Electron-phonon-driven three-dimensional metallicity in an insulating cuprate

Abstract

The role of the crystal lattice for the electronic properties of cuprates and other high-temperature superconductors remains controversial despite decades of theoretical and experimental efforts. While the paradigm of strong electronic correlations suggests a purely electronic mechanism behind the insulator-to-metal transition, recently the mutual enhancement of the electron-electron and the electron-phonon interaction and its relevance to the formation of the ordered phases have also been emphasized. Here, we combine polarization-resolved ultrafast optical spectroscopy and state-of-the-art dynamical mean-field theory to show the importance of the crystal lattice in the breakdown of the correlated insulating state in an archetypal undoped cuprate. We identify signatures of electron-phonon coupling to specific fully symmetric optical modes during the buildup of a three-dimensional (3D) metallic state that follows charge photodoping. Calculations for coherently displaced crystal structures along the relevant phonon coordinates indicate that the insulating state is remarkably unstable toward metallization despite the seemingly large charge-transfer energy scale. This hitherto unobserved insulator-to-metal transition mediated by fully symmetric lattice modes can find extensive application in a plethora of correlated solids.

Keywords: cuprates; electron–phonon coupling; insulator–metal transition; ultrafast optics.

Fig. 1.

(A) Crystallographic structure of ${\mathrm{L}\mathrm{a}}_2{\mathrm{C}\mathrm{u}\mathrm{O}}_4$ in its low-temperature orthorhombic unit cell. The Cu atoms are depicted in black, the O atoms in red, and the La atoms in violet. The brown shading emphasizes the ${\mathrm{C}\mathrm{u}\mathrm{O}}_6$ octahedron in the center. (B) Schematic representation of the interacting density of states in undoped insulating (Left) and photodoped metallic (Right) ${\mathrm{L}\mathrm{a}}_2{\mathrm{C}\mathrm{u}\mathrm{O}}_4$. The O-2$p$, lower Hubbard band (LHB), upper Hubbard band (UHB), and quasiparticle (QP) peak are indicated. In the insulating case, the optical charge-transfer gap (${\mathrm{\Delta }}_{\text{CT}}$) is also specified. The blue arrow indicates the 3.10-eV pump pulse, which photodopes the material and creates particle–hole pairs across the charge-transfer gap. The multicolored arrow is the broadband probe pulse, which monitors the high-energy response of the material after photoexcitation. (C) Real part of the optical conductivity at 10 K, measured with the electric field polarized along the $a$ axis (violet solid curve) and the $c$ axis (brown solid curve). The shaded area represents the spectral region monitored by the broadband probe pulse in the nonequilibrium experiment. The theory data for the in-plane response are shown as a violet dashed curve. The $a$-axis response comprises a well-defined peak in correspondence to the optical charge-transfer gap around 2.20 eV and a tail extending toward low energies down to 1.00 eV. In contrast, the $c$-axis response is featureless and increases monotonically with increasing energy, as expected from a particle–hole continuum. Exp. and The. in C refer to the experimental and theoretical results, respectively.

Fig. 2.

(A and B) Color-coded maps of the differential optical conductivity ($\mathrm{\Delta }{\sigma }_1$) at 10 K with in-plane pump polarization and ($A$) in-plane and ($B$) out-of-plane probe polarization, as a function of probe photon energy and pump–probe time delay. The pump photon energy is 3.10 eV and the excitation photon density is $x_{ph}\hspace{0.17em}\sim$ 0.06 photons per copper atom. For in-plane probe polarization ($A$), we observe a significantly reduced $\mathrm{\Delta }{\sigma }_1$ above the optical CT edge at 1.80 eV, due to spectral weight redistribution to lower energies. For out-of-plane probe polarization ($B$), the depletion in $\mathrm{\Delta }{\sigma }_1$ is considerably weaker and rather featureless. Oscillatory behavior is visible in the color-coded map, hinting at coherently excited phonon modes. (C and D) Snapshots of the same data as in A and B at three different pump–probe time delays during the rise (0.10 and 0.17 ps) and the relaxation (1.50 ps) of the response. (E and F) Temporal traces of $\mathrm{\Delta }{\sigma }_1$ along the $a$ and $c$ axes. Each temporal trace results from the integration over the energy window indicated by the shaded areas in C and D. The in-plane trace ($E$) shows a dramatic suppression and slow recovery without clearly visible coherent oscillations. A small peak emerges in the rise of the response, due to the light-induced metallic state (E, Inset). The out-of-plane trace ($F$) shows a clear signal that mimics the fast in-plane response, but relaxes with a tail exhibiting pronounced coherent oscillations (highlighted in Inset).

Fig. 3.

(A) Residual reflectivity change (normalized to the largest amplitude) after subtraction of the recovering background, exhibiting coherent oscillations due to collective bosonic modes. (B) Fast Fourier transform of data in $A$. The data in $A$ and $B$ refer to different pump and probe polarizations as indicated in $B$. The traces have been selected in the probe spectral region that maximizes the oscillatory response (2.00 to 2.20 eV for the violet curve and 1.80 to 2.20 eV for the brown and the green curves). Different polarizations show the presence of a set of totally symmetric ($A_g$) phonon modes of the orthorhombic crystal structure. The asterisks in $B$ indicate the phonon energy measured by spontaneous Raman scattering (25). a.u., arbitrary units. (C) Calculated eigenvectors of the five modes of $A_g$ symmetry. Black atoms refer to Cu, red atoms to O, and violet atoms to La. Modes $A_g\left(1\right)$ and $A_g\left(2\right)$ involve staggered rotations of ${\mathrm{C}\mathrm{u}\mathrm{O}}_6$ octahedra. Modes $A_g\left(3\right)$ and $A_g\left(4\right)$ present large $c$-axis displacements of the La atom, which in turn modify the La–apical O distance. The only difference between them lies in the displacement of the apical O: While its out-of-plane motion is the same, its in-plane motion occurs in the opposite direction. Mode $A_g\left(5\right)$ is the breathing mode of the apical O. The phonon spectrum has been computed using density-functional theory.

Fig. 4.

($A-C$) Many-body calculations of the in-plane optical conductivity for the ${\mathrm{L}\mathrm{a}}_2{\mathrm{C}\mathrm{u}\mathrm{O}}_4$ unit cell. Comparison between the response for the undisplaced structure (brown curve) and the response for the structure displaced by 0.04 Å along the phonon coordinates is indicated (violet curves). For displacements along totally symmetric modes (an example is shown in $A$), a metallic state emerges and gives rise to Drude spectral weight below $\sim$1.00 eV. In contrast, for displacements along $B_g$ modes (examples are given in B and C), there is no metallization and hence no impact on the low-energy spectral weight inside the optical charge-transfer gap.