Visualizing the boundary modes of the charge density wave in a topological material

Charge density waves are quantum phenomena occurring in some materials, which involve a static modulation of conduction electrons and the periodic distortion of the lattice. These waves have been observed in numerous condensed matter materials, including high-temperature superconductors and quantum Hall systems.

While many studies have investigated these states, so far experimental observations of the boundary states that emerge from charge density waves are still scarce. In a recent paper, published in Nature Physics, researchers at Princeton University and other institutes worldwide have visualized the bulk and boundary modes of the charge density wave in the topological material Ta₂Se₈I.

“Our research group focuses on discovering and investigating novel topological properties of quantum matter utilizing various state-of-the-art experimental techniques that probe electronic structure of the materials,” Maksim Litskevich, co-author of the paper, told Phys.org. “In recent years, the physics community has experienced excitement exploring the intriguing and rich properties of Kagome materials, which intricately intertwine geometry, topology, and electronic interactions.”

Litskevich and his colleagues were pioneers in the study of charge density waves. A few years ago, they discovered the coexistence of a charge density wave, a many-body quantum state characterized by a spatial modulation of the electronic charge and an insulating energy gap, and a gapless edge mode in FeGe, one of the Kagome materials.

While the researchers observed these two coexisting states in FeGe, this does not necessarily imply that one state caused the other. In fact, the edge state could also be trivial (non-topological) or could alternatively originate from a topology that is unrelated to the charge density wave.

“Inspired by the study of Kagome compounds, our research team continued a search for a link between charge density wave and topology, turning attention to a quasi-one-dimensional compound, Ta₂Se₈I, which exhibits topological properties and undergoes a transition to the charge density wave state (below -10 degrees Celsius),” Litskevich said.

“Excitingly, our scanning tunneling microscopy measurements revealed an in-gap boundary mode (edge state) within a low-temperature charge density wave state, followed by its vanishing in the high-temperature Weyl semi-metal state.”

Litskevich and his colleagues found that the spatial periodicity and phase of the boundary mode oscillations they observed were closely related to the characteristics of the charge density wave in Ta₂Se₈I. This co-dependent relation suggests that there is an inherent relationship between the boundary mode and the charge density wave, a hypothesis that they later confirmed via theoretical modeling.

“For the first time, we thus bridged the gap between topological and charge density wave systems, marking a progressive step towards unraveling the complexities of the quantum world,” Litskevich said.

To carry out their experiments, the researchers employed an experimental technique called scanning tunneling microscopy (STM). STM, which relies on thin long needle-like probes to image materials at the atomic level, allowed them to closely investigate and examine the quasi-1D material Ta₂Se₈I.

“We performed our measurements on Omicron LT STM (LT = low-temperature) at a temperature range of 160 K to 300 K (-113 to 27 degrees Celsius) in ultra-high vacuum conditions,” Litskevich said. “STM utilizes a phenomenon of quantum tunneling between a sharp metallic tip and the conducting surface of the sample. Due to the quantum tunneling, mobile electrons can leak out between the tip and sample, thereby producing a tiny electrical current detected by the sensitive electronics.”

The tunneling current detected by the STM probes is subsequently used to image the surface of materials with subatomic definition. By analyzing the magnitude of the current as a function of applied voltage (a technique known as tunneling spectroscopy), the researchers were then also able to map out the population of electrons in the material by energy levels.

“In relation to our compound under study, Ta₂Se₈I, STM imaging allowed us to identify charge density wave state by highlighting the difference in the electrical current produced by the low and high charged regions,” Litskevich said. “Furthermore, upon directing our tunneling current from the tip to the atomically sharp edge of the sample, we detected an in-gap boundary mode in the charge density wave state of Ta₂Se₈I.”

Litskevich and his colleagues observed the first visualization of a unique topological boundary mode arising from the charge density wave of Ta₂Se₈I. The observation of this mode improves the understanding of charge density waves, paving the way for further studies in this field.

“The topological boundary mode we observed, associated with the charge density wave, exhibits a unique topology distinct from traditional quantum spin Hall edge modes,” Md Shafayat Hossain, co-author of the paper, told Phys.org. “Instead of the usual spectral flow of the associated momentum magnitude, we observe a ‘spectral pseudo flow’ of the momentum phase. Specifically, the wavevector phase of the charge density wave remains gapless and connects the phases of the gapped bulk, representing a highly exotic state.”

The researchers found that the insulating gap induced by the charge density wave in Ta₂Se₈I and its in-gap boundary mode is remarkably robust, persisting at temperatures up to 260 K. This temperature robustness could be favorable for various applications and could facilitate the development of new technologies that leverage this mode.

“The implications of our findings are multifaceted,” Hossain said. “The ground state of the charge-ordered phase in Ta₂Se₈I (our material platform) is predicted to be an axion insulator, a highly sought-after phase of matter. However, we find that Ta₂Se₈I lacks the topological surface state expected from a non-magnetic axion insulator.”

While the observations gathered by Litskevich, Hossain and their colleagues highlight the topological nature of the charge-ordered phase, they cast doubts on some prior theoretical interpretations. Specifically, they suggest that in contrast with previous hypotheses, Ta₂Se₈I might not be an axion insulator.

“We anticipate that our work will inspire the broader scientific community to search for additional CDW (broken symmetry) phases in topological materials, thereby advancing the understanding of the interplay between these novel phenomena,” Hossain said. “In Prof. Zahid Hasan’s group at Princeton, we are dedicating focused efforts to discovering novel quantum phases of matter.”

The new phase identified by this research team opens new interesting research avenues. Building on their recent discovery, Litskevich, Hossain and their colleagues now plan to explore new quantum phenomena emerging from the interplay between charge density waves and a material’s topology. For instance, they will further examine the known parallels between charge density waves and superconductivities.

“Just as the intertwining of topology and superconductivity leads to topological superconductivity—a highly promising platform for topological quantum computations—topological charge density waves could also be important for future quantum computing and nanotechnologies,” Hossain added. “We intend to explore these possibilities further. Our immediate goal is to determine the order parameters associated with this exotic quantum state.”

In their next studies, Hossain and his colleagues also plan to investigate other quantum materials exhibiting charge density waves, in search of similar phenomena. Finally, they will continue their quest to uncover new phenomena in quantum materials and hope that this will lead to new interesting discoveries.

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