Tuning Electronic and Optical Anisotropy in Monolayer GaS via Vertical Electric Fields

Background

Graphene, the archetypal two‑dimensional material, boasts remarkable mechanical and electronic properties that have driven breakthroughs in transistors and electrochemical electrodes [1,2]. However, its zero band gap limits its use in conventional optoelectronic devices, and only modest gaps can be induced via surface functionalization or external fields [3–7]. Consequently, identifying alternative 2D materials with tunable electronic properties remains a priority for both fundamental science and applied technologies.

Recently, the family of gallium chalcogenides GaX (X = S, Se) has emerged as a stable class of 2D materials, attracting significant attention due to their unique physical and chemical characteristics and potential for solar‑energy conversion and optoelectronics [8–11]. A single GaX layer consists of a four‑atom sequence X–Ga–Ga–X with D₃h symmetry, forming covalent bonds within the plane.

Advanced applications demand materials whose electronic behavior can be precisely controlled. Strain engineering has proven effective in tailoring the band structure and loss spectra of GaS monolayers and other 2D systems [12]. Alternatively, applying an external electric field or illumination offers a versatile means to modulate electronic properties over a wide range [13–16]. For instance, a strong perpendicular field induces a sizable band gap in bilayer graphene [15,16], and multilayer BN also exhibits field‑dependent band‑gap tuning [17]. Nonetheless, the influence of a perpendicular field on the electronic structure of monolayer GaS remains unclear. Moreover, monolayer GaS possesses an intrinsic large negative crystal field, leading to pronounced optical anisotropy: the absorption coefficient for E⊥c is ~10³ cm⁻¹, roughly thirty times smaller than for E‖c [18]. Light‑emission polarization is tightly linked to near‑band‑edge transitions between the valence‑band maximum (VBM) and conduction‑band minimum (CBM). By exploiting an external electric field, one can potentially shift the band structure and optical response of GaS to meet diverse device requirements.

Here, we present a theoretical investigation of how a vertical electric field modulates the optical absorption spectra and electronic anisotropy of monolayer GaS. We calculate absorption for both E⊥c and E‖c orientations under a range of field strengths, analyze band structures and orbital contributions to explain the field‑dependent dipole transition, and map partial charge distributions and charge‑density differences. Our findings provide quantitative guidance for engineering tunable electronic and optoelectronic devices based on 2D GaS.

Methods

All calculations were carried out within density‑functional theory (DFT) using the Vienna Ab‑initio Simulation Package (VASP) [19] and the projector‑augmented wave (PAW) method [20]. Exchange–correlation effects were treated with the Perdew–Burke–Ernzerhof (PBE) generalized‑gradient approximation (GGA) [21], while the Heyd‑Scuseria‑Ernzerhof (HSE06) hybrid functional was employed to obtain accurate band‑gap values [22]. A four‑atom slab model (S–Ga–Ga–S) was constructed with a 15 Å vacuum spacing along the out‑of‑plane direction to suppress inter‑slab interactions. Brillouin‑zone sampling used a Monkhorst–Pack k‑point mesh of 27 × 27 × 1 for structural relaxation, with a kinetic‑energy cutoff of 450 eV for the plane‑wave basis. Convergence criteria were set to 10⁻⁵ eV for total energy and 0.01 eV Å⁻¹ for residual forces. Gaussian smearing (width 0.1 eV) handled partial occupancies. The imaginary part of the dielectric tensor, from which the optical absorption was derived, was computed via the Fermi‑golden‑rule approach [24]. Spin‑orbit coupling was omitted because its influence on the electronic and optical properties of GaS is negligible.

Results and Discussion

Figure 1a–b shows the fully relaxed geometry of monolayer GaS. The interlayer spacing is 4.66 Å, and the in‑plane lattice constant is 3.64 Å, slightly expanded relative to the bulk due to the absence of interlayer interactions [25]. The Ga–S and Ga–Ga bond lengths are 2.37 Å and 2.48 Å, respectively, while the S–Ga–S bond angle is 100.34°, in good agreement with previous studies [12]. The upper and lower Ga and S atoms are labeled Y^(1) and Y^(2) (Y = Ga, S).

a Top and b side views of the atomic configuration of GaS ML. The big green and small yellow spheres represent Ga and S atoms, respectively, and the upper and lower interlayer atoms are labeled as Y^(1)(Y = Ga, S) and Y^(2).

To assess the electric‑field effect on optical properties, we computed absorption spectra for transverse‑magnetic (TM, E‖c) and transverse‑electric (TE, E⊥c) polarizations under varying perpendicular fields. Figure 2 illustrates that the TM and TE absorption edges differ markedly, evidencing strong optical anisotropy. Without an external field, the TM and TE edges are separated by ~0.55 eV. Applying a field shifts both edges to lower energies and reduces their separation. At a critical field of ~5 V nm⁻¹, the anisotropy reverses: the TE edge becomes lower than the TM edge, indicating a switch from E‖c to E⊥c dominance (see Fig. 2b–d). Thus, the optical anisotropy of monolayer GaS is tunable by a vertical electric field.

