Simulating real-time electron dynamics in hBN by solving semiconductor Bloch differential equations

Resolving the real-time motion of electrons in complex systems is a key to enhancing the functionality and understanding the underlying mechanism of modern materials. Modern development in laser techniques of attosecond timescale gives us a tool to probe electron motion in a real-time resolution. However numerical simulation of the pump-probe spectroscopy experiments is a challenging task.

Solutions of Bethe-Salpeter equations [1,2] can give us the excitonic spectrum of the system, yet cannot give us time-resolved electron response to a laser beam. In our work, we propose to use the core-state-resolved Bloch equations (cBE) formalism [3,4], a set of differential equations derived from the microscopic model of the system written in the representation of second quantization. The non-equilibrium population of different bands can be extracted then from the time-dependent elements of the density matrix. Here we will show our calculations in which we are able to resolve the electron dynamics in hexagonal Boron Nitride (hBN) in a attosecond timescale.

[1] Henriques et al, J. Phys.: Cond. Mat. 32 025304 (2020)

[2] Rukelj et al, New J. Phys. 22  063052 (2020)

[3] Picón et al, J. Phys. 21 043029 (2019)

[4] Cistaro et al, Phys. Rev. Research 3 013144 (2021)