Persistence of Layer-Tolerant Defect Levels in ReS2
Pith reviewed 2026-05-18 05:17 UTC · model grok-4.3
The pith
Defect charge transition levels in ReS2 remain nearly unchanged from monolayer to bulk in both stacking types.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
Both donor- and acceptor-type charge transition levels remain nearly unchanged from monolayer to bulk in both AA and AB stacking. The associated two-level quantum system also retains its character across thicknesses. The invariance arises from the interplay between electronic energy minimization and structural relaxation, which together counteract quantum confinement and reduced dielectric screening, with the intrinsically weak interlayer coupling in ReS2 playing a crucial role.
What carries the argument
Interplay between electronic energy minimization and structural relaxation counteracting quantum confinement effects in weakly interlayer-coupled ReS2
If this is right
- ReS2 can serve as a platform for layer-tolerant single-photon emitters.
- Thickness-independent optoelectronic and quantum photonic applications become feasible.
- ReS2 behaves differently from other transition metal dichalcogenides in defect response to layering.
Where Pith is reading between the lines
- This behavior may simplify device fabrication by reducing sensitivity to exact layer number.
- Similar effects could be explored in other materials with weak interlayer interactions.
- Experiments could test if changing defect types alters the tolerance.
Load-bearing premise
The invariance of defect levels comes from the specific balance of electronic energy minimization and structural relaxation that counters confinement and screening changes due to weak interlayer coupling.
What would settle it
Observation of significant shifts in charge transition levels when increasing layer thickness from one to several layers in ReS2 samples would falsify the claim of persistence.
Figures
read the original abstract
Defects in two-dimensional (2D) semiconductors play a decisive role in determining their electronic, optical, catalytic and quantum properties. Understanding how defect energy levels respond to variations in layer thickness is essential for achieving reproducible and scalable device performance. We report the persistence of layer-tolerant defect levels in rhenium disulfide (ReS2), where both donor- and acceptor-type charge transition levels remain nearly unchanged from monolayer to bulk in both AA and AB stacking. The associated two-level quantum system also retains its character across thicknesses, enabling ReS2 to serve as a platform for layer-tolerant single-photon emitters. The invariance arises from the interplay between electronic energy minimization and structural relaxation, which together counteract quantum confinement and reduced dielectric screening. Additionally, the intrinsically weak interlayer coupling in ReS2 plays a crucial role. Our findings uncover the microscopic origin of this unique behavior, distinguishing ReS2 from other transitionmetal dichalcogenides and highlighting its potential for thickness-independent optoelectronic and quantum photonic applications.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript reports that in ReS2 both donor- and acceptor-type charge transition levels (CTLs) remain nearly unchanged when going from monolayer to bulk, for both AA and AB stackings. The invariance is attributed to the interplay between electronic energy minimization and ionic relaxation that counteracts quantum confinement and reduced dielectric screening, with the intrinsically weak interlayer coupling playing a key role. The associated two-level quantum system is claimed to retain its character across thicknesses, positioning ReS2 as a platform for layer-tolerant single-photon emitters.
Significance. If substantiated, the result identifies a microscopic mechanism that distinguishes ReS2 from other TMDs and supplies a concrete materials platform for thickness-independent defect-based quantum optics. The explicit linkage of the invariance to the competition between electronic minimization and structural relaxation, rather than a generic appeal to weak coupling, is a positive feature.
major comments (1)
- [§3 and §4] §3 (Computational Methods) and §4 (Results): the manuscript must demonstrate that charged-defect formation energies and the resulting CTLs are converged with respect to supercell size and electrostatic corrections for every thickness examined. Because the effective dielectric tensor, vacuum padding, and lateral cell dimensions change systematically from monolayer (large vacuum, low screening) to bulk (no vacuum, higher screening), the same finite supercell plus the same image-charge correction scheme can produce residual errors whose magnitude is comparable to the reported invariance (<0.1 eV). Without explicit convergence tables or plots that bound these errors uniformly across the thickness series, the observed thickness independence could arise from error cancellation rather than the claimed physical mechanism.
minor comments (2)
- [Figure 2] Figure 2 and associated text: the labeling of the two-level quantum system (donor and acceptor states) should include the explicit energy separation and the wave-function character (e.g., Re d-orbital vs. S p-orbital) for at least one representative thickness to allow direct comparison across the series.
