Ballistic edge modes play a crucial role in the Quantum Hall Effect, the earliest phenomenon central to topological condensed matter physics. While the Hall effect typically yields a linear magnetic field dependence, clean 2D systems exhibit intermittent plateaus. These plateaus coincide with the presence of edge modes that propagate along the boundary of the system. Investigating these edge modes and their properties, such as origin and equilibration, is key to advancing our understanding. One approach involves fabricating novel gate-defined structures, such as quantum point contacts, to modify and probe the behavior of these edge modes. Intriguingly, recent discoveries have unveiled the existence of edge modes even at zero magnetic field, prompting inquiries into their origin, stability, and nature. 2D hexagonal lattice systems offer an ideal experimental platform to delve into the physics of edges, leveraging electrical transport measurements conducted at low temperatures.

Since the discovery of superconductivity, it has captivated the physics community, sparking intense theoretical and experimental exploration. The quest for high-temperature superconductors remains a prominent pursuit, with cuprate superconductors standing as a notable example. These materials consist of layered 2D superconducting planes of copper oxides stacked in the z-direction, yet their underlying mechanism remains under scrutiny. Notably, in such superconductors, the presence of charge density wave (CDW) phases often competes with superconductivity. Similar phenomena are observed in simpler layered van der Waals superconductors like 2H-NbSe2, where CDW phases coexist with superconductivity. Understanding the relationship between CDW and layered 2D superconductivity presents an intriguing challenge. The recent emergence of layered Kagome lattice superconductors offers a fresh avenue to explore this intricate interplay.

Studying noise is crucial for understanding the underlying physical mechanisms in various materials and devices. There are three primary sources of noise, each conveying distinct information: thermal noise, shot noise, and low-frequency 1/f noise. While thermal and shot noises are independent of frequency, their origins stem from the distribution function and discreteness of "dressed-up" effective charges. On the other hand, low-frequency 1/f noise arises from fluctuation processes and charge dynamics. Using noise techniques, we can probe characteristics of phases and their transition in between, which averaged resistance measurements cannot provide.