Correlated electrons in low dimensions: from one-dimensional channels to two-dimensional networks

Chen-Hsuan Hsu^1*

¹Institute of Physics, Academia Sinica, Taipei, Taiwan

* Presenter:Chen-Hsuan Hsu, email:chenhsuan@gate.sinica.edu.tw

Low-dimensional nanoscale systems offer a compelling platform for exploring correlated electronic states. In one-dimensional (1D) systems, such as edges or hinges of topological materials [1,2], the influence of electron-electron interactions can be examined through the bosonization formalism. Building on this concept, recent works have explored phenomena beyond strictly 1D environments, including the transport features of quasi-1D quantum wires [3,4]. In this talk, we employ the bosonization formalism to discuss correlated electronic states in two-dimensional (2D) networks, stemming from 1D domain walls in twisted bilayer nanostructures. We construct operators that describe various scattering processes within these networks. We point out a category of scattering processes induced by a moiré periodic potential, which can lead to an insulating gapped bulk with gapless chiral edge modes at fractional fillings. We predict spectroscopic and transport features to detect the chiral edge modes. Notably, our approach allows us to complete a trio of investigations, exploring quantum Hall [5], quantum spin Hall [6], and quantum anomalous Hall states [7] from the coupled 1D systems.

*This work was financially supported by the National Science and Technology Council (NSTC), Taiwan through Grant No.NSTC-112-2112-M-001-025-MY3.

References:
[1] C.-H. Hsu et al., Semicond. Sci. Technol. 36, 123003 (2021).
[2] C.-H. Hsu et al., Phys. Rev. Lett. 121, 196801 (2018).
[3] C.-H. Hsu et al., Phys. Rev. Research 2, 043208 (2020).
[4] C.-H. Hsu et al., Phys. Rev. B 100, 195423 (2019).
[5] C. L. Kane et al., Phys. Rev. Lett. 88, 036401 (2002).
[6] J. Klinovaja and Y. Tserkovnyak, Phys. Rev. B 90, 115426 (2014).
[7] C.-H. Hsu et al., Phys. Rev. B 108, L121409 (2023).

Keywords: twisted bilayer systems, quantum anomalous Hall states, correlated electronic states, quantum-wire network, bosonization