29,30 Thus, how the electronic order responds to coherent phonons provides unique opportunities for studying and manipulating electron–phonon coupling in quantum materials and, importantly, maps the light-enriched phase diagram. Ultrafast laser-excited coherent phonons 28 can modulate the electronic structure in a momentum-dependent way, which can be characterized by band- and mode-projected electron–phonon coupling strengths.

By monitoring either phonon-mediated electron scattering processes 23 or band dynamics in the presence of coherent phonons, 24–27 selectively coupled phonon modes can be investigated. 14–22 In particular, time- and angle-resolved photoemission spectroscopy (trARPES) combines the direct measurement of the electronic structure with the ability to probe electron–phonon couplings on their intrinsic timescales-from femtoseconds on up. 6–13 When combined with advanced ultrafast spectroscopy techniques, it is now possible to study electron–phonon coupling in the time domain. Ultrafast laser excitation of quantum materials can provide unique access to new light-induced states and their dominant couplings. However, it remains challenging to experimentally extract momentum-resolved information about specific phonon modes interacting with particular electronic bands. For a comprehensive investigation of the electron–phonon coupling, one needs to determine the electron–phonon matrix element g m n ν ( k, q )⁠, which measures the coupling strength for the electron scattering from an initial state in band n with momentum k to a final state in band m with momentum k + q⁠, via a phonon with mode ν at wave vector q⁠. 1 Techniques such as Raman, 3 neutron, 4 and x-ray scattering 5 can probe phonon modes in the frequency domain and provide information about the integrated electron–phonon coupling over all electronic bands. Recently, first-principle calculations of electron–phonon coupling have made it possible to predict the properties and behaviors of real materials. Despite decades of research, the physics underlying these phases is still elusive.

The correlated interactions of electrons and atoms in crystalline materials, including electron–phonon coupling, 1,2 play a crucial role in stabilizing emergent quantum phases such as charge density wave (CDW) order and superconductivity.

Wave state