[Paper Review] Pressure Induced Compression of Flatbands in Twisted Bilayer Graphene

Bheema Lingam Chittari, Nicolas Leconte+2 more|arXiv (Cornell University)|Jul 31, 2018

Graphene research and applicationsMaterials Science3 citations

TL;DR

This paper demonstrates that applying hydrostatic pressure to twisted bilayer graphene (tBLG) compresses the moiré flatband bandwidth, enabling access to magic-angle-like flatbands at larger twist angles (up to ~1.5°) than possible at zero pressure (~1.0°). Using a continuum model Hamiltonian, the authors show that pressures of ~2.5 GPa—achievable via hydraulic press—reduce the moiré period, enhancing the effective Coulomb interaction by ~50% and increasing the elastic energy resisting commensurability strains by a factor of ~2, thereby facilitating the study of correlated electron phases.

ABSTRACT

We investigate the bandwidth compression due to out of plane pressure of the moire flatbands near charge neutrality in twisted bilayer graphene for a continuous range of small rotation angles of up to $\sim2.5^{\circ}$. The flatband bandwidth minima angles are found to grow linearly with interlayer coupling ω and decrease with Fermi velocity. Application of moderate pressure values of up to 2.5 GPa achievable through a hydraulic press should allow accessing a flatband for angles as large as $\sim 1.5$^{\circ}$ instead of $\sim 1 \circ$ at zero pressure. This reduction of the moiré pattern length for larger twist angle implies an increase of the effective Coulomb interaction scale per moire cell by about 50% and enhance roughly by a factor of $\sim 2$ the elastic energy that resists the commensuration strains due to the moire pattern. Our results suggest that application of pressure on twisted bilayer graphene nanodevices through a hydraulic press will notably facilitate the device preparation efforts required for exploring the ordered phases near magic angle flatbands.

Motivation & Objective

• To investigate how external pressure affects the bandwidth of moiré flatbands in twisted bilayer graphene near charge neutrality.
• To identify a pressure-tunable pathway to achieve flatbands at larger twist angles than the conventional ~1° magic angle.
• To quantify the enhancement of effective Coulomb interaction and elastic energy resistance due to pressure-induced reduction in moiré period.
• To provide a roadmap for experimental device fabrication by showing that pressure can relax the stringent twist angle control required for flatband formation.

Proposed method

• The study employs a continuum model Hamiltonian for tBLG, incorporating valley-K Dirac fermions, interlayer tunneling, and stacking-dependent potentials.
• The Hamiltonian includes a phase-shifted momentum operator to account for layer rotation and is solved within the first harmonic approximation of the moiré potential.
• Bandwidths are calculated as a function of twist angle, Fermi velocity, and interlayer coupling strength ω, with pressure effects modeled through changes in interlayer tunneling and lattice spacing.
• The effective Coulomb interaction scale is derived as U_eff ∝ θ, reflecting the inverse dependence on moiré length ℓ_M ∝ 1/θ.
• The analysis uses the Murnaghan equation of state and ab initio-derived bulk moduli to model pressure response in different stacking configurations.
• Density of states (DOS) and local DOS are computed to assess the impact of pressure and twist angle on flatband width and coherence.

Experimental results

Research questions

• RQ1 Can hydrostatic pressure be used to achieve flatband bandwidth minima at larger twist angles than the conventional ~1° magic angle?
• RQ2 How does pressure affect the effective Coulomb interaction strength in the moiré unit cell?
• RQ3 To what extent does pressure enhance the elastic energy that resists commensurability strains in the moiré superlattice?
• RQ4 What is the quantitative relationship between pressure, interlayer coupling ω, and the magic angle for bandwidth minimization?

Key findings

• Applying pressures up to ~2.5 GPa via a hydraulic press enables access to flatbands at twist angles as large as ~1.5°, compared to ~1.0° at zero pressure.
• The flatband bandwidth minima angles increase linearly with interlayer coupling ω and decrease with Fermi velocity, as predicted by the model.
• The effective Coulomb interaction scale increases by approximately 50% when the twist angle increases from ~1.0° to ~1.5° due to the reduced moiré period.
• The elastic energy resisting commensurability strains increases by a factor of approximately 2 due to the shorter moiré lattice constant under pressure.
• The bandwidth minimum condition is described by a single line equation relating twist angle, ω, and Fermi velocity, enabling systematic tuning of flatband properties.
• The results suggest that pressure application can significantly reduce the experimental difficulty of achieving flatbands in tBLG devices, especially for angles beyond the narrow ~1° window.