Ultrafast investigations of the electron-phonon interaction

Two of the most impor tant aspects of the correlated electron chimera (Fig. V.1 b) are the electron and lattice degrees of freedom. One example of the electron-lattice interaction is the Peierls instability, discussed in the previous Section. Another is the phonon-mediated mechanism responsible for the creation of Cooper pairs in the BCS theory of (conventional) superconductivity. As evidenced by the following two examples, insight into this impor tant interaction can be won through the use of ultrafast time-resolved measurement techniques.

Electron pump – lattice probe

Let us feed the electron part of the chimera and see how the lattice part reacts. A convenient system for such studies is elemental bismuth, with its interesting crystal structure and lattice dynamics, together with a high atomic number, suitable for hard X-ray scattering. The Bi lattice structure is shown in Figure V.14, where the pair of atoms in each unit cell is indicated, with a separation along the c3 axis described by the coordinates x = (0.5±0.0332) a0, where a0 is the rhombohedral lattice constant. The deviation of these values from a0/2 is due to the Peierls instability discussed earlier. The atoms of a pair vibrate against one another in the A1g optical phonon mode, with a frequency of 2.9 THz. An ultrafast laser pulse excites the electronic system in Bi, altering its electronic state and, via the electronphonon interaction, causes a sudden (i.e., on the electronic time-scale) weakening of the interatomic potential – due to the par tial occupation of normally unoccupied anti-bonding orbitals (see Fig. V.15 a). As a result, the (slowly-moving) atoms no longer find themselves at potential minima, and they begin to oscillate coherently in the A1g phonon mode. This displacive excitation oscillation has been directly observed with pump-probe hard- X-ray diffraction at the laser-sliced FEMTO beamline at the SLS synchrotron (see Fig. V.15 b) [17]. The dependence of the interatomic potential on the degree of electronic excitation was determined in this experiment by observing a linear drop in the phonon frequency with increasing pulse fluence (inset in Fig. V.15 b), in excellent quantitative agreement with density functional theory calculations (see Fig. V.16 a) [18, 19]. With the extremely low flux at the laser-sliced FEMTO beamline (see Chapter II), each point in Figure V.15 b requires typically one minute of measurement time; with a more weakly scattering system than bismuth, this time increases by orders of magnitude. The ultra-high peak brightness of the SwissFEL, together with its 100–400 Hz repetition rate and the vir tually continuous tuning of the pump-probe delay, will allow detailed investigations of subtle diffraction features from technologically interesting but weakly scattering materials.

Lattice pump – electron probe

We have seen how pumping the electron par t of the correlated electron chimera influences the lattice. Can we also per form the inverse? In a purely optical experiment, Rini et al. have excited a par ticular phonon mode in a perovskite manganite and recorded the effect on the electron system [20]. With the replacement of Pr by the smaller Ca ion, the crystal structure of PrMnO3 undergoes a local tilt of the MnO6 octahedra, in the form of an or thorhombic distortion (see Fig. V.17). The electron hopping from Mn to Mn proceeds via an oxygen-mediated super-transfer mechanism, which depends on the orbital overlap between neighboring sites, and this overlap is sensitive to the octahedron tilt. Hence the distortion causes a decrease in the Hubbard model bandwidth parameter W, therefore giving rise to an insulating phase. Indeed, orthorhombic Pr1-xCaxMnO3 is insulating over a wide range of compositions and temperatures. At a phonon energy of 71 meV (ν = 17.2 THz, in the mid-IR), the Mn-O distance in Pr0.7Ca0.3MnO3 undergoes a periodic modulation, implying also a modulation in the Hubbard bandwidth W: one can hence envisage a dynamic metal-insulator transition. Rini et al. searched for this effect by per forming an IR-pump/visible-probe experiment [20], using the reflectivity of visible light to query the electron system. Their results are shown in Figure V.18. Note that IR-excitation leaves the system in its electronic ground-state. Using the visible reflectivity as a probe of electronic structure implies that one is sensitive only to changes in the electronic structure in the immediate vicinity of the Fermi energy. A more complete probe of local and cooperative electronic effects is possible using soft-X-ray spectroscopies such as XANES and RIXS. Hence an IRpump / soft-X-ray probe experiment at the SwissFEL has great potential for delivering a more complete picture of this type of dynamic MIT. A multitude of fur ther possibilities exist for SwissFELbased pump-probe investigations of the correlatedelectron chimera. We have seen that resonant soft-X-ray diffraction and inelastic scattering are sensitive to charge-, magnetic-, and even orbital-order, and the suggestion has been made that with a suitable pump pulse, one can melt the order and monitor its recovery. One could also excite and detect cooperative excitations of these ordered phases, such as orbitons [10], with resonant frequencies in the THz regime, accessible to the SwissFEL. Another possibility [21] is to use photo-excitation to effectively change the filling number, i.e., “photo-doping” the correlated electron system, and to use the SwissFEL to detect the resulting effects on the lattice and electronic systems.