Joint density of states and charge density wave in 2H-structured transition metal dichalcogenides

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Abstract

The joint density of states of two different 2H-structured transition metal dichalcogenides (TMDs) with and without charge density wave (CDW), Na0.05TaS2 and Cu0.09NbS2, respectively, are compared. While there is a clear maximum at the 3×3 charge density wavevector for Na0.05TaS2, the joint density of states for Cu0.09NbS2 does not show such behavior, consistent with the absence of CDW in the system. Our results illustrate that the joint density of states well represents the charge instability in 2D systems.

Introduction

The layered transition metal dichalcogenides (TMDs) have attracted considerable attention since they were discovered more than three decades ago [1], for their simple crystalline structures but rich ground states such as charge density wave (CDW) and superconducting states. So far, the mechanism for CDW in this system is still in hot debate. Someone proposed that the CDW phase transition was originated from the traditional Fermi surface nesting mechanism because of the long parallel Fermi surface sections [2]; while others argued that the CDW might involve the scattering between saddle band points, which cause a singularity in the density of states, and thus an anomaly in the dielectric response function [3]. However, the caveats of both scenarios were debated [2], [4]. Recently, the authors proposed a so-called “Fermi patch” mechanism for Na doped 2H-TaS2 [5], where electronic states across the entire Brillouin zone (BZ) participate in the CDW formation, as a result of the strong coupling nature of the system. As charge fluctuations with indefinite momenta are allowed across the Fermi patches of the BZ, one central question is why the 3×3 superlattice is favored. For cuprate superconductors, it has been demonstrated that, the autocorrelation of spectral function, A(k,ω), C(q,ω)A(k,ω)A(k+q,ω)dkcould give a reasonable account for the charge modulations observed by STM [6], [7]. This joint density of states describes the phase space for scattering of electrons from the state at k to the state at k+q by certain modes with wavevector q. Therefore, one would expect that it peaks at the ordering wavevector for ω=0 near the phase transition of a static order. Through such autocorrelation analysis, the phase space for charge fluctuations of different momenta were studied. It was shown that the collaboration of all these states favors maximal charge instability at the ordering wavevectors. As Fermi patches are quite ubiquitous in 2H-TMDs and other correlated systems, the Fermi patch mechanism might be a general theme of CDW. As an important crosscheck of its general applicability, in this paper we examine whether this mechanism could account for the absence of CDW in systems like 2H-NbS2.

We compared the joint density of states of Cu0.09NbS2, a 2H-TMD compound without CDW transition [8], [9], with that of Na0.05TaS2, whose CDW transition temperature is 65 K. While the latter has a clear peak structure at the 3×3 superlattice wavevector, the former shows a broad continuum, which indicates that the charge fluctuations in Cu0.09NbS2 do not have a prevailing wavevector, consistent with the absent CDW. Our results indicate that the joint density of states could well characterize the CDW fluctuations in 2H-TMDs.

Section snippets

Experimental

High quality Cu0.09NbS2 and Na0.05TaS2 single crystals were synthesized by the vapor-transport technique, where the dopant concentrations were determined by energy dispersion X-ray fluorescence (EDX). Angle-resolved photoemission spectroscopy (ARPES) experiments were performed with a Scienta R4000 electron analyzer and 21.2 eV photons from a Helium gas discharge lamp. The angular resolution is 0.3 and the total energy resolution is 10meV at 11 K. The samples were cleaved and measured in

Results and discussion

Figs. 1a and b show the photoemission intensity maps integrated within 10 meV around Fermi energy (EF) for 2H-Na0.05TaS2 and 2H-Cu0.09NbS2, respectively. They both have a hexagonal hole pocket around Γ(A) point and six hole pockets around K(H) points. The 2H-Cu0.09NbS2 Fermi surfaces are sharper compared to those of 2H-Na0.05TaS2. According to the band structure calculations of 2H-Cu0.09NbS2, these pockets are ascribed to the Nb 4d-derived orbital [10]. Although one unit cell for 2H-Cu0.09NbS2

Conclusion

In summary, the electronic structures of 2H-Cu0.09NbS2 and 2H-Na0.05TaS2 were investigated. The joint density of states analysis of these isostructural and isoelectronic materials show that Na0.05TaS2 favors the 3×3 superlattice charge instability, but Cu0.09NbS2 does not favor any specific ordering. Our results illustrate that the joint density of states analysis can be applied to study the electronic origin of charge density waves in 2H-TMD compounds.

Acknowledgments

We gratefully acknowledge the helpful discussion with Prof. C.Y. Kim and Prof. H.Q. Lin. The author gratefully acknowledges the support of K.C. Wong Education Foundation, Hong Kong. This work was supported by NSFC, MOST (973 Project no. 2006CB601002 and no. 2006CB921300), STCSM of China.

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