Charge-density-waves (CDW) is one of the most fundamental collective quantum phenomena in solids. Charge density waves display periodic modulations of the charge with a period that is commensurate or incommensurate to the underlying lattice. Most CDW states are driven by the nesting topology of Fermi surfaces (FSs), i.e., the matching of sections of FS to others by a wave vector, where the electronic susceptibility has a divergence. A single-particle energy gap opens in the nested regions of the FSs at the transition, which leads to the lowering of the electronic energies of the system.

CDW also has collective excitations referred to as an amplitude mode (AM) and a phase mode. Phase excitation corresponds to the translational motion of the undistorted condensate. In ideal case, the phase mode should locate at zero energy since the translational motion does not change the condensation energy. In reality, due to the presence of impurity or defects, the phase mode is pinned at finite frequency, usually in the microwave frequency range. The pinning/depinning of phase mode has dramatic effect on charge transport properties. By applying dc electric field, the phase mode can be driven into a current-carrying state, usually referred to as sliding CDW, leading to nonlinear current-voltage characteristics. On the other hand, the amplitude mode involves the ionic displacement and has a finite energy. For most CDW materials, the amplitude mode has an energy scale of about 10 meV. Generally, amplitude modes can be treated as optical phonons, reflecting the oscillations of ions. Nevertheless, its effect on low temperature physical properties of CDW condensate has been much less studied.

Nan-Lin Wang’s group recently studied a complex CDW compound LaAgSb2, which crystallizes in simple tetragonal ZrCuSi2 structures and experiences two CDW phase transitions around 207 K and 184 K, respectively. The modulation wave vectors corresponding to the CDW orderings were identified to be (0.026, 0, 0) for the higher temperature transition and (0, 0, 0.16) for the lower one by early X-ray diffractions, both of which are unusually small. Wang’s group successfully grew large pieces of LaAgSb2 single crystals and studied their charge excitation and dynamical properties by performing optical spectroscopy and ultrafast pump-probe measurements. The development of energy gaps were clearly observed below the phase transition temperatures in optical conductivity, which removes most part of the free carrier spectral weight. Time resolved measurement demonstrated the emergence of strong oscillations upon entering the CDW states, which were illuminated to come from the amplitude mode of CDW collective excitations. The frequencies of them are surprisingly low: only 0.12 THz (about 0.5 meV) for the CDW order with higher transition temperature and 0.34 THz (about 1.4 meV) for the lower one, which shall be caused by their small modulation wave vectors. Furthermore, the amplitude and relaxation time of photoinduced reflectivity stayed unchanged across the two phase transitions, which might be connected to the extremely low energy scales of amplitude modes.

The very low energy scales of amplitude modes were not observed in any other known CDW materials. This work has been published in Physical Review Letter 118, 107402 (2017). Rong-Yan Chen (a postdoctor in Prof. Nan-Lin Wang’s group and now in the faculty of Department of Physics, Beijing Normal University) is the leading author of this work. The work was supported by the National Science Foundation of China, the National Key Research and Development Program of China, and the Collaborative Innovation Center of Quantum Matter in Beijing, China.

PhysRevLett.118.107402