Advanced processing of differential phase contrast data: Distinction between different causes of electron phase...

Area of Science:

• Materials Science
• Condensed Matter Physics
• Electron Microscopy

Background:

• Differential phase contrast (DPC) microscopy, a high-resolution technique, measures lateral momentum transfer in electron probes interacting with specimens.
• This momentum transfer is typically used to deduce electric fields and local charge density via the divergence of the electric field.
• Experimental data indicates that the curl of the measured vector field is often non-zero, suggesting additional physical phenomena.

Purpose of the Study:

• To apply Helmholtz decomposition to measured vector fields obtained from DPC microscopy.
• To interpret the physical significance of both the curl-free (divergence-free) and divergence-free (curl-free) components of these vector fields.
• To demonstrate the utility of the curl component for measuring geometric phases arising from crystal structure irregularities.

Main Methods:

• Utilized high-resolution differential phase contrast microscopy (also known as first moment microscopy or momentum resolved STEM).
• Applied the Helmholtz decomposition theorem to split measured electron momentum transfer vector fields into curl-free and divergence-free parts.
• Analyzed the physical implications of each component, particularly focusing on the interpretation of non-zero curl.

Main Results:

• Successfully decomposed the measured vector fields into their constituent curl-free and divergence-free components.
• Provided a detailed physical interpretation for both components of the vector field.
• Demonstrated that non-zero curl components in the measured momentum transfer can be directly correlated with geometric phases.

Conclusions:

• Helmholtz decomposition offers a powerful framework for interpreting DPC microscopy data.
• The curl component of the electron momentum transfer vector field is a sensitive probe for geometric phases.
• This method enables the characterization of crystal structure defects, such as screw dislocations, through the measurement of geometric phases.