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Calculate Electronic Band Structure with GW Approximation and Plasmon-Pole Approach

This tutorial explains how to calculate the electronic band structure of a hexagonal boron nitride (BN) monolayer 1 using the GW Approximation with the Godby–Needs plasmon-pole model and Quantum ESPRESSO.

Quantum ESPRESSO version

This tutorial applies to Quantum ESPRESSO version 6.3 and later.

The plasmon-pole approach 2 samples only at zero frequency and uses the Godby–Needs model along the imaginary axis. The method is enabled via the SternheimerGW code. The full-frequency integration tutorial provides a more complete introduction to GW workflows. Only plasmon-pole-specific aspects are covered below.

1. Understand the plasmon-pole workflow

Expand to view detailed input parameters

The plasmon-pole-specific components of the SternheimerGW input file include:

Truncation: For isotropic systems, a spherical truncation is used by default. For films and other anisotropic systems (such as the BN monolayer), "2d" truncation is recommended. The Wigner-Seitz (ws) truncation is more general but computationally expensive for larger systems.

Linear solver configuration: The thres_coul and thres_green values control solver accuracy. The max_iter_coul and max_iter_green values set iteration limits — if exceeded, a different solver is tried automatically.

Plasmon-pole frequencies: When using the Godby–Needs model, exactly two frequencies must be specified:

\[ \omega_1 = 0 \qquad \omega_2 = \text{i} \omega_\text{p} \]

These are used to construct an approximation of the screened Coulomb interaction.

2. Create and submit the job

Follow the instructions in the full-frequency GW tutorial for creating and executing the GW workflow job and inspecting results.

For this 2D material, the z-dimension of the k-grids and q-grid is set to 1. The recommended settings are: plane-wave cutoff of 80 Ry, k-grid of 8 × 8 × 1, and q-grid of 4 × 4 × 1.

3. Examine the results

The indirect band gap of the BN monolayer is ~6.460 eV, between the Γ and M Brillouin Zone special points. This result is in good agreement with other first-principles calculations 3.

4. Video walkthrough

The animation below demonstrates the creation and execution of a GW band structure computation on a BN monolayer using Quantum ESPRESSO with the plasmon-pole model.

  1. Wikipedia Boron nitride nanosheet ↩

  2. J. Lischner, S. Sharifzadeh, J. Deslippe, J.B. Neaton, and S.G. Louie: "Effects of self-consistency and plasmon-pole models on GW calculations for closed-shell molecules"; Phys. Rev. B 90, 115130 (2014) ↩

  3. D. Wickramaratne, L. Weston, and C.G. Van de Walle: "Monolayer to Bulk Properties of Hexagonal Boron Nitride"; J. Phys. Chem. C, 2018, 122 (44), pp 25524–25529 ↩