# Sub-picosecond spin dynamics of excited states in the topological insulator Bi$_2$Te$_3$

## TL;DR

This study uses advanced photoemission techniques to explore ultrafast spin dynamics of excited electrons on Bi$_2$Te$_3$ surface, revealing spin relaxation processes and the dominance of electron-electron interactions in sub-picosecond regimes.

## Contribution

It provides the first detailed time-resolved analysis of spin textures and relaxation mechanisms of surface states in a topological insulator using fs-resolved photoemission.

## Key findings

- High-energy surface state relaxes in ~0.5 ps
- Spin dynamics of Dirac and low-energy states are coupled
- Electron-electron scattering dominates over electron-phonon interactions

## Abstract

Using time-, spin- and angle-resolved photoemission, we investigate the ultrafast spin dynamics of hot electrons on the surface of the topological insulator Bi$_2$Te$_3$ following optical excitation by fs-infrared pulses. We observe two surface-resonance states above the Fermi level coexisting with a transient population of Dirac fermions that relax in about $\sim$2 ps. One state is located below $\sim$0.4 eV just above the bulk continuum, the other one at $\sim$0.8 eV inside a projected bulk band gap. At the onset of the excitation, both states exhibit a reversed spin texture with respect to that of the transient Dirac bands, in agreement with our one-step photoemission calculations. Our data reveal that the high-energy state undergoes spin relaxation within $\sim$0.5 ps, a process that triggers the subsequent spin dynamics of both the Dirac cone and the low-energy state, which behave as two dynamically-locked electron populations. We discuss the origin of this behavior by comparing the relaxation times observed for electrons with opposite spins to the ones obtained from a microscopic Boltzmann model of ultrafast band cooling introduced into the photoemission calculations. Our results demonstrate that the nonequilibrium surface dynamics is governed by electron-electron rather than electron-phonon scattering, with a characteristic time scale unambiguously determined by the complex spin texture of excited states above the Fermi level. Our findings reveal the critical importance of detecting momentum and energy-resolved spin textures with fs resolution to fully understand the sub-ps dynamics of transient electrons on the surface of topological insulators.