- [Abstract] The abstract states that the invariance 'arises from the interplay between electronic energy minimization and structural relaxation' but does not quantify the separate contributions; a short decomposition (e.g., fixed-geometry vs. relaxed calculations) would strengthen the mechanistic claim.
Simulated Author's Rebuttal
We thank the referee for the careful reading of our manuscript and the positive assessment of its significance. We address the major comment on convergence of charged-defect calculations below and will revise the manuscript to incorporate additional supporting data.
read point-by-point responses
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Referee: [§3 and §4] §3 (Computational Methods) and §4 (Results): the manuscript must demonstrate that charged-defect formation energies and the resulting CTLs are converged with respect to supercell size and electrostatic corrections for every thickness examined. Because the effective dielectric tensor, vacuum padding, and lateral cell dimensions change systematically from monolayer (large vacuum, low screening) to bulk (no vacuum, higher screening), the same finite supercell plus the same image-charge correction scheme can produce residual errors whose magnitude is comparable to the reported invariance (<0.1 eV). Without explicit convergence tables or plots that bound these errors uniformly across the thickness series, the observed thickness independence could arise from error cancellation rather than the claimed physical mechanism.
Authors: We agree that explicit convergence tests are essential to rule out error cancellation, particularly given the systematic changes in dielectric environment and vacuum padding across thicknesses. In the original calculations we employed 5×5 supercells with 20 Å vacuum for monolayers and the Freysoldt–Neugebauer–Van de Walle correction for all cases, but we did not present thickness-resolved convergence tables. In the revised manuscript we will add an appendix containing (i) formation-energy convergence versus supercell size (4×4 to 7×7) for monolayer, bilayer and bulk ReS2, (ii) comparison of two correction schemes (FNV and a simple Makov–Payne extrapolation), and (iii) a plot of CTL variation with cell size that remains below 0.04 eV once the 5×5 cell is reached for every thickness. These additional data confirm that residual errors are smaller than the reported layer invariance and do not alter the physical conclusion. revision: yes
Circularity Check
No circularity: invariance derived from explicit DFT formation-energy differences and relaxation effects
full rationale
The paper computes donor and acceptor charge transition levels directly from total-energy differences in supercell DFT calculations for monolayer, few-layer, and bulk ReS2 in both AA and AB stackings. The reported near-invariance is attributed to the explicit cancellation between quantum-confinement shifts, dielectric-screening changes, electronic minimization, and ionic relaxation, with weak interlayer coupling invoked as an additional physical factor. No equations redefine the target invariance in terms of itself, no fitted parameters are relabeled as predictions, and no load-bearing self-citations or uniqueness theorems from prior author work are used to force the result. The derivation therefore remains independent of its inputs and is self-contained against standard first-principles defect methodology.
Axiom & Free-Parameter Ledger
axioms (1)
- domain assumption Standard density-functional approximations and supercell models suffice to capture defect charge transition levels in layered ReS2
Reference graph
Works this paper leans on
-
[1]
Point Defects in Monolayer ReS 2 The lower lattice symmetry of ReS 2 results in two crystallographically inequivalent sulfur sites, S1 and S2, which are considered for vacancy ( VS1, VS2) and antisite (ReS1, ReS2) defects. In addition, rhenium vacancies (VRe) and antisites where sulfur substitutes for rhenium (SRe) are also studied. The relaxed atomic geo...
-
[2]
Defect Transition Levels of Point Defects To further elucidate the stability of defect charge states, the corresponding charge transition levels are pre- sented in Fig. 1(c). Sulfur vacancies ( VS1, VS2) remain stable in the neutral charge state over the entire Fermi level range, as shown in Fig. 1(a) and 1(b); consequently, 4 1L 2L 3L 4L Bulk Forma/g415o...
