A computational study suggests that the atomic structure at a Na3Bi crystal's surface is associated with a different pattern of unusual surface electronic states. In the stoichiometric, charge-compensated model, both terminations carried connected surface Fermi arcs. In the non-stoichiometric, charge-uncompensated model, the calculated pattern instead combined an arc on the top surface with closed loops on the bottom surface.
The study examines whether realistic Na3Bi (100) models retain double surface Fermi arcs or whether changes in the modeled bulk and surface conditions reshape them. Here, the terms arcs and loops describe the shape and connection of calculated surface-state features: one model kept arcs on both surfaces, while the other produced different global connections on the two surfaces.
The work is an arXiv preprint dated 20 August 2026, not an experimental report. Its conclusions apply to the particular slab constructions and calculation settings used in the analysis.
Two surface constructions
The researchers compared two first-principles-derived tight-binding models of finite Na3Bi (100) slabs. One represented a stoichiometric, charge-compensated surface, labeled CC. The other represented a non-stoichiometric, charge-uncompensated surface, labeled CU. The modeled atomic termination—the surface structure used in each slab—was the main feature being compared, while slab thickness and chemical potential were also varied computationally.
The computational framework used QE calculations and PAOFLOW to construct the tight-binding model. The resulting bands were compared with density-functional-theory bands. The two descriptions agreed over the low-energy window extending 1 electron-volt above and below the Fermi level, while disagreements appeared beyond that range.
The main analysis used slabs 60 layers thick after the researchers compared different thicknesses. In the CC structure, calculated cusps sharpened as the slab grew, but there was very little change between 40 and 60 layers. The authors therefore treated the 60-layer structures as sufficiently converged for the analyses that followed, although they did not report a numerical convergence threshold.
Arcs on both surfaces, or loops on one
For the CC structure, the analysis found double surface Fermi arcs from both terminations, without momentum separation between the arcs. Near the projected Dirac point, the CC states were strongly hybridized with the bulk. In ordinary terms, the calculated states showed substantial mixing between surface-associated and bulk-associated behavior, and the authors judged that the study's criteria for spin suppression were satisfied.
The authors did not expect the suppression to be exact or to change in a strictly monotonic way in a finite slab. The reported interpretation is therefore tied to the modeled states near the projected Dirac point and to the criteria used in that calculation.
The CC calculation also showed a quantum spin Hall effect signature in selected states on opposite surfaces. Their spin directions were opposite and equal in magnitude in the reported comparison, a pattern the authors used to support that signature within the model.
The CU structure produced a more complicated surface picture. Its top surface retained an arc, while the bottom surface showed closed loops. The inner loop touched one projected Dirac point, and the outer loop encircled both projected Dirac points. The study therefore distinguished the loops' global shape from the connected double-arc pattern found in the CC structure.
The CU inner-loop states nevertheless showed local behavior associated with an arc. They became more delocalized as they approached a Dirac point, while their spin-expectation magnitude decreased. The authors considered those changes consistent with local arc-like behavior even though the full feature was a closed loop.
The CU model also retained a quantum spin Hall signature. Bands associated with opposite surfaces had opposing velocities and opposing spin polarizations, but their spin magnitudes were unequal. The calculation thus linked opposite surface-state directions with opposite spin behavior without showing identical polarization strength on the two surfaces.
A result about modeled surfaces
Taken together, the comparison points to a difference between local and global behavior. Near the Dirac points, the calculated states continued to show features associated with bulk-surface hybridization, spin suppression and spin-momentum locking—the relationship between a state's motion and its spin polarization—while the overall connection of the surface features differed between the two terminations. The authors suggest that termination choice could be explored as a way to tune these modeled surface states.
The calculation does not establish that every realistic Na3Bi (100) surface will display the reported arcs or loops. It also does not show that the modeled states would be experimentally realized under self-consistent surface-charge conditions, or that changing the termination would improve transport or spintronic-device performance. The supplied analysis reports no statistical uncertainty or experimental validation.
The models were truncated at the surface without modified surface parameters and omitted charge effects such as the Coulomb potential associated with a surface dipole. The Fermi level was pinned to the bulk value, and the analysis assumed that surface charges would not materially change the band structure. The authors also could not carry out sufficiently large density-functional-theory calculations to obtain accurate surface tight-binding parameters.
The analysis was restricted to two explicit termination models. Further work would need to test whether self-consistent surface charge and surface-dipole potentials change the reported connectivity, whether explicitly fitted surface parameters preserve the loops and spin-momentum-locking behavior, and how additional realistic reconstructions alter the calculated arcs and loops. The transport consequences of the different surface-state directions also remain to be quantified.
Questions left open
The authors present the comparison as a basis for further modeling of surface effects and charge self-consistency beyond the two slab constructions. Experimental or larger-scale computational validation would be needed to test whether the termination-dependent arc and loop connectivity survives under more complete surface conditions.
The paper acknowledges funding from the Illinois Physics department and computing resources from the Illinois Campus Cluster Program. It states that associated data are available under reasonable request; code availability and conflicts of interest were not reported in the supplied analysis.
Paper data and sources
Original title: Effects of the surface on double surface Fermi arcs in a realistic tight-binding model of Na$_3$Bi (100)
Authors: Vasilios K. Passias, Lucas K. Wagner
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text