Photoinduced Enhancement of the Charge Density Wave Amplitude

Symmetry breaking and the emergence of order is one of the most fascinating phenomena in condensed matter physics. It leads to a plethora of intriguing ground states found in antiferromagnets, Mott insulators, superconductors, and density-wave systems. Exploiting states of matter far from equilibrium can provide even more striking routes to symmetry-lowered, ordered states. Here, we demonstrate for the case of elemental chromium that moderate ultrafast photoexcitation can transiently enhance the charge-density-wave (CDW) amplitude by up to 30% above its equilibrium value, while strong excitations lead to an oscillating, large-amplitude CDW state that persists above the equilibrium transition temperature. Both effects result from dynamic electron-phonon interactions, providing an efficient mechanism to selectively transform a broad excitation of the electronic order into a well-defined, long-lived coherent lattice vibration. This mechanism may be exploited to transiently enhance order parameters in other systems with coupled degrees of freedom.

Figure 1

Static x-ray diffraction data. (a) Schematic real space representation of the atomic positions in Cr in the presence of a CDW. The corresponding charge density modulation with the CDW amplitude $A$ and the scattering geometry are also shown. (b) The potential energy surface for the CDW amplitude $A$. In the low-temperature ground state, the potential energy surface is shifted towards a nonvanishing value due to the electron-phonon (ep) coupling. (c) $\mathrm{X}$-ray diffraction from a Cr thin film recorded with synchrotron radiation around the (002) Bragg peak (in photons per second) measured at a film temperature of 115 K. The intensity is increased (reduced) at the positions of the CDW satellites for low (high) $q$ values (indicated by arrows). Insets: Diffraction patterns (linear scale) collected with the $\mathrm{x}$-ray free-electron laser at two different momentum transfers $q=2-2\delta$ and $q=2+2\delta$ in the ground state, corresponding to different incident angles of $\mathrm{x}$ rays.

Figure 2

Time resolved x-ray diffraction data. (a) Time dependence of the intensity in the vicinity of the CDW satellite at $q=2-2\delta$ (see Fig. 1) for a series of pump fluences (incident, $p$ polarization). (b) The black and red lines show the normalized transient intensity difference $\mathrm{\Delta }{I}_{\mathrm{CDW}}(\tau )=[I_{\mathrm{CDW}}(\tau )-I_{\mathrm{RT}}]/|I_{\mathrm{CDW},0}-I_{\mathrm{RT}}|$ at $q=2-2\delta$, where $I_{\mathrm{CDW}}$ is the data in (a), $I_{\mathrm{RT}}$ was measured at room temperature above $T_N$ without CDW, and $I_{\mathrm{CDW},0}$ was measured in the low-temperature ground state. The intensity difference rises above its initial value of one for low fluences and drops below zero as the fluence increases (indicated by arrows). The blue line shows $\mathrm{\Delta }{I}_{\mathrm{CDW}}(\tau )$ at $q=2+2\delta$ for a fluence of $2{\mathrm{mJ}/\mathrm{cm}}^2$ and starts at $-1$ due to destructive interference.

Figure 3

Interpretation of the time resolved x-ray diffraction data. (a),(b) $\mathrm{X}$-ray data around $q=2-2\delta$ (a) and the integral along the vertical direction (b) in photons per second recorded at time delays ${\tau }_0$ before 0 ps (blue solid line), ${\tau }_1=0.11\mathrm{ps}$ (black dashed line, $5{\mathrm{mJ}/\mathrm{cm}}^2$), ${\tau }_2=0.22\mathrm{ps}$ (magenta squares, $5{\mathrm{mJ}/\mathrm{cm}}^2$), and ${\tau }_3=0.45\mathrm{ps}$ (red circles, $1{\mathrm{mJ}/\mathrm{cm}}^2$). The time delays represent significant instants in the first period of the oscillation in Fig. 2. Insets in (a): Schematic representations of the charge density modulation that are consistent with the x-ray data for different time delays. The charge density at 0.11 ps is similar to the room temperature case, where no CDW is present. The scale bar in (a) shows $0.025{\AA }^{-1}$.

Figure 4

Enhancement of the CDW amplitude. (a),(b) The normalized intensity of the CDW satellite peak (see the caption of Fig. 2) as a function of the pump fluence and time delay for $q=2-2\delta$ (a) and $q=2+2\delta$ (b). (c) The transient amplitude of the CDW at 0.22 ps (top, first minimum of the oscillation in Fig. 2) and 0.45 ps (bottom, first maximum of the oscillation in Fig. 2) extracted as line scans along the white lines in (a) and (b). (d) A schematic illustration of the mechanism behind the enhancement of the CDW amplitude due to dynamic electron-phonon interaction. The potential energy surfaces are drawn for the dynamic CDW amplitude, shown on the horizontal axis. $A_0$ is the amplitude of the CDW in the ground state, $A_1$ is the quasiequilibrium position after the excitation, and $A_F$ is its position after 10 ps. The transient amplitude $A(\tau )$ was fitted by the following equation $A(\tau )=A_F+B\cos (2\pi {\tau }^{\prime }/{\tau }_P)\exp (-{\tau }^{\prime }/{\tau }_D)-C\exp (-{\tau }^{\prime }/{\tau }_{\mathrm{ep}})$, where $B$ is the amplitude, ${\tau }_P$ the period, and ${\tau }_D$ the damping time of the oscillation, ${\tau }^{\prime }=\tau -{\tau }_0$, ${\tau }_0$ is the offset of the oscillation, $C=A_F-A_1$, and $t_{\mathrm{ep}}$ is the decay time for the shift of the quasiequilibrium towards $A_F$ [23].