Charge Dynamics near Phase Transitions in Two-Dimensional Systems

Strongly correlated materials manifest some of the most intriguing behaviors found in condensed matter physics. However, their understanding remains a challenge because they cannot be described using standard theoretical approaches, as such systems are complex and typically have many competing degrees of freedom. Many strongly correlated systems are realized in layered or highly anisotropic materials, and they behave as effectively two-dimensional systems. When the dimensionality is reduced, fluctuations due to the competition between degrees of freedom are more pronounced and easier to observe. Anomalous transport properties are one of the hallmarks of strongly correlated materials; thus, charge transport measurements have proven remarkably effective for their study. This thesis focuses on three very different two-dimensional (2D) materials using charge transport to understand the origin of some of the observed behaviors. The electron system (ES) in Si metal-oxide-semiconductor field-effect transistors (MOSFETs) is a model strongly correlated system with only the interplay of Coulomb interactions and disorder. The insight from this simple system can help to build a more general picture of strongly correlated materials. Second, atomically thin layers of WSe2 produce a unique 2D system to study the universality of the correlated phenomena observed in Si MOSFETs. Finally, the Cu-O planes of La-214 compounds with charge and spin stripe order are complex materials, which behave effectively as 2D, with the interplay of many orders. By varying the dopant of the La-214 compound, the origin of the correlated behaviors can be probed. In the first two materials, the 2D MIT is controlled by applying a gate voltage. The existence of the 2D MIT is supported by an abundance of experimental data but remains poorly understood. Within experimental systems, both electron-electron interactions and disorder are present; however, the theory of their interplay is not fully developed. Studies performed on highly disordered Si MOSFETs suggest the importance of Coulomb interactions for the glassy dynamics observed at low electron densities. Therefore, the first study discussed in this thesis explores relaxations of conductivity in a strongly disordered 2DES with screened Coulomb interactions after the system is quenched—revealing the necessity of long-range Coulomb interactions for the existence of the collective (glassy) relaxation dynamics. Additionally, we have shown that, in the 2DES of the Si MOSFET weakly thermally coupled to the environment, abnormally long relaxations are observed in the presence of short-range interactions, suggesting that the system is in the proximity to a many-body-localized phase. Thus our results also demonstrate a promising new platform for exploring the breakdown of thermalization and MBL in real materials. Evidence of quantum criticality associated with the MIT has been almost exclusively studied in Si MOSFETs. Our second study reveals quantum criticality in WSe2 field-effect transistors showing that transition metal dichalcogenides are viable systems for the low-temperature investigation of the 2D MIT. Our scaling analysis found that the critical exponents agree with those found in low-disordered Si MOSFETs in the presence of local magnetic moments. These findings pave the way for further studies of the fundamental quantum mechanical properties of 2D transition metal dichalcogenides. The final study focuses on fluctuations of charge order (CO) and the magnetoresistance (MR) of stripe-ordered La-214 cuprates. The dynamics of CO are thought to be relevant for the unconventional properties of the normal state and high-temperature superconductivity. We report observations of dynamic charge stripes close to the charge order (and structural) transition in response to temperature perturbations but absent in magnetic field in La1.875Ba0.125CuO4. These dynamic behaviors are only observed when the transition is approached from the charge-ordered state. Additionally, a comparative analysis of the MR of several La-214 single crystals is presented to establish which behaviors are characteristic of the family of materials as opposed to dopant specific. Together, these three studies contribute to understanding the complex interplay of orders found in strongly correlated materials.