Time- and angle-resolved photoemission spectroscopy

Time- and angle-resolved photoemission spectroscopy (TrARPES) is an advanced experimental technique used to investigate the dynamics of electrons in materials on ultrafast timescales. It combines time-resolved techniques with angle-resolved photoemission spectroscopy (ARPES) to capture the evolution of electron behavior in real-time and reveal important information about the electronic structure and dynamics of a material. TrARPES is particularly useful for studying materials with complex electronic behaviors, such as superconductors, topological materials, and quantum materials. 

Key Concepts:

1. Photoemission Spectroscopy (ARPES):

   • ARPES is a standard technique that provides detailed information about the energy and momentum of electrons in a material by measuring the energy and angle of photoelectrons emitted when the material is illuminated by light (usually ultraviolet or X-ray).

   • It produces a band structure map that reveals how electrons behave in different energy states in momentum space (k-space), essentially showing the electronic structure of the material.

   • The angle at which the emitted electrons are detected provides information about the momentum of those electrons, while the energy provides information about their energy state.

2. Time-Resolved Aspect:

   • TrARPES extends traditional ARPES by introducing time resolution. This is achieved using femtosecond (fs) laser pulses to probe the material in real time.

   • A short laser pulse is used to excite the electrons, and subsequent pulses measure the changes in the electronic structure as the system evolves over time. This allows the tracking of ultrafast dynamics such as electron scattering, phase transitions, and relaxation processes.

   • The time resolution of TrARPES can be on the order of femtoseconds (10⁻¹⁵ seconds), enabling the study of fast phenomena like electron-hole pair dynamics, electron-phonon interactions, and even the ultrafast formation of new electronic states.

3. Angle-Resolved Aspect:

   • The angle-resolved part refers to detecting the angle at which the photoelectrons are emitted after excitation. This allows the measurement of the momentum of the electrons, which provides information about the band structure and the electron's energy dispersion in the material.

   • By mapping the angle of the emitted electrons, researchers can obtain high-resolution momentum-resolved information about the electronic structure at different points in time, helping to reveal how it changes dynamically in response to external excitations.

How it Works:

1. Excitation: The material is exposed to an ultrafast laser pulse (often femtosecond scale) that excites the electrons in the material. This pulse can induce changes in the material's electronic structure.

2. Photoemission: After excitation, the electrons in the material are ejected from the surface by photons from a second laser pulse (or sometimes the same laser if it's ultrafast enough). These emitted photoelectrons are then detected.

3. Time Delay: By varying the time delay between the excitation pulse and the probe pulse, the evolution of the photoelectron spectrum can be tracked over time.

4. Momentum and Energy Measurement: The energy and angle of the emitted photoelectrons are measured, allowing the reconstruction of the energy vs. momentum map of the electrons, which gives detailed information about the electronic states.