The calculated optical absorption spectra of the GaS ML a without an external electric field and b–d with an external electric field of 4, 5, and 8 V nm⁻¹, respectively. The absorption edge is labeled. Red and green lines represent TM and TE light, respectively.

Figure 3a shows the zero‑field band structure. The CBM lies at Γ, while the VBM sits between Γ and K, confirming an indirect gap. DFT and HSE give gaps of 2.35 eV and 3.46 eV, respectively, consistent with literature [12,26]. Under an external field (Fig. 3b–d), the VBM shifts to Γ once the field exceeds ~5 V nm⁻¹, converting the gap to direct. Simultaneously, the band gap monotonically narrows with increasing field (Fig. 3e), a manifestation of the Stark effect observed in h‑BN [27] and MoS₂ [28]. The field induces a potential difference ΔU = −d E* e between the two Ga–S layers (d is the interlayer distance, E* the screened field), lifting the VBM and reducing the gap.

Band structure of GaS ML a without an external electric field and b–d with an external electric field of 4, 5, and 8 V nm⁻¹, respectively. The dashed lines indicate the Fermi levels, which are set to zero. e Variation of the energy gap with the external electric field for GaS ML.

To elucidate the origin of the anisotropy reversal, we projected the band contributions onto atomic orbitals (Fig. 4). In zero field, the CBM and VBM are primarily composed of Ga s and p_z orbitals and S p_z orbitals, respectively, while the lower valence bands arise from in‑plane S p_x + p_y states. With an 8 V nm⁻¹ field, the upper and lower layers contribute asymmetrically: the CBM is dominated by s and p_z of the upper GaS layer and p_z of the lower layer. The in‑plane p_x + p_y states of the upper and lower layers separate in energy by ~3.05 eV at Γ, reflecting the field‑induced asymmetry. The lower‑energy p_x + p_y of the upper layer surpass the S p_z states, becoming the new VBM and shifting it to Γ. This orbital reordering underlies the transition from E‖c to E⊥c absorption preference.

The decomposed projected band structure of the GaS ML. The top panel represent the s (a), p_x + p_y (b) , and p_z (c) orbits without an external electric field; the middle and last panels present the contributions of s (d, g), p_x + p_y (e, h), and p_z (f, i) orbits from the upper and lower interlayer of GaS with an external electric field of 8 V nm⁻¹, respectively.

Spatial maps of the partial charge at CBM and VBM (Fig. 5a–b) further illustrate the field‑induced changes. At zero field, the CBM is an s‑type spherical distribution localized on S atoms, while the VBM consists of a z‑oriented dumbbell from S p_z. When the field reaches the critical value, the VBM transforms into a dumbbell perpendicular to z, formed by p_x + p_y. According to parity selection rules, transitions between states of the same parity are allowed for in‑plane (xy) polarization, whereas transitions between opposite parities are allowed for out‑of‑plane (z) polarization. Consequently, for fields below 5 V nm⁻¹ the lowest CBM–VBM transition is accessible only to TM (E‖c) light; above 5 V nm⁻¹ it becomes accessible only to TE (E⊥c) light, confirming the anisotropy reversal.

Charge‑density difference plots (Fig. 5c–d) reveal that the applied field redistributes electrons: more charge accumulates on the S atoms while the interlayer Ga–Ga interaction weakens. This asymmetry reduces interlayer coupling and strengthens intralayer Ga–S bonding, creating an effective crystal field that governs the observed optical anisotropy.

Partial density of states of the CBM and VBM of GaS ML without (a) and with (b) an external electric field of 8 V nm⁻¹, respectively. Spatial charge density difference and the vertical section along (1-100) plane of GaS ML without (c) and with (d) an external electric field of 8 V nm⁻¹, respectively. The positive and negative density (contours) are, respectively, shown with yellow (solid lines) and blue (dashed lines) colors, and the contour interval is 0.005 eÅ⁻³.

Conclusions

In summary, first‑principles DFT calculations demonstrate that a perpendicular electric field can reversibly tune both the electronic band structure and optical anisotropy of monolayer GaS. A critical field of ~5 V nm⁻¹ induces an indirect‑to‑direct band‑gap transition, narrows the gap, and flips the dominant dipole transition from E‖c to E⊥c. The underlying mechanism is an electric‑field‑induced asymmetry in the interlayer electronic states, reflected in projected band contributions and charge‑density differences. These findings provide a clear pathway for designing 2D GaS‑based devices with field‑controlled optical and electronic properties.