-
[3]
Variations in band edges and band gaps are directly influenced by the ICS in layered systems
Interlayer Coupling Strength (ICS) Interlayer coupling strength, alongside quantum con- finement effect and screening effect, plays a crucial role in determining the properties of low-dimensional layered materials. Variations in band edges and band gaps are directly influenced by the ICS in layered systems. As shown in Fig. S1(a) and (b), ReS 2 exhibits minim...
-
[4]
3(a)], we analyze the contributions in Eq
Quantum Confinement Effect (QCE) and Screening Effect (SE) In order to explain the minimal change in defect tran- sition levels with dimensionality [shown in Fig. 3(a)], we analyze the contributions in Eq. 6 and Eq. 8. The term EN DL is influenced by the quantum confinement effect. From Fig. S9 and S10 of SM, the defect levels relative to the band edges remain ...
work page 2019
-
[5]
K. Ko, M. Jang, J. Kwon, and J. Suh, Native point defects in 2d transition metal dichalcogenides: A per- spective bridging intrinsic physical properties and devic e applications, J. of Appl. Phys. 135, 10.1063/5.0185604 (2024)
-
[6]
A. Singh and A. K. Singh, Origin of n-type con- ductivity of monolayer mos 2, Phys. Rev. B 99, 10.1103/physrevb.99.121201 (2019)
-
[7]
J. Jiang, C. Ling, T. Xu, W. Wang, X. Niu, A. Za- far, Z. Yan, X. Wang, Y. You, L. Sun, J. Lu, J. Wang, and Z. Ni, Defect engineering for modulating the trap states in 2d photoconductors, Adv. Mater. 30, 10.1002/adma.201804332 (2018)
-
[8]
H.-Y. Chen, H.-C. Hsu, J.-Y. Liang, B.-H. Wu, Y.-F. Chen, C.-C. Huang, M.-Y. Li, I. P. Radu, and Y.-P. Chiu, Atomically resolved defect- engineering scattering potential in 2d semiconductors, ACS Nano 18, 17622–17629 (2024)
work page 2024
- [9]
-
[10]
M. Turunen, M. Brotons-Gisbert, Y. Dai, Y. Wang, E. Scerri, C. Bonato, K. D. J¨ ons, Z. Sun, and B. D. Gerardot, Quantum photonics with layered 2d materials, Nat. Rev. Phys. 4, 219–236 (2022)
work page 2022
-
[11]
M. Dey, S. Meher, and A. K. Singh, Carbon with Stone- Wales defect as quantum emitter in h-BN, Phys. Rev. B 111, 10.1103/physrevb.111.104109 (2025)
-
[12]
A. Arora, P. K. Nayak, S. Bhattacharyya, N. Maity, A. K. Singh, A. Krishnan, and M. S. R. Rao, Interlayer exci- tonic states in MoSe 2/MoS2 van der Waals heterostruc- tures, Phys. Rev. B 103, 10.1103/physrevb.103.205406 (2021)
-
[13]
M. Mandal, N. Maity, P. K. Barman, A. Srivastava, A. K. Singh, P. K. Nayak, and K. Sethupathi, Probing angle-dependent thermal conductivity in twisted bilayer MoSe2, Phys. Rev. B 108, 10.1103/physrevb.108.115439 (2023)
-
[14]
S. Mishra, N. Maity, and A. K. Singh, Symmetry-assisted anomalous hall conductivity in a crs 2-crbr3 heterostruc- ture, Phys. Rev. B 110, 10.1103/physrevb.110.125406 (2024)
-
[15]
K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, Atomically thin MoS 2: a new direct-gap semiconductor, Phys. Rev. Lett. 105, 10.1103/physrevlett.105.136805 (2010)
-
[16]
Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Cole- man, and M. S. Strano, Electronics and optoelectron- ics of two-dimensional transition metal dichalcogenides, Nat. Nanotechnol. 7, 699–712 (2012)
work page 2012
-
[17]
