[Paper Review] Charge Density Wave Order and Superconductivity in Janus MoXH Monolayers

J. Seeyangnok, U. Pinsook+1 more|arXiv (Cornell University)|Jan 6, 2026

2D Materials and Applications1 citations

TL;DR

The paper shows that Janus MoXH monolayers host an intrinsic commensurate CDW ground state driven by soft phonons at the M point, and examines how CDW interacts with superconductivity and can be tuned by strain, doping, and temperature.

ABSTRACT

Two-dimensional Janus hydrogenated transition metal chalcogenides provide an unusual platform where lattice instabilities, electron-phonon coupling, and superconductivity are strongly intertwined. Using first-principles calculations, we demonstrate that Janus 2H and 1T MoXH (X = S, Se) monolayers host an intrinsic, commensurate charge density wave (CDW) ground state originating from soft phonon modes at the Brillouin zone M point. Real-space supercell optimizations confirm that the CDW reconstruction lowers the total energy and fully stabilizes the lattice, eliminating the imaginary phonon modes present in the high-symmetry metallic structures. Analysis of the electronic susceptibility shows that the CDW instability is not driven by Fermi surface nesting, but instead arises from strong electron-phonon coupling. We further reveal a material-dependent interplay between CDW order and superconductivity. In 1T MoSH, CDW formation enhances low-energy phonon contributions and strengthens electron-phonon coupling, leading to an increased superconducting transition temperature. In contrast, for 1T MoSeH and 2H MoSeH, the CDW phase suppresses electron-phonon coupling and reduces superconductivity. Finally, we show that thermal fluctuations, compressive strain, and carrier doping can selectively suppress CDW order and restore superconductivity. These results establish Janus MoXH monolayers as a tunable two-dimensional system for exploring lattice-driven charge ordering and its competition with superconductivity.

Motivation & Objective

• Investigate lattice instabilities and possible CDW formation in Janus MoXH monolayers (X = S, Se).
• Determine whether CDW is driven by Fermi-surface nesting or electron–phonon coupling.
• Assess how CDW order affects electron–phonon coupling and superconductivity.
• Explore external control parameters (strain, doping, temperature) to manipulate CDW and superconductivity.

Proposed method

• Compute phonon dispersions of high-symmetry Janus MoXH structures and identify soft modes at M.
• Perform real-space 2x2 CDW supercell relaxations to confirm commensurate CDW ground states.
• Analyze electronic susceptibility (Re[χ0], Im[χ0]) and phonon linewidths to distinguish nesting from electron–phonon coupling effects.
• Compare CDW ground states with strained/doped high-symmetry structures to evaluate changes in electron–phonon coupling and Tc.
• Use ab initio molecular dynamics to assess CDW stability up to finite temperatures (~50 K).
• Examine orbital-resolved electronic structures to understand bands near the Fermi level in both phases.

Figure 1: Phonon dispersions and lattice instabilities in hydrogenated Mo-based monolayers. a–c , Phonon dispersion relations of (a) 1T–MoSH, (b) 2H–MoSeH, and (c) 1T–MoSeH calculated for the high-symmetry structure (HSS, red lines) and the CDW phase (blue lines) along the high-symmetry path $\Gamma

Experimental results

Research questions

• RQ1 Is the observed CDW in Janus MoXH monolayers driven by Fermi-surface nesting or momentum-dependent electron–phonon coupling?
• RQ2 How does CDW formation influence electron–phonon coupling and the superconducting Tc in different MoXH polymorphs?
• RQ3 Can strain, doping, or temperature suppress CDW and restore or enhance superconductivity?
• RQ4 What is the nature of the CDW ground state and its stability in 2x2 supercells across S and Se variants?
• RQ5 How does CDW order reshape the electronic structure and EPC hotspots in these materials?

Key findings

• CDW order is intrinsic and commensurate, arising from soft phonons at the M point in 1T–MoSH, 1T–MoSeH, and 2H–MoSeH.
• The CDW instability is driven by strong momentum-dependent electron–phonon coupling, not Fermi-surface nesting.
• Structural relaxation yields a stable 2x2 CDW phase with no imaginary phonons, replacing the high-symmetry metallic structure.
• In 1T–MoSH, CDW enhances low-energy phonon contributions and strengthens electron–phonon coupling, increasing Tc.
• In 1T–MoSeH and 2H–MoSeH, CDW suppresses electron–phonon coupling and reduces Tc.
• CDW can be suppressed by thermal fluctuations, compressive strain, or carrier doping, but suppression behavior is material-dependent (notably not fully suppressible in 1T–MoSeH).
• Superconductivity always emerges within a pre-existing CDW background (Tc < TCDW) across studied systems.

Figure 2: Interplay between phonon softening and electronic susceptibility in Janus MoXH monolayers. Rows correspond to ( a ) 1T–MoSH, ( b ) 1T–MoSeH, and ( c ) 2H–MoSeH. Left panels show the momentum-dependent phonon linewidth $\gamma(\mathbf{q},\nu{=}1)$ of the lowest-energy (ZA) phonon mode along