Flat bands in ultra-wide gap two-dimensional germanium dioxide

TL;DR

This work reveals that free-standing 2D GeO$_2$ monolayers host ultra-wide band gaps and strong excitonic effects, underpinned by nearly flat O-$p$ valence bands that remain tunable via strain and buckling. By combining DFT (PBE and HSE06) with a tight-binding MLWF framework and solving the Bethe–Salpeter equation, the authors map the electronic structure across eight polymorphs, identify indirect exciton ground states, and quantify large exciton binding energies. They additionally assess dynamical stability with phonons and AIMD, showing most phases are stable under moderate conditions or when supported by substrates, and they analyze optical response and anisotropy, including substrate effects. The findings suggest 2D GeO$_2$ as a versatile UWBG platform for high-power, deep-UV optoelectronics and exploration of correlation effects, with flat-band engineering offering a route to design materials with ultra-large electronic gaps in 2D oxide systems.

Abstract

We employ first principles density-functional theory (DFT) and the Bethe-Salpeter equation (BSE) in the framework of tight-binding based maximally localized Wannier functions (MLWF-TB) model to investigate the electronic and optical properties of free-standing two-dimensional (2D) germanium dioxide phases. All investigated 2D GeO2 polymorphs exhibit ultra-wide band gaps and strong excitonic effects, with flat O-p-derived valence bands tunable under strain. These features allow the design of flat band materials with ultra large electronic gaps in low-dimensional systems, making these materials promising for devices operation at higher voltages and temperatures than conventional semiconductor materials.

Figures (20)

• Figure 1: Ball-and-stick representations of the optimized geometries of germanium dioxide layers within DFT-GGA for a) P-3m1, b) P6/mmm, c) Pbcm, d) Pmma, e) P4m2(1), f) P4m2(2), g) Pmmm(1) and h) Pmmm(2) phases. Red (gray) spheres represent oxygen (germanium) atoms. The unit cells are shown in dashed lines.
• Figure 2: Phonon dispersion curves for germanium dioxide layers: a) P-3m1, b) P6/mmm, c) Pbcm, d) Pmma, e) P4m2(1), f) P4m2(2), g) Pmmm(1) and h) Pmmm(2).
• Figure 3: AIMD calculations at 300K for a) P-3m1, b) P6/mmm, c) Pbcm, d) Pmma, e) P4m2(1), f) P4m2(2), g) Pmmm(1) and h ) Pmmm(2). The snapshots at 10 ps simulation time are shown.
• Figure 4: Orbital projected band structure of germanium dioxide layers. a) P-3m1, b) P6/mmm, c) Pbcm, d) Pmma, e) P4m2(1), f) P4m2(2), g) Pmmm(1) and h) Pmmm(2). The Fermi levels are set as zero.
• Figure 5: Three-dimensional electronic band structures for 2D germanium oxide phases: a) P-3m1, b) P6/mmm, c) Pbcm, d) Pmma, e) P4m2(1), f) P4m2(2), g) Pmmm(1) and h) Pmmm(2). The highest valence band (red) and the lowest conduction band (yellow) are shown.