Coexistence of Elastic Modulations in the Charge Density Wave State of 2H-NbSe₂

Abstract

Bulk and single-layer 2H-NbSe 2 exhibit identical charge density wave order (CDW) with a quasi-commensurate 3×3 superlattice periodicity. Here we combine scanning tunnelling microscopy (STM) imaging at T = 1 K of 2H-NbSe 2 with firstprinciples density functional theory (DFT) calculations to investigate the structural atomic rearrangement of this CDW phase. Our calculations for single-layers reveal that six different atomic structures are compatible with the 3×3 CDW distortion, although all of them lie on a very narrow energy range of at most 3 meV per formula unit, suggesting the coexistence of such structures. Our atomically resolved STM images of bulk 2H-NbSe 2 unambiguously confirm this by identifying two of these structures. Remarkably, these structures differ from the X-ray crystal structure reported for the bulk 3×3 CDW which, in fact, is also one of the six DFT structures located for the single-layer. Our calculations also show that due to the minute energy difference between the different phases, the ground state of the 3×3 CDW could be extremely sensitive to doping, external strain or internal pressure within the crystal. The presence of multi-phase CDW order in 2H-NbSe 2 may provide further understanding of its low temperature state and the competition between different instabilities.

Ising Superconductivity and Magnetism in NbSe2

“…We then fit our results to an expansion of the total energy as a function of m [Eq. (2)] to determine χ.…”

“…The transition metal dichalcogenides (TMD) exhibit an astonishing variety of phenomena and phase transitions, which includes charge-density waves (CDWs) [1][2][3][4][5], superconductivity [6], and magnetism [7]. Bulk 2H-NbSe 2 , which is one of the canonical transition metal dichalcogenides, exhibits a rich phase diagram, which includes a superconducting and a CDW phase [1].…”

Siesta: Recent developments and applications

“…Careful analysis of theoretical and experimental STM images for different bias potentials allowed to identify two of these structures that can coexist in the same image. 180 In a different work, 181 the temperature dependency of the electronic Lindhard response function in blue bronze K 0.3 MoO 3 was studied. This system has a rather complex monoclinic structure, with twenty formula units per unit cell where MoO 6 octahedra form chains along one direction (baxis).…”

Topological charge density wave in monolayer NbSe2

“…Experimentally, the heavily electron-doped monolayer NbSe 2 also hosts a 2×2 CDW order [41]. Ab initio calculations have established the modulated crystal structure of the triangular 3a 0 [42][43][44] and stripe 4a 0 [45] CDW phases of monolayer 2H-NbSe 2 , but the crystal structure of the 2×2 CDW is not known. Due to the wide application of NbSe 2 [23,46] and the important role of substrate strain in monolayer materials, it is crucial to understand the structural ground state and electronic properties of this phase.…”