Bose condensation has shaped our understanding of macroscopic quantum phenomena, having been realized in superconductors, atomic gases, and liquid helium. Excitons are bosons that have been predicted to condense into either a superfluid or an insulat
ing electronic crystal. Using the recently developed momentum-resolved electron energy-loss spectroscopy (M-EELS), we study electronic collective modes in the transition metal dichalcogenide semimetal, 1T-TiSe$_2$. Near the phase transition temperature, T$_c$ = 190 K, the energy of the electronic mode falls to zero at nonzero momentum, indicating dynamical slowing down of plasma fluctuations and crystallization of the valence electrons into an exciton condensate. Our study provides compelling evidence for exciton condensation in a three-dimensional solid and establishes M-EELS as a versatile technique sensitive to valence band excitations in quantum materials.
One of the most fundamental properties of an interacting electron system is its frequency- and wave-vector-dependent density response function, $chi({bf q},omega)$. The imaginary part, $chi({bf q},omega)$, defines the fundamental bosonic charge excit
ations of the system, exhibiting peaks wherever collective modes are present. $chi$ quantifies the electronic compressibility of a material, its response to external fields, its ability to screen charge, and its tendency to form charge density waves. Unfortunately, there has never been a fully momentum-resolved means to measure $chi({bf q},omega)$ at the meV energy scale relevant to modern elecronic materials. Here, we demonstrate a way to measure $chi$ with quantitative momentum resolution by applying alignment techniques from x-ray and neutron scattering to surface high-resolution electron energy-loss spectroscopy (HR-EELS). This approach, which we refer to here as M-EELS, allows direct measurement of $chi({bf q},omega)$ with meV resolution while controlling the momentum with an accuracy better than a percent of a typical Brillouin zone. We apply this technique to finite-q excitations in the optimally-doped high temperature superconductor, Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (Bi2212), which exhibits several phonons potentially relevant to dispersion anomalies observed in ARPES and STM experiments. Our study defines a path to studying the long-sought collective charge modes in quantum materials at the meV scale and with full momentum control.
