Ordered electronic states in 2D quantum materials: imaging effects of hydrostatic pressure at the atomic scale

Abstract text (incl. figure legends and references)

Introduction

Charge density waves (CDW) are an ordered electronic state with periodic modulation of electron density and periodic lattice distortion (PLD) modulation of the atomic positions.¹ CDW is represented by an order parameter Ψ =Δe^iφ characterized by a phase φ, giving position of the CDW with relation to the lattice, and amplitude,Δ, giving the value of the energy gap.¹ In some quantum materials, CDW are in competition / coexistence with the superconducting phase.^2-3 The nature of this relationship is still not well understood. Application of pressure is one experimental approach used to probe the nature of this relationship. ³ However, this also leads to the necessity to understand effects of pressure on the nature and the structure of the CDW at the atomic scale.

Objectives

Here, we have used atomic-scale transmission electron microscopy imaging to determine the influence of applied pressure on the structural properties of 1T-TaS₂ and the CDW at the atomic-scale.⁴

Materials & Methods

1T-TaS₂ samples were exposed to hydrostatic pressures of up to 2.5 GPa in a diamond anvil cell (DAC) (Fig.1 (a)). Pressurized samples were then prepared for TEM investigations through mechanical exfoliation. In high-resolution TEM (HRTEM) imaging CDW wave vectors and their respective phases are accessible and their evolution as a function of applied pressure can be mapped at the atomic scale.⁴

Results

A HRTEM image from a pressurized sample characterized by a deformation defect is shown in Fig. 1(b). Strong coupling of lattice and electronic degrees of freedom means that changes in lattice structure and ensuing deformation defects due to the applied pressure have an effect on the structure of the CDW electronic state. The modulation of CDW around the structural defect is shown in Figs 1(d)-(e). The magnitude of the CDW wave-length |λ₁| and the respective phase φ₁ are shown as intensity maps in Figs. 1(d) and (e) respectively. The high and low intensity in the magnitude images respectively show the elongated or shortened CDW wavelength. The magnitude of the CDW wavelength and its phase are strongly modulated in the vicinity of the deformation defects. This strong modulation is characterized by (1) CDW strain which leads to local changes in the modulation wavelenght (2) Topological phase defects in the CDW order parameter in form of CDW dislocations (marked by dotted circles in Figs. 1(c)-(d)).

Conclusion

In conclusion we have mapped the atomic-scale response of the CDW order parameter in 1T-TaS₂ exposed to 2.5 GPa hydrostatic pressure. The CDW order parameter responds to the lattice defects arising from the applied pressure by showing an elastic-like strain response and topological phase defects in the electronic order.

References

[1]^.J. Wilson, F. D. Salvo, and S. Mahajan, Adv. Phys. 24, 117 (1975).

[2] E. Fradkin et al., Rev. Mod. Phys. 87, 457 (2015)

[3] A. F. Kusmartseva et al., Phys. Rev. Lett. 103, 236401(2009)

[4] M. K. Kinyanjui et al.Phys. Rev. B 104, 125106(2021)

FIG. 1 (a) Diamond anvil cell set-up used for pressure experiments. (b) A HRTEM image showing a deformation defect in a 1T-TaS₂ sample pressurized up to 2.5 GPa (b) FT of the HRTEM image with the Bragg spots from the atomic lattice (solid circles) and super lattice spots from the CDW ( triangles). Temperature intensity maps representing (d) the magnitude (e) phase map of CDW wavelength. The dotted circles show the positions of CDW dislocations