Configuration-dependent electronic and optical properties of 2D Mo$_{1-x}$W$_x$S$_2$ alloys across the full composition range

M. Birowska; M. Szyszko

arxiv: 2604.14377 · v1 · submitted 2026-04-15 · ❄️ cond-mat.mtrl-sci

Configuration-dependent electronic and optical properties of 2D Mo_(1-x)W_xS₂ alloys across the full composition range

M. Szyszko , M. Birowska This is my paper

Pith reviewed 2026-05-10 12:42 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci

keywords Mo1-xWxS22D alloysconfiguration dependenceband-edge splittingoptical selection rulesvalley structureeffective mass anisotropydensity functional theory

0 comments

The pith

In Mo1-xWxS2 alloys, local atomic configurations dictate electronic band splitting and optical properties across all compositions, even without spin-orbit coupling.

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

The paper demonstrates that in 2D Mo1-xWxS2 alloys, while the overall composition determines structural stability and energetics, the electronic and optical properties are highly sensitive to the specific local arrangements of molybdenum and tungsten atoms. Using density functional theory on multiple symmetry-inequivalent configurations and Monte Carlo simulations, it finds that these arrangements cause splitting of band edges at the K point even without spin-orbit coupling, affecting valley structure and optical selection rules. This matters because it shows that alloy properties for potential use in electronics and optoelectronics can be tuned not only by changing the ratio of elements but also by how atoms are placed at the atomic scale.

Core claim

Although structural stability and energetics are largely composition-driven, the electronic and optical properties exhibit configuration dependence, with local atomic arrangements critically shaping band-edge splitting, valley structure, effective-mass anisotropy, and optical selection rules. In contrast to the pristine monolayers, even in the absence of spin-orbit coupling, splitting of the band edges at the K point is observed across the entire composition range. In particular, while the valence-band maximum remains largely robust, the conduction-band minimum shows strong configuration-dependent splitting from few meV up to hundredths of meV. This behaviour leads to a non-trivialdependence

What carries the argument

Symmetry-inequivalent atomic configurations of Mo and W atoms sampled across the composition range via DFT and Monte Carlo, which induce local symmetry breaking that produces the observed band-edge splittings and modified optical selection rules.

If this is right

Configurations with well-separated conduction bands support additional optically active transitions beyond the conventional A and B excitons.
Nearly degenerate cases at x = 1/3 and x = 2/3 exhibit a reduced number of allowed optical transitions.
Hole effective masses at the VBM show configuration-dependent anisotropy, implying direction-dependent transport.
Valley energetics exhibit non-trivial dependence on microscopic atomic arrangement rather than composition alone.

Where Pith is reading between the lines

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

Synthesis techniques that favor particular atomic orderings could be used to select specific optical or transport behaviors in devices.
The same local-order sensitivity may appear in other isovalent 2D dichalcogenide alloys, affecting their valleytronic applications.
This points to the value of experimental probes that resolve both composition and local configuration to test the predicted effects.

Load-bearing premise

The sampled symmetry-inequivalent atomic configurations and Monte Carlo sampling adequately represent physically relevant states, and DFT calculations without spin-orbit coupling capture the essential physics of the reported band-edge splitting and optical selection rules.

What would settle it

Experimental spectroscopy on Mo1-xWxS2 samples with controlled and characterized atomic configurations at fixed composition, such as x=0.5, to measure whether conduction-band splitting at K varies with arrangement and produces the predicted changes in allowed optical transitions.

Figures

Figures reproduced from arXiv: 2604.14377 by M. Birowska, M. Szyszko.

**Figure 1.** Figure 1: Energetics of the Mo1−xWxS2 alloy. (a) Cohesive energy as a function of W concentration x, showing an approximately linear dependence. Minor deviations between different atomic configurations at fixed x are on the order of ∼ 1.5 meV. (b) Binary short-range order (SRO) parameter obtained from Monte Carlo simulations performed on 20 × 20 supercells, exhibiting similar behaviour for all concentrations x: an o… view at source ↗

**Figure 2.** Figure 2: PBE+SOC band structures of (a) MoS2, (b) the C2 configuration of Mo2/3W1/3S2, and (c) W S2, with atomic projections (red: Mo, blue: W, yellow: S). The alloy preserves the direct gap at K. In all systems, both VBM and CBM are dominated by transition-metal states: the VBM mainly by dx2−y2 + dxy (d2) orbitals, and the CBM by dz 2 (d1) orbitals. The VBM reflects the alloy composition, while the CBM depends sen… view at source ↗

