Zhaoyu Han - Quantum Hall

(Fractional) quantum Hall physics

Topics

Solvable lattice Hamiltonians with fractional Hall coefficients
A two-fluid theory of composite bosons & fermions and quantum Hall proximity effect
Quantum Hall ferromagnetism

Solvable lattice Hamiltonians with FQH coefficients

The conventional commuting projector construction for solvable models cannot work for topological orders without gappable boundary conditions, such as those with fractional Hall coefficients. We circumvent this limitation by considering the effects of small additional non-commuting terms.

Relevant Publications:

ZH and Jing-Yuan Chen. J. High Energ. Phys. 2023, 130 (2023). arXiv: 2208.13785
ZH and Jing-Yuan Chen. Phys. Rev. B 105, 155130 (2022). arXiv: 2107.02817

Talk slides:

Solvable Lattice Hamiltonians with Fractional Hall Conductivity.

A two-fluid theory

Composite boson or fermion pictures for fractional quantum Hall (FQH) effects are convenient for different scenarios. In this work, we consider a two-fluid description based on both theories, trying to describe the Hall fluid in a spatially varying magnetic field. We found a novel effect called the "quantum Hall proximity effect," which states that at an FQH-to-metal interface, the quantized transverse response will penetrate into the small magnetic field regime, much like how superconductivity may penetrate into a proximate metal. Moreover, we also obtain novel descriptions for soliton excitations in fractional quantum Hall states.

Relevant Publication:

ZH, Kyung-Su Kim, Steven A. Kivelson, and Thors Hans Hansson. Phys. Rev. B 108, 195117 (2023). arXiv: 2308.10190

Quantum Hall ferromagnetism

Degenerate landau levels usually exhibit quantum Hall ferromagnetism due to their flatness. In two experimental works with scanning single-electron transistor, this phenomena was observed in the Landau fans of two materials: magic angle twisted bilayer graphene and monolayer WSe2. Simple theoretical models are provided to explain the observed data, especially the gap size as a function of magnetic field.

Relevant Publications:

Jiachen Yu, Benjamin A Foutty, ZH, Mark E Barber, Yoni Schattner, Kenji Watanabe, Takashi Taniguchi, Philip Phillips, Zhi-Xun Shen, Steven A Kivelson, and Benjamin E Feldman. Nat. Phys. 18, 825–831 (2022). arXiv: 2108.00009
Benjamin A. Foutty, Vladimir Calvera, ZH, Carlos R. Kometter, Song Liu, Kenji Watanabe, Takashi Taniguchi, James C. Hone, Steven A. Kivelson, Benjamin E. Feldman. Phys. Rev. X 14, 031018 (2024). arXiv: 2401.01486