Electronic Structure and Transport in InSe Nanoribbons: Edge Effects and Hydrogen Passivation

Background

Atomically thin two‑dimensional (2D) materials have revolutionised nanoelectronics because their reduced dimensionality endows unique electronic properties and device potential [1–4]. One‑dimensional (1D) nanoribbons derived from these layers or built atom‑by‑atom further enhance quantum confinement and allow edge functionalisation [5–9]. Edge passivation, for instance with hydrogen, can stabilise dangling bonds and prevent structural reconstruction [16–17].

InSe, a layered metal chalcogenide semiconductor, has recently been exfoliated to a monolayer, revealing extraordinary electron mobility and unique optoelectronic behaviour [24–28]. While extensive theoretical work has examined bulk and monolayer InSe [29–38], the electronic properties of its 1D nanoribbons remain largely unexplored. This work fills that gap by providing first‑principles insights into the role of edge geometry and hydrogenation on InSe nanoribbon transport.

Methods

Three canonical edge terminations of the honeycomb lattice—zigzag (Z), armchair (A), and Klein (K)—are considered. A ribbon is designated by its width number n and the pair of edge types (e.g., n-ZZ, n-AA, n-KK, n-ZK, n-KZ). Hydrogen passivation is represented as n-HZZH, n-HAAH, n-HKKH, n-HZKH, and n-HKZH.

Initial geometries use a Se–In–In–Se quadruple layer (lattice constant 4.05 Å) before full relaxation. Calculations employ the Atomistix Toolkit (ATK) with a local spin density approximation (LSDA‑PZ) functional and a double‑ζ plus polarization (DZP) basis. A 3000 eV plane‑wave cutoff, 1 × 1 × 100 k‑point mesh, and 300 K electronic temperature are used. A 15 Å vacuum layer isolates periodic images.

Transport properties are simulated by partitioning each ribbon into left/right electrodes and a central scattering region. Spin‑dependent current is obtained via the Landauer–Büttiker formula [40–42]:

I_σ(V_b) = (e/h) ∫ T_σ(E,V_b) [f_L(E‑μ_L) – f_R(E‑μ_R)] dE

where σ = ↑, ↓ and the transmission spectrum T_σ is calculated from the retarded Green’s function and electrode couplings.

Results and Discussion

Top and side views of 6‑HZKH (a) and 11‑HAAH (b) InSe nanoribbons. Width number n, width w_z, and lattice constants c_z or c_a are marked.

Unlike graphene, no edge reconstruction occurs in either bare or hydrogen‑passivated InSe ribbons, and all structures are energetically stable.

For bare n-ZZ ribbons, the electronic structure is metallic and magnetic, except for the narrow 2‑ZZ case which becomes semiconducting after reconstruction. Spin‑polarised bands originate from Se p orbitals at the edges, with a net magnetic moment up to 0.71 μ_B per primitive cell (e.g., 4‑ZZ). Hydrogen passivation transforms ribbons with n ≤ 4 into non‑magnetic semiconductors and ribbons with n > 4 into metals. The transition is governed by the energy difference E_d between left and right edge states, which follows an inverse dependence on width: E_d ≈ −0.45 eV + 4 eVÅ/(w_z − 4 Å). This trend mirrors the width‑dependent gaps in zigzag graphene and BN nanoribbons [12–15].

Minimal energy difference E_d between edge states versus n and w_z. Red curve is the fit.

KK and HKKH ribbons show weak width dependence; both remain metallic. The combination of Z and K edges yields mixed band characters and metallic behaviour in both n‑ZK and n‑KZ ribbons.

Band structures and Γ‑point Bloch states of 4‑KK (a), 4‑HKKH (b), 4‑KZ (c), and 4‑ZK (d) nanoribbons.

Armchair ribbons (AA and HAAH) are non‑magnetic semiconductors. Hydrogenation enlarges the band gap. Their gaps exhibit an odd–even oscillation with width, converging to 1.15 eV for wide ribbons. For AA ribbons, gaps are narrower than the monolayer; for HAAH ribbons, gaps are wider. The evolution of Bloch states at the valence band maximum (VBM) and conduction band minimum (CBM) reflects the edge contributions.

Band structures of 4‑ and 5‑AA (a) and 4‑ and 5‑HAAH (b) nanoribbons; gap evolution versus n (c) with Bloch states at VBM and CBM.

The I‑V response of metallic ribbons shows striking NDR and spin polarization. In 4‑ZZ and 4‑KK bare ribbons, a single dominant transport channel (band z₁) leads to a peak‑to‑valley ratio > 10 under 0.5–1.2 V bias. The spatial mismatch between wave functions of adjacent bands suppresses transmission beyond the peak, producing NDR. Spin splitting of band z₀ yields spin‑polarised current in the linear regime. In contrast, the H‑passivated 4‑HKKH ribbon saturates without NDR.

(a) Spin‑up (filled) and spin‑down (empty) I‑V curves for 4‑ZZ, 4‑KK, and 4‑HKKH ribbons. (b) and (c) Corresponding transmission spectra for 4‑ZZ.

Conclusions

Edge chemistry governs the electronic behaviour of InSe nanoribbons. Bare Z and K edges are metallic and magnetic; hydrogenation can drive a semiconductor‑to‑metal transition in Z ribbons as width grows. All Z and K ribbons—bare or H‑passivated—remain metallic except for the narrowest cases. AA and HAAH ribbons are non‑magnetic semiconductors with band gaps that oscillate with width and approach the monolayer value at large widths. Notably, the I‑V characteristics of bare ZZ and KK ribbons display pronounced single‑band NDR and spin‑polarised currents, offering potential for nanoscale electronic and spintronic devices.

Abbreviations

1D

One‑dimensional

2D

Two‑dimensional

A

Armchair

CBM

Conduction band minimum

K

Klein

VBM

Valence band maximum

Z

Zigzag