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arxiv: 2606.10139 · v1 · pith:XFEI2BTRnew · submitted 2026-06-08 · ❄️ cond-mat.mtrl-sci

Predicting Defect States: A Quick Screening Protocol for Substitutional Point Defect Engineering

Hyosik Kang , Lukas Muechler This is my paper

Pith reviewed 2026-06-27 15:31 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords point defectstight-bindingsubstitutional defectsin-gap statesscreening protocolWannier Hamiltoniansdefect engineeringMoS2
0
0 comments X

The pith

A tight-binding protocol predicts the number and character of defect in-gap states by altering only on-site energies in the host Hamiltonian.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents a unit-cell-based tight-binding method to screen substitutional point defects without computing large supercells. It extracts Wannier Hamiltonians from small relaxed cells of the host and a defect proxy, replicates the host Hamiltonian, and models the defect by shifting only the on-site energy at the substitution site while keeping all hopping terms fixed. Validation on transition-metal substitutions in MoS2, carbon substitutions in h-BN, and NV centers in diamond shows that the approach reproduces the count of in-gap states, their degeneracies, and whether they sit shallow or deep relative to the band edges. Absolute energy positions can shift, but the qualitative features hold across two- and three-dimensional hosts.

Core claim

The protocol extracts Wannier tight-binding Hamiltonians from small, fully relaxed unit cells of the host and defect-like systems, replicates the host Hamiltonian to construct a supercell model, and introduces the defect by modifying only the on-site energies at the substitution site while leaving the hopping parameters unchanged. This captures the number of in-gap states, their degeneracies, and their shallow or deep character relative to host band edges in three systems despite quantitative deviations in absolute energies.

What carries the argument

The on-site-energy-only modification inside a replicated host tight-binding Hamiltonian extracted from unit-cell Wannier functions.

If this is right

  • The method enables rapid pre-screening of many substitutional configurations in both 2D and 3D hosts without repeated large-cell relaxations.
  • It identifies the correct degeneracy and relative positioning of defect levels for simple substitutions and for substitution-vacancy complexes.
  • The protocol fails to capture charge redistribution effects that occur for vacancies of highly electronegative atoms or for spin-polarized charge states.
  • Quantitative energy positions may deviate from full calculations while the count and character of states remain reliable.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same on-site shift could be calibrated once per element pair and then reused across many host lattices to map defect trends quickly.
  • Extending the protocol to include a few adjusted hopping terms near the defect site might improve absolute energy accuracy without losing speed.
  • The approach could be combined with high-throughput databases to flag promising defect candidates before any supercell DFT is run.

Load-bearing premise

A substitutional defect can be approximated by changing only the on-site energy at the defect site while leaving all hopping parameters identical to those of the pristine host.

What would settle it

A full supercell calculation on one of the three tested systems that yields a different number of in-gap states or a different shallow-versus-deep assignment than the protocol predicts.

Figures

Figures reproduced from arXiv: 2606.10139 by Hyosik Kang, Lukas Muechler.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic workflow of the unit-cell-based tight [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Band structures of Ce [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Band structures of C [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Band structures of NV [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Band structures of V [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
read the original abstract

Point defects in crystalline materials play a central role in determining electronic, optical, and magnetic properties. However, systematic exploration of defect configurations remains computationally expensive because large supercell calculations are required to approximate isolated defects under periodic boundary conditions. We present a unit-cell-based tight-binding protocol that enables rapid pre-screening of substitutional defects. The protocol extracts Wannier tight-binding Hamiltonians from small, fully relaxed unit cells of the host and defect-like systems, replicates the host Hamiltonian to construct a supercell model, and introduces the defect by modifying only the on-site energies at the substitution site while leaving the hopping parameters unchanged. We validate the protocol across three diverse systems: isostructural substitutional defects in transition-metal dichalcogenides (M$_\mathrm{Mo}$ MoS$_2$, M = Ce, Zr, Nb, Tc, and Ru), symmetry-breaking carbon substitutions in hexagonal boron nitride (C$_\mathrm{B}$C$_\mathrm{N}$ h-BN), and nitrogen-vacancy (NV$^-$) centers in diamond. These case studies span two-dimensional and three-dimensional hosts, simple substitutions, and substitution-vacancy complexes. In all cases, the protocol successfully captures the number of in-gap states, their degeneracies, and their shallow or deep character relative to host band edges, despite some quantitative deviations in absolute energy positions. We further identify limitations for vacancies of highly electronegative atoms and for charge-state or spin-polarization effects, both of which involve self-consistent charge redistribution not captured by the protocol.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript presents a unit-cell-based tight-binding protocol for rapid pre-screening of substitutional point defects. Wannier Hamiltonians are extracted from small relaxed unit cells of the host and a defect-like system; the host Hamiltonian is tiled into a supercell, and the defect is introduced by altering only the on-site energy at the substitution site while leaving all hopping parameters unchanged. Validation on three systems—isostructural substitutions in TMDs (M_Mo MoS2 for M=Ce,Zr,Nb,Tc,Ru), symmetry-breaking C substitutions in h-BN, and NV- centers in diamond—shows that the protocol reproduces the number, degeneracies, and shallow/deep character of in-gap states relative to host band edges, despite quantitative deviations in absolute energies. Limitations are explicitly noted for vacancies of highly electronegative atoms and for charge-redistribution or spin-polarization effects.

