupling with spontaneous polarization, leading to a net macroscopic polarization.
• The dielectric response reduces the effective stacking energy, softening the domain walls and making them more susceptible to field-induced reconfiguration.
• The domain wall width increases with decreasing electric field and diverges at a critical field E_w^crit ≈ 2.47 V/Å for MoS2, independent of lattice mismatch.
• The model predicts a critical field E_AB^crit ≈ 2.37 V/Å for bilayer breakdown, slightly below E_w^crit, indicating a regime where domain structure becomes unstable.
• Numerical and analytical solutions of the 1D FK model confirm that domain wall width scales as w ∝ 1 / sqrt( E^2 - E_w^crit^2 ) near the critical field.
• The model explains the observed field- and twist-angle-dependent hysteresis in recent experiments on bilayer graphene and hBN as a consequence of field-tunable domain dynamics.