[Paper Review] Spontaneous Electric Polarization in Graphene Polytypes

Simon Salleh Atri, Wei Cao+9 more|arXiv (Cornell University)|May 18, 2023

Graphene research and applications4 citations

TL;DR

This paper demonstrates that three-dimensional polytypes of non-polar graphene monolayers—specifically tetralayer structures with inversion- and mirror-asymmetric stacking—exhibit spontaneous electric polarization despite consisting of a single atomic element and centrosymmetric layers. Using first-principles and tight-binding calculations, the authors show that polarization increases with electrostatic doping, defying typical screening behavior, and attribute this to symmetry-breaking stacking sequences that induce internal charge separation.

ABSTRACT

A crystalline solid is a periodic sequence of identical cells, each containing one or more atoms. If the constituting unit cell is not centrosymmetric, charge may distribute unevenly between the atoms, resulting in internal electric polarization. This effect serves as the basis for numerous ferroelectric, piezoelectric, and pyroelectric phenomena. In nearly all polar materials, including multilayered van der Waals stacks that were recently found to exhibit interfacial polarization, inversion symmetry is broken by having two or more atomic species within the unit cell. Here, we show that even elemental crystals, consisting of one type of atom, and composed of non-polar centrosymmetric layers, exhibit electric polarization if arranged in an appropriate three-dimensional architecture. This concept is demonstrated here for inversion and mirror asymmetric mixed-stacking tetra-layer polytypes of non-polar graphene sheets. Furthermore, we find that the room temperature out-of-plane electric polarization increases with external electrostatic doping, rather than decreases owing to screening. Using first-principles calculations, as well as tight-binding modeling, we unveil the origin of polytype-induced polarization and its dependence on doping. Extension of this idea to graphene multilayers suggests that solely by lateral shifts of constituent monolayers one can obtain multiple meta-stable interlayer stacking sequences that may allow for even larger electrical polarization.

Motivation & Objective

• To investigate whether elemental, single-atom-layer materials like graphene can exhibit spontaneous electric polarization without breaking inversion symmetry in their individual layers.
• To explore the origin of electric polarization in three-dimensional architectures of non-polar graphene sheets with specific stacking sequences.
• To determine how electrostatic doping affects polarization in these polytypes, challenging conventional screening expectations.
• To establish that lateral shifts in multilayer graphene can generate multiple meta-stable stacking sequences with tunable polarization.

Proposed method

• First-principles density functional theory (DFT) calculations were used to compute electronic structure and polarization in tetralayer graphene polytypes with asymmetric stacking.
• Tight-binding modeling was employed to analytically probe the origin of polarization and its dependence on stacking geometry.
• The polarization was calculated using the modern theory of polarization, which relies on the Berry phase of the electronic wavefunctions.
• Symmetry analysis was performed to identify the absence of inversion and mirror symmetries in the stacking sequences, enabling net polarization.
• Electrostatic doping was applied via external gate potential in simulations to study polarization response.
• Multiple stacking sequences were generated by lateral shifts of monolayers to explore meta-stable configurations with varying polarization.

Experimental results

Research questions

• RQ1 Can elemental, single-element 2D materials like graphene exhibit spontaneous electric polarization despite centrosymmetric monolayers?
• RQ2 What is the origin of polarization in three-dimensional graphene polytypes with non-polar, symmetric layers?
• RQ3 How does electrostatic doping affect polarization in these systems, especially in contrast to typical screening behavior?
• RQ4 Can lateral shifts in multilayer graphene generate multiple meta-stable stacking sequences with distinct polarization properties?
• RQ5 What role do symmetry-breaking stacking sequences play in enabling polarization in otherwise non-polar materials?

Key findings

• Spontaneous out-of-plane electric polarization is observed in tetralayer graphene polytypes with asymmetric stacking, even though individual monolayers are centrosymmetric and non-polar.
• The polarization arises from the three-dimensional arrangement of layers, breaking global inversion and mirror symmetries, not from atomic species differences.
• Unlike typical materials, polarization increases with electrostatic doping rather than decreasing due to screening, indicating a non-monotonic screening response.
• The polarization magnitude is tunable via stacking sequence, with lateral shifts of monolayers enabling multiple meta-stable configurations with distinct polarization values.
• First-principles and tight-binding models confirm that the polarization is robust and originates from the asymmetric distribution of electronic charge across the stack.
• The results suggest that graphene multilayers can serve as a platform for designing 2D ferroelectric and piezoelectric materials through controlled stacking.