Our group specializes in ultrafast spectroscopic methods, enabling in-depth studies of material chemistry in intricate environments and the control of quantum phenomena on femtosecond timescales. In the first part of this seminar, I will discuss the role of lithium in various systems from its contribution to symmetry breaking (LiNbO
3), to an exotic quantum material (polar metal LiOsO
3), to unravel the reasons behind the low hopping rate of lithium ions at the surface of a solid-state electrolyte (Li
xLa
(2-x)/3TiO
3). All these systems share the common feature that Li occupies a symmetry-broken state which we can selectively probe using extreme-ultraviolet second-harmonic generation spectroscopy (XUV-SHG), a novel spectroscopy pioneered in my group. In the second part I will discuss recent results on 1
T-TiSe
2, a prototypical charge-density-wave (CDW) compound that also exhibits strong excitonic correlations in its low-temperature phase.
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