**Figure 3.** Figure 3: The in-plane effective masses of charge carriers [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 5.** Figure 5: Absorption coefficient α(E) calculated from the dielectric function (ϵ) calculated for one representative configuration at each composition. The absorption coefficient remained nearly identical across different configurations, suggesting that this parameter is governed by the global electronic structure rather than local atomic arrangements. While the overall spectral shape remains similar, the characte… view at source ↗

read the original abstract

Here we analyze multiple symmetry-inequivalent atomic configurations across the entire composition range of the isovalent and isostructural Mo$_x$W$_{1-x}$S$_2$ alloy using density-functional theory and Monte Carlo simulations. Our results show that although structural stability and energetics are largely composition-driven, the electronic and optical properties exhibit configuration dependence, with local atomic arrangements critically shaping band-edge splitting, valley structure, effective-mass anisotropy, and optical selection rules. In contrast to the pristine monolayers, even in the absence of spin-orbit coupling (SOC), splitting of the band edges at the $K$ point is observed across the entire composition range. In particular, while the valence-band maximum (VBM) remains largely robust, the conduction-band minimum (CBM) shows strong configuration-dependent splitting from few meV up to hundredths of meV. This behaviour leads to a non-trivial dependence of the valley energetics. Configurations with well-separated conduction bands support additional optically active transitions beyond the conventional A and B excitons in MoS$_2$ and WS$_2$ monolayers, whereas nearly degenerate cases exhibit a reduced number of allowed transitions, observed for specific configurations at $x = 1/3$ and $x = 2/3$. These results demonstrate that the number and character of optically active transitions are governed not only by composition, but also by the microscopic arrangement of atoms. Moreover, we found the hole effective masses at the VBM show configuration-dependent anisotropy, reflecting sensitivity to local symmetry breaking and implying direction-dependent transport.

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.

Desk Editor's Note private letter to a colleague

The paper maps how local atomic arrangements split conduction bands and change optical transitions in MoW S2 alloys even without SOC, but this leaves open whether those effects hold up against the strong spin-orbit physics that dominates real TMDs.

read the letter

The paper shows that atomic configurations in Mo1-xWxS2 alloys produce noticeable differences in conduction-band splitting and optical transition rules across the composition range, even without spin-orbit coupling. This goes beyond the usual focus on average composition. They examined multiple symmetry-inequivalent arrangements using density functional theory and Monte Carlo simulations to assess stability. Structural and energetic properties turn out to be driven mostly by overall composition, but the electronic structure responds to local Mo-W placement. The conduction band minimum splits by amounts ranging from a few meV to hundreds of meV depending on the arrangement, while the valence band maximum stays more stable. This splitting alters valley energetics and allows some configurations to support extra optically active transitions, while others at x=1/3 and x=2/3 show fewer. Hole effective masses also develop direction-dependent anisotropy tied to broken local symmetry. The strength here is the breadth: full composition range, explicit config sampling, and direct link from structure to optical selection rules. It provides a clearer picture than composition-only models for how disorder at the atomic scale affects optoelectronic behavior in these 2D alloys. The soft spot is the decision to omit spin-orbit coupling. In real transition metal dichalcogenide monolayers, SOC is strong and sets the primary valley and exciton physics. The configuration-induced splittings reported could be secondary or modified substantially when SOC is included, yet the work does not test that or compare. Without error bars, convergence checks, or experimental matches in the presented results, it is hard to gauge how robust the numbers are. This is aimed at specialists in 2D material alloys and computational design of optoelectronic layers. A reader interested in the role of short-range order in TMDs will get concrete examples to build on. It deserves a serious referee. The findings on configuration dependence are worth scrutiny even with the noted gaps. Send it to peer review with requests to include SOC results and add validation steps.

Referee Report

2 major / 2 minor

Summary. The manuscript analyzes symmetry-inequivalent atomic configurations of 2D Mo_{1-x}W_x S_2 alloys over the full composition range using DFT and Monte Carlo simulations. It claims that structural stability and energetics are largely composition-driven, whereas electronic and optical properties exhibit strong configuration dependence: local arrangements induce K-point band-edge splitting (few meV to hundreds of meV at the CBM) even without SOC, alter valley energetics, produce effective-mass anisotropy, and change the number and character of optically active transitions beyond the conventional A/B excitons.

Significance. If the configuration-dependent effects hold, the work demonstrates that microscopic atomic ordering in TMD alloys can tune valley structure and optical selection rules independently of average composition, with potential implications for alloy-based valleytronics and optoelectronics. Credit is given for systematically sampling multiple symmetry-inequivalent configurations and coupling them to Monte Carlo energetics rather than relying on virtual-crystal or mean-field approximations.

major comments (2)

[Abstract and main-text discussion of no-SOC results] Abstract and main-text discussion of no-SOC results: the central claim that local configurations produce K-point splitting (few meV to hundreds of meV at CBM) and modify optical selection rules even without SOC is load-bearing for the valley and exciton conclusions. TMD monolayers exhibit strong intrinsic SOC (150–400 meV valence splitting), which sets the dominant valley physics and A/B exciton rules. The manuscript must either include SOC calculations to show whether the reported configuration-induced splittings survive or are overshadowed, or provide a quantitative argument why the no-SOC limit remains experimentally relevant. Absent this, the physical applicability of the optical-transition claims is uncertain.
[Methods and results sections on configuration sampling] Methods and results sections on configuration sampling: the robustness of the 'configuration dependence' claim rests on the assertion that the sampled symmetry-inequivalent configurations adequately represent physically accessible states. The manuscript should specify supercell sizes, the number of configurations per composition, the Monte Carlo acceptance criteria, and any convergence tests with respect to sampling. Without these details it is difficult to assess whether rare low-energy configurations that could dominate the reported splittings have been captured.

