Holographic imaging of the complex charge density wave order parameter

Abstract

The charge density wave (CDW) in solids is a collective ground state combining lattice distortions and charge ordering. It is defined by a complex order parameter with an amplitude and a phase. The amplitude and wavelength of the charge modulation are readily accessible to experiment. However, accurate measurements of the corresponding phase are significantly more challenging. Here we combine reciprocal and real space information to map the full complex order parameter based on topographic scanning tunneling microscopy (STM) images. Our technique overcomes limitations of earlier Fourier space based techniques to achieve distinct amplitude and phase images with high spatial resolution. Applying this analysis to transition metal dichalcogenides provides striking evidence that their CDWs consist of three individual charge modulations whose ordering vectors are connected by the fundamental rotational symmetry of the crystalline lattice. Spatial variations in the relative phases of these three modulations account for the different contrasts often observed in STM topographic images. Phase images further reveal topological defects and discommensurations, a singularity predicted by theory for a nearly commensurate CDW. Such precise real space mapping of the complex order parameter provides a powerful tool for a deeper understanding of the CDW ground state whose formation mechanisms remain largely unclear.

References in corpus (12)

• Electronic crystals: an experimental overview
• Controlling many-body states by the electric-field effect in a two-dimensional material
• Dislocations and vortices in pair density wave superconductors
• Topological Defects Coupling Smectic Modulations to Intra-unit-cell Nematicity in Cuprate
• Atomic-scale Electronic Structure of the Cuprate d-Symmetry Form Factor Density Wave State
• Commensurate Stripes and Phase Coherence in Manganites Revealed with Cryogenic Scanning Transmission Electron Microscopy
• Influence of domain walls in the incommensurate charge density wave state of Cu intercalated 1$T$-TiSe${}_2$
• Commensurate $4a_0$ period Charge Density Modulations throughout the $B{i}_{2}S{r}_{2}CaC{u}_2{O}_{8+x}$ Pseudogap Regime
• Bending and Breaking of Stripes in a Charge-Ordered Manganite
• Stripe and short range order in the charge density wave of 1T-Cu${}_x$TiSe${}_2$
• Short-range phase coherence and origin of the 1T-TiSe2 charge density wave
• Experimental evidence for a Bragg glass density wave phase in a transition-metal dichalcogenide

Cited by in corpus (11)

• Quantum textures of the many-body wavefunctions in magic-angle graphene
• Locally commensurate charge-density wave with three-unit-cell periodicity in YBCO
• Hydrodynamics of plastic deformations in electronic crystals
• Charge order from structured coupling in VSe${}_2$
• Visualization of alternating triangular domains of charge density waves in 2H-NbSe${}_2$ by scanning tunneling microscopy
• Origin of chirality in transition-metal dichalcogenides
• Melting of unidirectional charge density waves across twin domain boundaries in GdTe${}_3$
• Topologically trivial gap-filling in superconducting Fe(Se,Te) by one dimensional defects
• Stacking of charge-density waves in 2H-NbSe${}_2$ bilayers
• Delusive chirality and periodic strain pattern in moiré systems
• Multiband charge density wave exposed in a transition metal dichalcogenide