2D Mott Insulators

Mott insulating behavior is induced by strong electron correlations and can lead to exotic states of matter such as unconventional superconductivity and quantum spin liquids. The Crommie group is exploring this behavior in several different 2D systems.

2D Mott insulators emerge when the Coulomb interaction (U) exceeds the bandwidth (W) in partially-filled band systems that can be described by 2D Hubbard-like models.1 Bulk 1T-TaS2 and the surface of bulk 1T-TaSe2 are layered transition metal dichalcogenides (TMDs) that have long been known to host unusual insulating phases in the star-of-David charge density wave (CDW) state.2-4 The insulating nature of these bulk systems, however, is complicated by interlayer CDW stacking whose effects on the insulating phase remain controversial. Atomically-thin 1T-TMDs offer an ideal platform to differentiate the contributions of electron correlation and interlayer coupling in quasi-2D materials since single-layer systems can be fully characterized in the absence of interlayer coupling.

Fig. 1: STM image of single-layer 1T-TaSe2 exhibits the star-of-David phase. A sketch of this phase can be seen. Each maximum in the wavefunction corresponds to a 13-atom cluster of Ta atoms. (STM imaging: Crommie group; growth: Mo, Shen groups).

We have performed a combined scanning tunneling spectroscopy (STS), angle-resolved photoemission (ARPES), and theoretical study of the electronic structure of single-layer 1T-TaSe2 (Fig. 1a). Our results show that single-layer 1T-TaSe2 TaSe2 hosts a Mott-insulating ground state that exhibits exotic orbital texture.5 This is very different behavior compared to the metallic 1H phase of TaSe2. The metallic phase can be thought of as resulting from the fact that the amplitude for an electron to hop from one Ta atom to another, t, exceeds the Coulomb repulsion, U, that two electrons feel when they occupy the same orbital site (Fig. 2a). By contrast, when TaSe2 adopts the 1T phase the Ta atoms distort into a star-of-David CDW (Figs. 1, 2b) and the distance that an electron must hop from the center of one star-of-David cluster to another is larger than for Ta-Ta hopping in the 1H phase. This causes t to become smaller than the size of U, precisely the condition required for the formation of a Mott insulator1 (Fig. 2b).

Fig. 2: (a) TaSe2 in the 1H phase is a metal since electrons hop easily between Ta atoms so that the hopping amplitude (t) is greater than the Coulomb repulsion (U) felt by two electrons on the same site. (b) TaSe2 in the 1T phase is a Mott insulator since star-of-David CDW formation makes it harder for electrons to hop between the centers of adjacent stars-of-David. t thus reduces below U, the condition for Mott insulator formation.

The Mott insulating nature of single-layer 1T-TaSe2 can be seen in our STM spectroscopy data. Single-layer 1T-TaSe2 was grown via molecular beam epitaxy (MBE) by the S. K. Mo and Z. X. Shen groups and characterized via STM by the Crommie group. STM images show the characteristic star-of-David CDW (Figs. 1a, b). STM spectroscopy of single-layer 1T-TaSe2 shows a clear Mott-insulating energy gap of ~110 meV (Fig. 3). dI/dV mapping of the electronic wavefunctions of this single-layer Mott insulator reveals novel orbital texture (i.e., the electronic wavefunction spatial distribution).

Fig. 3: STM dI/dV spectroscopy for single-layer 1T-TaSe2 shows a ~ 110 meV Mott insulating gap at V=0. (STM spectroscopy: Crommie group; growth: Mo, Shen groups).

As seen in Fig. 4, the valence states show an electronic wavefunction that is localized to the centers of the star-of-David clusters (Figs. 4c, c) while the conduction band at C1 exhibits state density that is pushed out to the star-of-David periphery (Fig. 4d). At higher energies the star-of-David wavefunctions exhibit complex patterns involving both the inner and outer star-of-David Ta atoms.

Fig. 4: dI/dV maps are shown of the same patch of single-layer 1T-TaSe2 for different energies, as indicated. Valence band states show state density smoothly distributed over each star-of-David cluster, but conduction band states show novel orbital texture.

This behavior is explained by the fact that single-layer 1T-TaSe2 is a 2D Mott insulator. This is in contradiction to a simple electron counting argument that creates expectation that 1T-TaSe2 should be a metal, since there are 13 Ta4+ ions in a star-of-David unit cell and each carries one d-electron. An odd number of electrons per unit cell usually leads to metallic behavior, and conventional DFT calculations of 1T-TaSe2 band structure additionally predict that it should be a metal (Fig. 5a). However, when an on-site energy of U = 2 eV is added to the calculation (in a DFT + U treatment) then an energy gap does open up in the band structure as expected for a Mott insulator (Fig. 5b).

Fig. 5: (a) Conventional DFT bandstructure for single-layer 1T-TaSe2 is metallic (as expected since each unit cell has 13 Ta4+ ions, and they each provide one d-electron). (b) DFT+U bandstructure shows the opening of a Mott insulating energy gap. The energy gap size is independent of the magnetic groundstate.

The theoretical DFT+U band structure leads to a density-of-states (DOS) and electronic wavefunction patterns that match many of the features seen experimentally.5 5 For example, the experimental DOS features marked V1, C1, C2, and C3 in Fig. 4a are all reproduced in the theoretical DOS Fig. 6a. The theoretical valence band orbital texture (Figs. 6b, c) also matches the experimental features of Fig. 4 well, as does the higher-energy conduction band features (Figs. 6f-h). The low-energy conduction band features (circled in Figs. 4b, e), however, are strikingly different for the experiment (Fig. 4) compared to the DFT + U theory (Fig. 6). The most likely explanation for this is that strong electron correlations in single-layer 1T-TaSe2 cannot be accounted for using current DFT techniques.

Fig. 6: Theoretical density of states and wavefunction distributions (local density of states) for single-layer 1T-TaSe2 at different energies calculated via DFT+U. Comparison of this simulation to the experimental data of Fig. 4 shows that DFT+U correctly captures many features of the 1T-TaSe2 electronic structure, but cannot reproduce the novel orbital texture seen in the low-energy conduction bands (panels d, e (circled regions)).

References

1. Metal-insulator transitions. Masatoshi Imada, Atsushi Fujimori, Yoshinori Tokura. Rev. Mod. Phys. 70, 1039 (1998)

2. Electrical, structural and magnetic properties of pure and doped 1T-TaS2. P. Fazekas, E. Tosatti. Philos. Mag. B 39, 229-244 (1979).

3. Spectroscopic signatures of a bandwidth-controlled Mott transition at the surface of 1T-TaSe2. L. Perfetti, A. Georges, S. Florens, S. Biermann, S. Mitrovic, H. Berger, Y. Tomm, H. Hochst, M. Grioni. Phys. Rev. Lett. 90, 166401 (2003).

4. Mott phase at the surface of 1T-TaSe2 observed by scanning tunneling microscopy. Stefano Colonna, Fabio Ronci, Antonio Cricenti, Luca Perfetti, Helmuth Berger, Marco Grioni. Phys. Rev. Lett. 94, 036405 (2005).

5. 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