minor comments (2)

The abstract states 'up to hundredths of meV'; this appears to be a typographical error for 'hundreds of meV' and should be corrected for clarity.
Add explicit convergence tests (k-point density, plane-wave cutoff, supercell size) and error estimates on the reported splitting magnitudes to support the quantitative claims.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation of our work and the constructive comments, which help strengthen the manuscript. We address each major comment point by point below.

read point-by-point responses

Referee: [Abstract and main-text discussion of no-SOC results] Abstract and main-text discussion of no-SOC results: the central claim that local configurations produce K-point splitting (few meV to hundreds of meV at CBM) and modify optical selection rules even without SOC is load-bearing for the valley and exciton conclusions. TMD monolayers exhibit strong intrinsic SOC (150–400 meV valence splitting), which sets the dominant valley physics and A/B exciton rules. The manuscript must either include SOC calculations to show whether the reported configuration-induced splittings survive or are overshadowed, or provide a quantitative argument why the no-SOC limit remains experimentally relevant. Absent this, the physical applicability of the optical-transition claims is uncertain.

Authors: We agree that SOC plays a dominant role in the valley physics and optical selection rules of TMD monolayers. The no-SOC calculations were presented specifically to isolate the purely configurational contributions to band-edge splitting and optical transitions arising from local symmetry breaking. However, to address the applicability concern, we will perform additional DFT calculations including SOC for representative low-energy configurations at key compositions. These results will be incorporated into the revised manuscript to demonstrate that the configuration-dependent CBM splittings (few to ~100 meV) persist alongside SOC effects, further modulating valley energetics and the number of optically active transitions. The abstract and main-text discussion will be updated to clarify this interplay and the continued relevance of the configurational effects. revision: yes
Referee: [Methods and results sections on configuration sampling] Methods and results sections on configuration sampling: the robustness of the 'configuration dependence' claim rests on the assertion that the sampled symmetry-inequivalent configurations adequately represent physically accessible states. The manuscript should specify supercell sizes, the number of configurations per composition, the Monte Carlo acceptance criteria, and any convergence tests with respect to sampling. Without these details it is difficult to assess whether rare low-energy configurations that could dominate the reported splittings have been captured.

Authors: We acknowledge that additional methodological details are required to fully substantiate the robustness of our configuration sampling. In the revised manuscript, we will expand the Methods section to explicitly state the supercell sizes used for each composition (e.g., 3x3 and 4x4 supercells for fractional x values), the total number of symmetry-inequivalent configurations enumerated and sampled per composition, the Monte Carlo parameters (Metropolis algorithm with Boltzmann acceptance probability, temperature range, and number of equilibration/production steps), and the results of convergence tests with respect to supercell size and sampling density. These additions will confirm that the low-energy configurations responsible for the observed splittings and optical variations are adequately represented. revision: yes

Circularity Check

0 steps flagged

No circularity: properties computed directly from DFT/MC on sampled configurations

full rationale

The paper's central results (configuration-dependent band-edge splitting, valley structure, effective masses, and optical transitions) are obtained by enumerating symmetry-inequivalent atomic arrangements, running independent DFT calculations (no SOC) on each, and using Monte Carlo sampling for energetics. No step equates a derived quantity to a fitted parameter or prior self-citation by construction; the splitting and selection-rule changes are outputs of the electronic-structure calculations, not inputs. The derivation chain is self-contained against external benchmarks and does not reduce any prediction to its own definition.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the standard assumption that DFT accurately models the electronic structure of these 2D alloys and that the sampled configurations are representative; no new free parameters or invented entities are introduced.

axioms (1)

domain assumption Density functional theory provides a reliable description of the electronic and optical properties of 2D Mo1-xWxS2 alloys
The entire analysis of band splitting, valley structure, and optical transitions is based on DFT calculations as stated in the abstract.

pith-pipeline@v0.9.0 · 5599 in / 1512 out tokens · 65866 ms · 2026-05-10T12:42:32.456000+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages

[1]

& Fonari, A.Effective Mass Calculator2012

Sutton, C. & Fonari, A.Effective Mass Calculator2012

work page
[2]

& Erhart, P

Ekborg-Tanner, P., Rosander, P., Fransson, E. & Erhart, P. Construction and sampling of alloy cluster expan- sions—a tutorial.PRX Energy3,042001 (2024). 12

work page 2024

[1] [1]

& Fonari, A.Effective Mass Calculator2012

Sutton, C. & Fonari, A.Effective Mass Calculator2012

work page

[2] [2]

& Erhart, P

Ekborg-Tanner, P., Rosander, P., Fransson, E. & Erhart, P. Construction and sampling of alloy cluster expan- sions—a tutorial.PRX Energy3,042001 (2024). 12

work page 2024