CDWs and Superconductivity in 2D Materials

Charge density waves (CDWs) and conventional superconductivity share similarities in that they are both collective phenomena that can arise from electron-phonon coupling, and they both can also be influenced by dimensionality and electron-electron interactions. The Crommie group is currently exploring these phenomena in different single-layer 2D materials, such as the transition metal dichalcogenides (TMDs) (materials of the form MX2, where M = transition metal and X = chalcogen) as well as bilayer systems (for more information on bilayer systems look here).

1D CDWs are most commonly described as a Peierls distortion, which arises from a combination of Fermi surface nesting and electron-phonon coupling that leads to the softening of a phonon at wavevector q = 2kF.1 This causes dimerization of the lattice and a charge distortion at q = 2kF as well as the opening of an energy gap at kF (Fig. 1).

Fig. 1: (a) A half-filled metallic band with no CDW, including an undistorted 1D lattice. (b) Electronic structure of a 1D half-filled band after formation of a CDW. The lattice is seen to dimerize.

In TMD materials the situation can be a bit more complex due to the existence of multiple bands, electron-electron correlations, and spin-orbit coupling. The mechanisms causing CDWs are still debated in different TMD materials, with some favoring electronic-based mechanisms due to Fermi surface nesting or van Hove singularities and others favoring strong electron-phonon coupling.2 Motivation for understanding this behavior comes from the fact that CDW order can affect other aspects of TMD behavior, such as superconductivity, Mott insulator formation, magnetic ordered states, and quantum spin liquid formation.

A strategy that the Crommie group has pursued to explore this topic in TMD materials is to characterize the local electronic structure as a material is thinned down to the single-layer limit.3-6 This removes the effects of interlayer coupling, thus simplifying the band structure (since electrons can’t hop between layers) and reducing electronic screening (which enhances electron-electron correlations). In some cases TMD CDWs have been predicted to significantly change their properties upon thinning. An example is NbSe2, where thinning down to a single-layer was predicted to reduce the number of bands crossing EF, thus altering the NbSe2 Fermi surface (Figs. 2a, b) and causing the NbSe2 CDW to change its periodicity.7.

Fig. 2: (a) Sketch of bulk NbSe2 in the 2H phase, including bandstructure and Fermi surface. (b) Sketch of single-layer NbSe2 in the 1H phase, including bandstructure and Fermi surface.

The Crommie group tested these predictions by measuring single-layer NbSe2 sheets grown via molecular beam epitaxy (MBE) using scanning tunneling microscopy (STM) (NbSe2 growth was performed by the S.K. Mo and Z.X. Shen groups, STM measurements were performed by the Crommie group). As predicted,7 the electronic structure of single-layer NbSe2 was found to differ significantly from bulk values (Figs. 3a, b).4

Fig. 3: (a)-(b) STM spectroscopy of single-layer NbSe2, including close-up structure at EF (a narrow pseudogap feature is seen) (STM spectroscopy: Crommie group; growth: S. K. Mo and Z. X. Shen groups). (c) STM spectroscopy of bulk NbSe2 has a much wider pseudogap feature than single-layer NbSe2 (from PNAS 110, 1623 (2013).

The single-layer NbSe2 CDW, however, was observed to have the same periodicity and Tc as bulk NbSe2 (Fig. 4). This suggests that electron-phonon coupling plays a stronger role in this material than postulated Fermi surface nesting or van Hove singularity-based mechanisms.4

Fig. 4: STM image of single-layer NbSe2 shows 3x3 CDW (also visible in Fourier transform). (STM imaging: Crommie group; growth: Mo, Shen groups).

We also observed that the superconducting critical temperature of NbSe2 reduces from Tc = = 7K in the bulk to only Tc ≈ 1.5K in single layers (Tc values measured in collaboration with A. Zettl’s group) (Fig. 5). Thinning NbSe2 down to the single-layer limit thus has no effect on the CDW but weakens superconductivity.4

Fig. 5: Resistance vs. temperature for single-layer NbSe2 shows a superconducting transition temperature of Tc ≈ 1.5K. (Conductivity measurement: Zettl group).

The Crommie group has additionally explored the formation of different CDW phases in single-layer TaSe2 (in collaboration with S.K. Mo and Z.X. Shen). In the 1H phase single-layer TaSe2 was observed to exhibit a 3x3 CDW very similar to what is observed in NbSe2 (Fig. 6).5

Fig. 6: (a)-(b) Sketch of structure of 1H-TaSe2. (c) Large scale STM image of single-layer 1H-TaSe2. (d) Close-up STM image of single-layer 1H-TaSe2 shows a 3x3 CDW. (STM images: Crommie group; growth: Mo, Shen groups).

