Multiple Electronic Phases Coexisting under Inhomogeneous Strains in the Correlated Insulator

Abstract

Monolayer transition metal dichalcogenides (TMDs) can host exotic phenomena such as correlated insulating and charge-density-wave (CDW) phases. Such properties are strongly dependent on the precise atomic arrangements. Strain, as an effective tuning parameter in atomic arrangements, has been widely used for tailoring material's structures and related properties, yet to date, a convincing demonstration of strain-induced dedicate phase transition at nanometer scale in monolayer TMDs has been lacking. Here, a strain engineering technique is developed to controllably introduce out-of-plane atomic deformations in monolayer CDW material 1T-NbSe₂ . The scanning tunneling microscopy and spectroscopy (STM and STS) measurements, accompanied by first-principles calculations, demonstrate that the CDW phase of 1T-NbSe₂ can survive under both tensile and compressive strains even up to 5%. Moreover, significant strain-induced phase transitions are observed, i.e., tensile (compressive) strains can drive 1T-NbSe₂ from an intrinsic-correlated insulator into a band insulator (metal). Furthermore, experimental evidence of the multiple electronic phase coexistence at the nanoscale is provided. The results shed new lights on the strain engineering of correlated insulator and useful for design and development of strain-related nanodevices.

Keywords: charge-density-wave; correlated insulator; inhomogeneous strain; scanning tunneling microscopy.

Figure 1

Nanoscale control of strains in monolayer 1T‐NbSe₂. a) Schematic of the MBE growth of monolayer 1T‐NbSe₂ islands on SiC(0001) substrates that are covered with BLG wrinkles. The BLG wrinkles are controllably generated when the annealing temperature exceeds 1350 °C. The NbSe₂ islands are then epitaxially grown on and off the BLG wrinkles by directly evaporating Nb and Se atoms under a rich Se environment. b) Representative STM image of monolayer 1T‐NbSe₂ islands on and off the BLG wrinkles (V _s = –2.0 V, I_t = 5 pA). The BLG wrinkles can be clearly identified as one‐dimensional protrusions with the apparent heights, exhibiting in the STM images of about 1 nm. c,d) Nanoscale control of monolayer 1T‐NbSe₂ islands on and off the BLG wrinkles via an in‐situ STM manipulation technique (V _s = –1.0 V, I_t = 5 pA).

Figure 2

Atomic structures of monolayer 1T‐NbSe₂ under strains. a) Large‐scale STM image of monolayer 1T‐NbSe₂ islands on BLG wrinkles (V _s = –2.0 V, I_t = 5 pA). b) Zoomed‐in atomic‐resolution STM image of monolayer NbSe₂ on pristine BLG (V _s = –1.0 V, I_t = 2 nA). a₁/a₂ and b₁/b₂ represent the basis vectors of 1 × 1 atomic lattices and √13 × √13 CDW lattices, respectively. c) The height profile along the blue arrow in panel b. d) Zoomed‐in atomic‐resolution STM image of monolayer NbSe₂ on BLG wrinkle (V _s = –1.0 V, I_t = 1.5 nA). The center Nb atom in each SOD is marked by the pink dot. e) The height profile along the red arrow in panel d, demonstrating the apparent height and width of the wrinkle in the STM image are about 1.10 and 7.57 nm, respectively. f) Schematic of the strain distribution. g) CDW formation energy ΔE _CDW as a function of the strain ε. Positive and negative ε represent tensile and compressive strains, respectively. The dashed line is a guide to the eyes.

Figure 3

Electronic structures of monolayer 1T‐NbSe₂ under strains. a) Typical STM image of monolayer NbSe₂ islands on BLG wrinkles (V _s = –1.0 V, I_t = 1.5 nA). The intrinsic superlattice constant of monolayer NbSe₂ in the CDW phase without strain x ₀ is marked by the double‐headed arrow. The multiphase coexisting behavior induced by inhomogeneous strains is marked in the panel. b–e) Typical STS spectra acquired at the center of SOD clusters marked in panel a (V _s = –1.0 V, I_t = 1.5 nA). Δx is the difference between x and x ₀, where x is the measured average superlattice constant in three dimensions by considering the nearest two neighbors of CDW clusters. Δx > 0 and Δx < 0 represent tensile and compressive strains, respectively. The energy gap E _gap can be acquired from the STS spectra, as marked in the panels. f) The average energy gap E _gap and the corresponding error bars as a function of Δx/x ₀.

Figure 4

Strain‐tuned band structures of monolayer 1T‐NbSe₂ in the CDW phase. a–c) DFT calculations of the band structures of 1T‐NbSe₂ in the CDW phase under the strains ε = –3%, 0%, and 3%, respectively. The dashed and solid blue lines represent the up and down spin bands, respectively. The $d_{z^2}$ orbital is highlighted by the red dots, and the size of the dots is proportional to the Nb central‐atom $d_{z^2-r^2}$ orbital character within each SOD cluster. The real‐space charge density distribution of the $d_{z^2}$ orbital is given in the inset of panel b. d–f) Corresponding schematic energy level diagrams of 1T‐NbSe₂ in the CDW phase under the strains ε = –3%, 0%, and 3%, respectively. Without consideration of the strong electronic correlation, there is a flat band $d_{z^2}$, which is mainly contributed by the central Nb atom of each SOD cluster. Once the flat band is at the Fermi level, strong electronic correlation further splits the flat band into UHB and LHB. g) Theoretical calculation of the energy gap and the total magnetic moment per SOD cluster of 1T‐NbSe₂ in the CDW phase as a function of ε.