Understanding the correlated orders in layered materials

Abstract

The emergence of correlated phases in low-dimensional quantum materials presents a platform for discovering new physics and phenomenon. These emergent orders such as charge density wave (CDW), magnetism, superconductivity, and their coexistence arise from the strong relationship between electron–electron, electron–phonon, and spin–orbit interactions. Understanding how these correlated orders emerge, compete, and coexist remains a key challenge in condensed matter systems. This thesis work explores the fundamental mechanisms and experimental signatures of such correlated orders in a different two dimensional (2D) layered materials using STM, STS, and HRTEM. We begin by developing a theoretical understanding for CDW formation and magnetic ordering in 2D systems. We discuss Peierls instability, Fermi surface nesting (FSN), Kohn anomalies, and excitonic condensation as distinct pathways to charge ordering. We further explore the implications of the Mermin-Wagner theorem and the role of magnetic anisotropy in stabilizing long-range order in 2D magnets. These insights set the stage for understanding the interplay between competing and cooperative correlated orders in real materials. Our first experimental study focuses on the CDW phase transition in 1T-TiSe2, a transition metal dichalcogenide (TMDC). By performing temperature-dependent STM/STS on samples with varying levels of Ti intercalation, we capture the spatial evolution of CDW modulations and their impact on the LDOS. These observations are further supported by complementary Raman spectroscopy and reveal that Ti doping Tune the CDW transition temperature offering insight into how disorder and electron doping tune the emergent phase. The second study explores Fe5−𝑥GeTe2, a van der Waals ferromagnet exhibiting 𝑇𝑐 above room temperature. STM imaging unveils the coexistence of two structural ordering patterns, specifically, √3𝑎 ×√3𝑎 and 2𝑎 × 1𝑎 modulations, which exhibit distinct spectroscopic features. SQUID magnetometry measurements provide bulk magnetic characterizations, while density functional theory (DFT) results offer insight into different Fe site with Te hybridization and magnetic anisotropy. Together, these techniques reveal the close connection between local atomic arrangements and macroscopic magnetic properties in Fe-based vdW magnets. Our third detailed investigation is on Mn-doped CsV3Sb5, a kagome metal of intense current interest due to its exotic electronic states, including time-reversal symmetry-breaking charge order. We discover 𝜋-phase shifts in Cs atomic positions across step edges and capture temperature-induced Cs desorption, exposing the underlying Sb surface. Low-temperature STM studies reveal three surface regions with low-Cs disordered, √ 3𝑎 × √ 3𝑎 ordered (half-Cs), and high-Cs disordered regions. STS measurements across these regions show distinct features in the LDOS, including a spectral shift from 88 meV to 171 meV, depending on local Cs ordering. These findings suggest that Cs atoms not only reconstruct into an ordered-disordered structure but also modulate the local electronic states, highlighting the correlation among the Cs atoms over the surface. Collectively, the results in this thesis underscore the power of STM and STS in elucidating the relationship between surface structure and electronic behavior in strongly correlated systems. By combining real-space imaging with spectroscopy and theoretical models, we demonstrate how external perturbations such as doping, temperature, and disorder can drive or suppress various correlated orders. This work provides a framework for engineering emergent quantum phases in layered materials and offers guiding principles for future investigations into symmetry breaking phenomena in quantum matter.