My Current Research Interests

The first direction I am interested in is the study of 2-dimensional Moiré materials, in particular the twisted bilayer graphene (TBG). The TBG is a superlattice known as the Moiré pattern formed by twisting and stacking two layers of graphene. At the so-called magic twist angle 1.1 degree, topological flat bands with strong interactions are formed in TBG, where electrons show remarkable interacting phenomena including superconductivity and correlated insulators. I am interested in understanding the mechanism of the strongly correlated phases in TBG and other Moiré materials, as well as predicting novel topological responses/phases in these systems. Recently, we have found an interesting Moiré model of graphene which can realize Kagome flat bands. My future interests include exploring topological superconductivity in Moiré systems, etc.

Another direction of my interest is on the interaction effects in topological phases of matter and topological phase transitions, e.g., the classification of gapless topological phases. Recently, I have been interested in the study of the effect of disorders and superconducting proximity in quantum Hall (QH) systems. A paradigm example is the the edge states of the v=2/3 FQH state, which after equilibration is known to have a charge 2e/3 downstream edge mode and a charge neutral upstream mode. We recently showed that under superconducting proximity, the edge states can be driven into infinitely many distinct gapless phases with downstream mode and upstream mode carrying different charges. These phases are stable against disorders. Moreover, they give rise to new quantized nonlocal resistances of the FQH-SC junction, which are different from the quantized Hall response. I am interested in generalizing the theory to study the phases of generic topological edge states with SC proximity or other type of interactions.

I am also interested in studying the quantum chaos, dynamics and entanglement of many-body quantum systems. We have studied the quantum integrability and chaos of 1+1 dimensional chiral Majorana fermions with 4-fermion interactions. In the large N fermion flavor limit, we can define a chiral Sachdev-Ye-Kitaev model, which is exactly solvable and show quantum chaos behavior. We also identify a transition from integrability to chaos at N=7. I am interested in further studying the integrability and chaos of generic 1+1D chiral models. More generally, I am interested in understanding the relations among different defining properties of quantum chaos, such as the level statistics, eigenstate-thermalization hypothesis, and the out-of-time-ordered correlation, etc. For instance, I have been developing a new method of the entanglement Hamiltonian superdensity matrix for obtaining the conserved quantities in the entanglement Hamiltonian of a quantum system. I am also studying to generalize the entanglement entropy into generic spacetime (e.g., timelike) slices. 

Another recent research direction of mine proposes a quantum breakdown model simulating the electrical breakdown of dielectrics, which shows surprisingly rich quantum dynamical properties of quantum chaos, many-body localization, and Hilbert space fragmentation. The model has an exponential U(1) symmetry, defined by a symmetry charge decaying exponentially in spatial coordinates. The ground states of the model can enter a spontaneous symmetry breaking phase, which surprisingly has no Goldstone modes. This suggests a new class of unconventional phases of matter never revealed before.

Selected Work

Pok Man Tam, Hao Chen, Biao Lian, Quantized Transport of Disordered Superconducting ν=2/3 Fractional Quantum Hall Edges, arXiv 2505.20398

Kaiyuan Gu, Kai Torrens, Biao Lian, Inevitable First Order Phase Transitions in 3D Quantum Hall Systems, arXiv 2406.11976

Yu-Min Hu, Biao Lian, The Bosonic Quantum Breakdown Hubbard Model, Phys. Rev. B 112, L100504 (2025)

Xinyu Liu, Alexander McDonald, Tokiro Numasawa, Biao Lian, Shinsei Ryu, Quantum Quenches of Conformal Field Theory with Open Boundary, Phys. Rev. Lett. 134, 220404 (2025)

Bowei Liu, Hao Chen, Biao Lian, Entanglement Entropy in Timelike Slices: a Free Fermion Study, Phys. Rev. B 110, 144306 (2024)

Michael Scheer, Biao Lian, Twistronics of Kekulé Graphene: Honeycomb and Kagome Flat Bands, PRL 131, 266501 (2023)

Biao Lian, A Quantum Breakdown Model: from Many-body Localization to Chaos with Scars, PRB 107, 115171 (2023)

Yichen Hu, Biao Lian, Integrability of the ν=4/3 fractional quantum Hall edge states, Quantum, 6, 736 (2022)

Biao Lian, Conserved Quantities from Entanglement Hamiltonian, PRB 105, 035106 (2022)

TBG series of work (TBG I-VI): PRB 103, 205411 to 205416 (2021)

Biao Lian, Zhaochen Liu, Yuanbo Zhang, Jing Wang, Flat Chern Band from Twisted Bilayer MnBi2Te4, PRL 124, 126402 (2020)

Biao Lian, S. L. Sondhi, Zhenbin Yang, The chiral SYK model, JHEP 09, 067 (2019)

Biao Lian, Zhijun Wang, B. Andrei Bernevig, Twisted Bilayer Graphene: A Phonon Driven Superconductor, PRL 122, 257002 (2019)

Biao Lian, Fang Xie, B. Andrei Bernevig, The Landau Level of Fragile Topology, PRB 102, 041402 (2020)

Biao Lian, Xiao-Qi Sun, Abolhassan Vaezi, Xiao-Liang Qi, Shou-Cheng Zhang, Topological Quantum Computation Based on Chiral Majorana Fermions, PNAS, 115 (43), 10938 (2018)

Biao Lian, Juven Wang, Theory of Disordered v=5/2 Quantum Thermal Hall State: Emergent Symmetry and Phase Diagram, PRB, 97, 165124 (2018)

Biao Lian, Shou-Cheng Zhang, Wave Function and Emergent SU(2) Symmetry in v=1 Quantum Hall Bilayer, Phys. Rev. Lett. 120, 077601 (2018)

Biao Lian, Cumrun Vafa, Farzan Vafa, Shou-Cheng Zhang, Chern-Simons Theory and Wilson Loops in the Brillouin zone, PRB 95, 094512 (2017)

Biao Lian, Shou-Cheng Zhang, Five Dimensional Generalization of the Topological Weyl Semimetal, PRB, 94, 041105 (2016)

Gang Xu, Biao Lian, Peizhe Tang, Xiao-Liang Qi, Shou-Cheng Zhang, Topological Superconductivity on the surface of Fe-based superconductors, PRL, 117, 047001 (2016)

Jing Wang, Quan Zhou, Biao Lian, Shou-Cheng Zhang, Chiral Topological Superconductor and Half-Integer Conductance Plateau from Quantum Anomalous Hall Plateau Transition, PRB, 92, 064520 (2015)

Jing Wang, Biao Lian, Shou-Cheng Zhang, Universal Scaling of Quantum Anomalous Hall Plateau Transition, PRB, 89, 085106 (2014)

Jing Wang, Biao Lian, Haijun Zhang, Yong Xu, Shou-Cheng Zhang, Quantum Anomalous Hall Effect with Higher Plateaus, PRL, 111, 136801 (2013)

Biao Lian, Tin-Lun Ho, Hui Zhai, Searching for Non-Abelian Phases in the Bose-Einstein Condensate of Dysprosium, PRA, 85, 051606 (2012)

Publications

List of publications