B. Radisavljevic, A. Radenovic, J. Brivio, V. Gia- cometti, and A. Kis, Single-layer MoS 2 transistors, Nat. Nanotechnol. 6, 147–150 (2011)
work page 2011
-
[18]
M. Chhowalla, H. S. Shin, G. Eda, L.-J. Li, K. P. Loh, and H. Zhang, The chemistry of two-dimensional layered transition metal dichalcogenide nanosheets, Nat. Chem. 5, 263–275 (2013)
work page 2013
-
[19]
S. Bhattacharyya and A. K. Singh, Semiconductor- metal transition in semiconducting bilayer sheets of transition-metal dichalcogenides, Phys. Rev. B 86, 10.1103/physrevb.86.075454 (2012)
- [20]
-
[21]
A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C.-Y. Chim, G. Galli, and F. Wang, Emerg- ing photoluminescence in monolayer MoS 2, Nano Lett. 10, 1271–1275 (2010)
work page 2010
-
[22]
J. Qiao, X. Kong, Z.-X. Hu, F. Yang, and W. Ji, High-mobility transport anisotropy and linear dichro- ism in few-layer black phosphorus, Nat. Commun. 5, 10.1038/ncomms5475 (2014)
-
[23]
Z.-Y. Zhao and Q.-L. Liu, Study of the layer- dependent properties of mos 2 nanosheets with different crystal structures by dft calculations, Catal. Sci. Technol. 8, 1867–1879 (2018)
work page 2018
-
[24]
M. Kayyalha, J. Maassen, M. Lundstrom, L. Shi, and Y. P. Chen, Gate-tunable and thickness-dependent elec- tronic and thermoelectric transport in few-layer MoS 2, J. Appl. Phys. 120, 10.1063/1.4963364 (2016)
-
[25]
W. Choi, N. Choudhary, G. H. Han, J. Park, D. Ak- inwande, and Y. H. Lee, Recent development of two- dimensional transition metal dichalcogenides and their applications, Mater. Today 20, 116–130 (2017)
work page 2017
-
[26]
L. Jiao, W. Jie, Z. Yang, Y. Wang, Z. Chen, X. Zhang, W. Tang, Z. Wu, and J. Hao, Layer-dependent photore- sponse of 2D Mo 2 films prepared by pulsed laser deposi- tion, J. Mater. Chem. C 7, 2522–2529 (2019)
work page 2019
-
[27]
A. Singh, M. Dey, and A. K. Singh, Origin of layer-dependent electrical conductivity of tran- sition metal dichalcogenides, Phys. Rev. B 105, 10.1103/physrevb.105.165430 (2022)
- [28]
-
[29]
D. Wang and R. Sundararaman, Layer dependence of de- fect charge transition levels in two-dimensional material s, Phys. Rev. B 101, 10.1103/physrevb.101.054103 (2020)
- [30]
-
[31]
S. Manzeli, D. Ovchinnikov, D. Pasquier, O. V. Yazyev, and A. Kis, 2d transition metal dichalcogenides, Nat. Rev. Mater. 2, 10.1038/natrevmats.2017.33 (2017)
-
[32]
X. Meng, T. Pandey, J. Jeong, S. Fu, J. Yang, K. Chen, A. Singh, F. He, X. Xu, J. Zhou, W.-P. Hsieh, A. K. Singh, J.-F. Lin, and Y. Wang, Thermal conductivity enhancement in mos 2 under extreme strain, Phys. Rev. Lett. 122, 10.1103/physrevlett.122.155901 (2019)
-
[33]
J. Sun, X. Li, W. Guo, M. Zhao, X. Fan, Y. Dong, C. Xu, J. Deng, and Y. Fu, Synthesis methods of two- dimensional MoS 2: a brief review, Cryst. 7, 198 (2017)
work page 2017
-
[34]
G. E. Collins, K. W. Nebesny, C. D. England, L.-K. Chau, P. A. Lee, B. A. Parkinson, and N. R. Armstrong, Orientation and structure of monolayer - multilayer phthalocyanine thin films on layered semiconductor (MoS 2 and SnS 2) surfaces, J. Vac. Sci. Technolo. A 10, 2902–2912 (1992)
work page 1992
-
[35]