Significance. If the central approximation holds, the protocol offers an efficient computational pre-screening tool that reduces the need for large supercell DFT calculations in defect engineering across 2D and 3D materials. The work is strengthened by its explicit identification of failure modes and by testing across chemically and structurally diverse cases. Reproducibility is aided by reliance on standard Wannier-function tools.

major comments (1)
  1. [Abstract and protocol description] Abstract and protocol description (paragraph introducing the modeling choice): The assumption that hopping parameters remain identical to the pristine host when a substitutional defect is introduced solely by shifting on-site energies is introduced as an approximation without derivation from the paper's equations or independent verification (e.g., direct comparison of hopping integrals extracted from host versus defect-like unit cells). This assumption is load-bearing for the central claim of qualitative accuracy on state counts and character, particularly for the TMD and h-BN cases where the substituting atoms differ substantially in size, valence, and electronegativity from the host atoms.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thoughtful review and constructive criticism of our manuscript. We provide a point-by-point response to the major comment below and outline the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract and protocol description] Abstract and protocol description (paragraph introducing the modeling choice): The assumption that hopping parameters remain identical to the pristine host when a substitutional defect is introduced solely by shifting on-site energies is introduced as an approximation without derivation from the paper's equations or independent verification (e.g., direct comparison of hopping integrals extracted from host versus defect-like unit cells). This assumption is load-bearing for the central claim of qualitative accuracy on state counts and character, particularly for the TMD and h-BN cases where the substituting atoms differ substantially in size, valence, and electronegativity from the host atoms.

    Authors: The referee correctly identifies that the protocol relies on the approximation of unchanged hopping parameters, which is introduced to enable the use of small unit-cell calculations for pre-screening without requiring large supercells. This choice is motivated by the desire to isolate the effect of the on-site perturbation while preserving the host's band structure connectivity. Although the manuscript does not derive this from first principles equations, it is presented as a practical approximation whose validity is tested through the case studies. We agree that providing a direct comparison of the hopping integrals would enhance the justification. In the revised version, we will include such a comparison (extracted from the defect-like unit cells versus the host) in a new supplementary section or appendix, focusing on the TMD and h-BN systems to quantify the changes in hopping parameters and discuss their impact on the in-gap states. revision: yes

Circularity Check

0 steps flagged

No significant circularity; protocol is an explicit approximation validated externally

full rationale

The paper defines its screening protocol explicitly as an approximation (extract Wannier Hamiltonians from host and defect-like cells, tile host supercell, modify only on-site energies at substitution site while leaving hoppings unchanged). This modeling choice is stated upfront rather than derived from the paper's own equations. Validation proceeds by direct comparison to expected in-gap state counts, degeneracies, and characters in three independent systems, with acknowledged quantitative deviations and limitations. No self-citation chains, fitted inputs renamed as predictions, or self-definitional reductions appear in the derivation; the central claim rests on the external match to known defect physics rather than reducing to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim depends on one key modeling assumption that is introduced without independent derivation in the abstract.

axioms (1)
  • ad hoc to paper Hopping parameters remain unchanged when a substitutional defect is introduced by modifying only on-site energies
    Explicitly stated as the core of the protocol in the abstract description of the method.

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