In the 1T phase, however, single-layer TaSe2 is observed to have a completely different CDW structure. Here we observe a star-of-David √13 x √13 CDW distortion as shown in Fig. 7.8 Each maximum observed via STM in this CDW pattern (Fig. 7a) corresponds to a single star-of-David cluster (see sketch in Fig. 7c). Each cluster contains 13 Ta atoms, including the atom at the center. Reciprocal lattice vectors of the CDW (b1 and b2, obtained by Fourier transforming the STM image) are much smaller than the reciprocal lattice vectors of the atomic lattice (Figs. 7b, d)).

Fig. 7: (a) STM image of single-layer 1T-TaSe2 shows a star-of-David CDW (each bright maximum contains 13 Ta atoms). (b) Fourier transform of STM image in (a) shows reciprocal lattice of CDW (b1, b2) and atomic reciprocal lattice vectors (b1’, b2’). (c)-(d) Sketch of real space and reciprocal space structure of 1T-TaSe2. (STM images: Crommie group; growth: Mo, Shen groups).


1. Density Waves in Solids, George Gruner, CRC Press (1994).

2. On the Origin of Charge-density Waves in Select Layered Transition-metal Dichalcogenides, K Rossnagel, Journal of Physics: Condensed Matter 23, 213001 (2011).

3. Giant Bandgap Renormalization and Excitonic Effects in a Monolayer Transition Metal Dichalcogenide Semiconductor, Miguel M. Ugeda, Aaron J. Bradley, Su-Fei Shi, Felipe H. da Jornada, Yi Zhang, Diana Y. Qiu, Wei Ruan, Sung-Kwan Mo, Zahid Hussain, Zhi-Xun Shen, Feng Wang, Steven G. Louie, Michael F. Crommie, Nature Materials 13, 1091–1095 (2014).

4. Characterization of Collective Ground States in Single-Layer Nbse2, Miguel M. Ugeda, Aaron J. Bradley, Yi Zhang, Seita Onishi, Yi Chen, Wei Ruan, Claudia Ojeda-Aristizabal, Hyejin Ryu, Mark T. Edmonds, Hsin-Zon Tsai, Alexander Riss, Sung-Kwan Mo, Dunghai Lee, Alex Zettl, Zahid Hussain, Zhi-Xun Shen, Michael F. Crommie, Nature Physics 12, 92-97 (2016).

5. Persistent Charge-Density-Wave Order in Single-Layer TaSe2, Hyejin Ryu, Yi Chen, Heejung Kim, Hsin-Zon Tsai, Shujie Tang, Juan Jiang, Franklin Liou, Salman Kahn, Caihong Jia, Arash A Omrani, Ji-Hoon Shim, Zahid Hussain, Zhi-Xun Shen, Kyoo Kim, Byung Il Min, Choongyu Hwang, Michael F Crommie, Sung-Kwan Mo, Nano Letters 18, 689-694 (2018).

6. Observation of Topologically Protected States at Crystalline Phase Boundaries in Single-Layer Wse2, Miguel M. Ugeda, Artem Pulkin, Shujie Tang, Hyejin Ryu, Quansheng Wu, Yi Zhang, Dillon Wong, Zahra Pedramrazi, Ana Martín-Recio, Yi Chen, Feng Wang, Zhi-Xun Shen, Sung-Kwan Mo, Oleg V. Yazyev, Michael F. Crommie, Nature Communications 9 3401 (2018).

7. Effect of Dimensionality on the Charge-density Wave in Few-layer 2H-NbSe2, Matteo Calandra, I. I. Mazin, Francesco Mauri, Physical Review B 80, 241108(R) (2009).

8. Visualizing Exotic Orbital Texture in the Single-Layer Mott Insulator 1T-TaSe2, Yi Chen, Wei Ruan, Meng Wu, Shujie Tang, Hyejin Ryu, Hsin-Zon Tsai, Ryan Lee, Salman Kahn, Franklin Liou, Caihong Jia, Oliver R. Albertini, Hongyu Xiong, Tao Jia, Zhi Liu, Jonathan A. Sobota, Amy Y. Liu, Joel E. Moore, Zhi-Xun Shen, Steven G. Louie, Sung-Kwan Mo, Michael F. Crommie, arXiv:1904.11010.