N. Perea-L´ opez, Z. Lin, N. R. Pradhan, A. I˜ niguez- R´ abago, A. L. El ´ ıas, A. McCreary, J. Lou, P. M. Ajayan, H. Terrones, L. Balicas, and M. Terrones, CVD-grown monolayered MoS 2 as an effective photosensor operating at low-voltage, 2D Mater. 1, 011004 (2014)
work page 2014
-
[36]
J.-S. Kim, N. Maity, M. Kim, S. Fu, R. Juneja, A. Singh, D. Akinwande, and J.-F. Lin, Strain-Modulated Interlayer Charge and En- ergy Transfers in MoS 2/WS2 Heterobilayer, ACS Appl. Mater. Interfaces 14, 46841–46849 (2022)
work page 2022
-
[37]
Y. Yu, C. Li, Y. Liu, L. Su, Y. Zhang, and L. Cao, Controlled scalable synthesis of uniform, high-quality monolayer and few-layer MoS 2 films, Sci. Rep. 3, 10.1038/srep01866 (2013)
- [38]
- [39]
-
[40]
X. Li, W. Han, J. Wu, X. Qiao, J. Zhang, and P. Tan, Layer-number dependent optical properties of 2D mate- rials and their application for thickness determination, Adv. Funct. Mater. 27, 10.1002/adfm.201604468 (2017)
-
[41]
J. Hong, K. Li, C. Jin, X. Zhang, Z. Zhang, and J. Yuan, Layer-dependent anisotropic electronic structure of free - standing quasi-two-dimensional MoS 2, Phys. Rev. B 93, 10.1103/physrevb.93.075440 (2016)
-
[42]
S. Tongay, H. Sahin, C. Ko, A. Luce, W. Fan, K. Liu, J. Zhou, Y.-S. Huang, C.-H. Ho, J. Yan, D. F. Ogle- tree, S. Aloni, J. Ji, S. Li, J. Li, F. M. Peeters, and J. Wu, Monolayer behaviour in bulk ReS 2 due to elec- tronic and vibrational decoupling, Nat. Commun. 5, 10.1038/ncomms4252 (2014)
-
[43]
D. A. Chenet, B. Aslan, P. Y. Huang, C. Fan, A. M. van der Zande, T. F. Heinz, and J. C. Hone, In-plane anisotropy in mono- and few-layer res2 probed by ra- man spectroscopy and scanning transmission electron mi- croscopy, Nano Lett. 15, 5667–5672 (2015)
work page 2015
-
[44]
B. Jariwala, D. Voiry, A. Jindal, B. A. Chalke, R. Ba- pat, A. Thamizhavel, M. Chhowalla, M. Deshmukh, and A. Bhattacharya, Synthesis and characterization of ReS2 and ReSe 2 layered chalcogenide single crystals, Chem. Mater. 28, 3352–3359 (2016)
work page 2016
-
[45]
Y. Feng, W. Zhou, Y. Wang, J. Zhou, E. Liu, Y. Fu, Z. Ni, X. Wu, H. Yuan, F. Miao, B. Wang, X. Wan, and D. Xing, Raman vibrational spectra of bulk to monolayer ReS 2 with lower symmetry, Phys. Rev. B 92, 10.1103/physrevb.92.054110 (2015)
-
[46]
Y. Zhou, N. Maity, A. Rai, R. Juneja, X. Meng, A. Roy, Y. Zhang, X. Xu, J. Lin, S. K. Banerjee, A. K. Singh, and Y. Wang, Stacking-Order-Driven Optical Proper- ties and Carrier Dynamics in ReS 2, Adv. Mater. 32, 10.1002/adma.201908311 (2020)
-
[47]
G. Kresse and J. Furthm¨ uller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169–11186 (1996)
work page 1996
-
[48]
G. Kresse and J. Furthm¨ uller, Efficiency of ab- initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6, 15–50 (1996)
work page 1996
-
[49]
P. E. Bl¨ ochl, Projector augmented-wave method, Phys. Rev. B 50, 17953–17979 (1994)
work page 1994
-
[50]
G. Kresse and D. Joubert, From ultrasoft pseu- dopotentials to the projector augmented-wave method, 10 Phys. Rev. B 59, 1758–1775 (1999)
work page 1999
-
[51]
J. P. Perdew, K. Burke, and M. Ernzerhof, Gen- eralized gradient approximation made simple, Phys. Rev. Lett. 77, 3865–3868 (1996)
work page 1996
-
[52]
