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Physical Review Letters reports Nan-Lin Wang group’s recent progress in collective excitations of charge density wave systems
《物理评论快报》发表王楠林课题组关于电荷密度波体系红外和超快光谱研究工作

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.

 



Figure 1. The photoinduced reflectivity △R/R as a function of time delay and temperature of LaAgSb2 in ultrafast pump-probe measurement.
 

  电荷密度波是固体电子系统的一种集体凝聚现象,表现为晶体中电荷密度的周期性调制,一般也同时伴随着出现新的晶格周期。作为多粒子系统的一种演生现象,电荷密度波一直是凝聚态物理感兴趣的前沿课题之一。

  电荷密度波状态中不仅可以有单粒子激发同时还存在集体激发。单粒子激发最重要的特征是存在能隙,反映出凝聚后的电子系统具有更低的基态能量,这与超导凝聚的单粒子激发非常类似。集体激发有两种模式,一种是相位子激发,表现为电荷密度波的横向集体运动;另外一种是振幅子激发,表现为电荷密度的纵向振动。理想情况下,电荷密度波的横向集体运动并不改变电荷密度波的凝聚能,因而相位子激发不需要能量。由于电荷密度波自然携带电荷的原因,零能的相位子集体激发(即电荷密度波的集体横向运动)应该导致材料无电阻的理想导电行为(超导)。实际材料由于有各种缺陷的存在,会将相位子激发钉扎在有限能量(通常在微波能量区间),因而并不出现理想的导电,通常只有当施加电场超过钉扎相位子激发的阈值时,电荷密度波材料才会出现显著的非线性电流电压行为,表现为电阻的急剧下降。这些现象通常称为电荷密度波的滑移,受到广泛的关注。另一方面,电荷密度波的纵向振幅子集体激发由于与晶格耦合在一起,其表现类似于晶格振动的光频支声子。理论上人们估算,振幅子激发的能量一般在10 meV量级。实验上,人们的确在多种电荷密度波材料上观察到这个能量尺度的振幅子激发。但总的说来对振幅子集体激发的研究非常之少。

  最近王楠林教授领导的课题组研究了一种复杂的电荷密度波材料LaAgSb2,这是一种二维层状结构材料,分别在207K和184K发生两个电荷密度波相变。这两个相变对应的电荷密度波的调制波矢非常小(或者说实空间的调制周期非常大),尤其是高温对应的相变其超格子调制周期几乎接近原晶格周期的40倍。利用红外光谱,他们发现低频光电导谱存在显著的压制,揭示电荷密度波相变导致单粒子激发谱上有能隙打开,绝大部分自由载流子由于费米面上打开能隙而丢失。尤其有意义的是,利用超快泵浦探测他们发现低温存在两个集体激发模式,其能量尺度非常小,在低温极限下分别只有0.12 THz (~0.5 meV)和0.34 THz (~1.4 meV)。通过改变探测光波长等多种实验条件,他们确认这两个集体模式分别对应于两个电荷密度波相变的振幅子集体激发模式。这是首次在电荷密度波材料中观察到能量尺度如此之小的振幅子激发。该研究揭示它们与很小的电荷密度波波矢相关联,并讨论了其可能的物理效应。

  该研究工作对认识电荷密度波的激发行为(尤其是集体激发)具有意义,已发表在《物理评论快报》118, 107402 (2017)。王楠林教授的博士后陈荣艳(现已任职北京师范大学物理系)是该文章的第一作者。上述研究得到国家自然科学基金、科技部国家重点研发计划以及量子物质科学协同创新中心等项目经费的资助。

  图形说明:不同温度下波长800 nm泵浦光激发所诱导的探测光反射率相对变化(以颜色强度表示)随时间延迟的依赖行为。