[Paper Review] Electronic spectral properties of incommensurate twisted trilayer graphene

Bruno Amorim, Eduardo V. Castro|arXiv (Cornell University)|Jul 31, 2018

Graphene research and applications6 citations

TL;DR

This paper develops a momentum-space tight-binding formalism to model electronic spectral properties in incommensurate twisted trilayer graphene (tTLG), accounting for interlayer coupling beyond pairwise hybridization. The method enables accurate simulation of ARPES, total and local density of states, revealing that three-layer coupling induces significant spectral reconstruction, including repelled van Hove singularities and moiré-patterned local density modulations not captured by bilayer approximations.

ABSTRACT

Multilayered van der Waals structures often lack periodicity, which difficults their modeling. Building on previous work for bilayers, we develop a tight-binding based, momentum space formalism capable of describing incommensurate multilayered van der Waals structures for arbitrary lattice mismatch and/or misalignment between different layers. We demonstrate how the developed formalism can be used to model angle-resolved photoemission spectroscopy measurements, and scanning tunnelling spectroscopy which can probe the local and total density of states. The general method is then applied to incommensurate twisted trilayer graphene structures. It is found that the coupling between the three layers can significantly affect the low energy spectral properties, which cannot be simply attributed to the pairwise hybridization between the layers.

Motivation & Objective

• To address the challenge of modeling incommensurate multilayer van der Waals heterostructures with arbitrary lattice mismatch and misalignment.
• To extend existing momentum-space methods for bilayer systems to trilayer and multilayer configurations.
• To enable accurate computation of measurable spectral quantities such as ARPES intensity, total density of states (TDoS), and local density of states (LDoS).
• To investigate the role of three-layer coupling in shaping low-energy electronic properties in twisted trilayer graphene.
• To demonstrate that trilayer effects cannot be captured by pairwise bilayer approximations, especially in spectral reconstruction and spatial modulation.

Proposed method

• The method expands the electronic wavefunction in Bloch states of individual layers, including generalized umklapp scattering due to competing periodicities.
• It constructs an effective momentum-space Hamiltonian that incorporates interlayer hopping terms between all layers, accounting for arbitrary twist angles and lattice mismatches.
• The formalism computes spectral functions via integrals over the Brillouin zones of the constituent layers, generalizing prior bilayer results.
• ARPES intensity, TDoS, and LDoS are calculated using the eigenstates and eigenenergies of the effective Hamiltonian.
• A numerical mesh of 439,000 k-points around Dirac points is used, with a 20 meV broadening to simulate experimental resolution.
• The approach is validated by comparing computed spectral features with experimental trends in tTLG, particularly at van Hove singularities.

Experimental results

Research questions

• RQ1 How does three-layer coupling in incommensurate twisted trilayer graphene alter the low-energy electronic spectrum beyond pairwise bilayer interactions?
• RQ2 Can the momentum-space formalism accurately describe ARPES and scanning tunneling spectroscopy (STS) measurements in incommensurate multilayer systems?
• RQ3 What spectral signatures emerge from simultaneous three-layer hybridization, particularly in the local density of states?
• RQ4 To what extent do moiré patterns from layer 1–3 and 1–2/2–3 interference coexist and influence the spatial modulation of the local density of states?
• RQ5 Why does the standard bilayer approximation fail to capture the full spectral reconstruction in trilayer systems?

Key findings

• The three-layer coupling leads to a significant spectral reconstruction, with van Hove singularities from different bilayer pairs being repelled due to interlayer hybridization.
• The total density of states (TDoS) computed using the full trilayer model shows a distinct separation between van Hove singularities, unlike the bilayer-approximated TDoS.
• The local density of states (LDoS) exhibits additional moiré modulations due to interference between layers 1 and 3, which are absent in bilayer approximations.
• At ω = -0.106 eV, the LDoS of layer 3 displays a clear modulation with the periodicity of the 1–3 moiré lattice, confirmed by green star markers in the simulation.
• The method reveals that the trilayer system cannot be described as two independent bilayers, as the three-body coupling induces non-additive spectral effects.
• The formalism successfully captures complex spatial and momentum-space spectral features, including interference patterns from multiple layer pairs, essential for interpreting STS and ARPES data.