J. Klimeˇ s, D. R. Bowler, and A. Michaelides, Chemi- cal accuracy for the van der waals density functional, J. Phys. Condens. Matter 22, 022201 (2009)
work page 2009
-
[53]
J. Klimeˇ s, D. R. Bowler, and A. Michaelides, Van der waals density functionals applied to solids, Phys. Rev. B 83, 10.1103/physrevb.83.195131 (2011)
-
[54]
H. J. Monkhorst and J. D. Pack, Spe- cial points for brillouin-zone integrations, Phys. Rev. B 13, 5188–5192 (1976)
work page 1976
-
[55]
C. Freysoldt, B. Grabowski, T. Hickel, J. Neugebauer, G. Kresse, A. Janotti, and C. G. Van de Walle, First-principles calculations for point defects in solids , Rev. Mod. Phys. 86, 253–305 (2014)
work page 2014
-
[56]
C. G. Van de Walle and J. Neugebauer, First-principles calculations for defects and impurities: Applications to iii-nitrides, J. Appl. Phys. 95, 3851–3879 (2004)
work page 2004
-
[57]
M. Dey, A. Singh, and A. K. Singh, Formation of a small electron polaron in tantalum oxynitride: Origin of low mobility, J. Phys. Chem. C 125, 11548–11554 (2021)
work page 2021
-
[58]
M. Dey and A. K. Singh, Broad photolumines- cence from large Frank-Condon relaxation dynam- ics of hole polarons in LiGaO 2, Phys. Rev. B 108, 10.1103/physrevb.108.l041201 (2023)
-
[59]
Fully Ab Initio Finite-Size Corrections for Charged-Defect Supercell Calculations
C. Freysoldt, J. Neugebauer, and C. G. Van de Walle, Fullyab initiofinite-size corrections for charged- defect supercell calculations, Phys. Rev. Lett. 102, 10.1103/physrevlett.102.016402 (2009)
-
[60]
C. Freysoldt, J. Neugebauer, and C. G. Van de Walle, Electrostatic interactions between charged defects in supercells, physica status solidi (b) 248, 1067–1076 (2010)
work page 2010
-
[61]
C. Freysoldt and J. Neugebauer, First-principles calcula- tions for charged defects at surfaces, interfaces, and two- dimensional materials in the presence of electric fields, Phys. Rev. B 97, 10.1103/physrevb.97.205425 (2018)
-
[62]
Y. Zhou, N. Maity, J.-F. Lin, A. K. Singh, and Y. Wang, Nonlinear Optical Absorption of ReS 2 Driven by Stacking Order, ACS Photonics 8, 405–411 (2021)
work page 2021
-
[63]
P. Upadhyay, N. Maity, R. Kumar, P. K. Barman, A. K. Singh, and P. K. Nayak, Layer parity dependent Raman- active modes and crystal symmetry in ReS 2, Phys. Rev. B 105, 10.1103/physrevb.105.045416 (2022)
- [64]
- [65]
-
[66]
X.-F. Qiao, J.-B. Wu, L. Zhou, J. Qiao, W. Shi, T. Chen, X. Zhang, J. Zhang, W. Ji, and P.- H. Tan, Polytypism and unexpected strong in- terlayer coupling in two-dimensional layered ReS 2, Nanoscale 8, 8324–8332 (2016)
work page 2016
-
[67]
S.-H. Wei and S. B. Zhang, Chemical trends of de- fect formation and doping limit in II-VI semicon- ductors: The case of CdTe, Phys. Rev. B 66, 10.1103/physrevb.66.155211 (2002)
-
[68]
M. Dey, S. Chowdhury, S. Kumar, and A. Kumar Singh, Quantum confinement effect on defect level of hydro- gen doped rutile VO 2 nanowires, J. Appl. Phys. 131, 10.1063/5.0095834 (2022)
-
[69]
G.-J. Zhu, J.-H. Yang, and X.-G. Gong, Self-consistently determining structures of charged defects and defect ionization energies in low-dimensional semiconductors, Phys. Rev. B 102, 10.1103/physrevb.102.035202 (2020)
discussion (0)
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