Research
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. An interesting subarea is quantum Hall (QH) systems with half integer fillings. Recently, it is observed that the v=5/2 filling QH state shows a thermal Hall conductance inconsistent with the predicted Pfaffian or anti-Pfaffian state. While a lately proposed PH-Pfaffian state agrees with the experiment, it is not favored in numerical calculations. We studied that domain-wall disorders can possibly stabilize the PH-Pfaffian state, and we investigated the effects of such domain walls in heat capacity. The v=1/2+1/2 QH bilayer is another interesting system, which exhibits exciton superfluidity. We identified a new regime of intermediate layer distances governed by composite boson excitons, which may be related to the different superfluid transition point recently observed in graphene compared to that in GaAs. Besides, I am interested in studying the effect of interactions and disorders in the transport of quantum anomalous Hall (QAH) effect and topological superconductors. I am also interested in classifying gapless topological phases. A series of my work is on proposing the topological linking invariants in 3-dimensional nodal line superconductors and 5-dimensional Weyl semimetals.
Most recently, I am 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 (Lian, Sondhi, Yang, The chiral SYK model, JHEP 09, 067 (2019)). 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 studying 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 paper of mine proposes a quantum model for the electrical breakdown of dielectrics, which shows surprisingly rich physics of many-body localization, quantum chaos and quantum scars.
Selected Work
Yichen Hu, Biao Lian, The Bosonic Quantum Breakdown Hubbard Model, arXiv 2401.04309
Xinyu Liu, Alexander McDonald, Tokiro Numasawa, Biao Lian, Shinsei Ryu, Quantum Quenches of Conformal Field Theory with Open Boundary, arXiv 2309.04540
Michael Scheer, Biao Lian, Twistronics of Kekulé Graphene: Honeycomb and Kagome Flat Bands, PRL 131, 266501 (2023)
Bowei Liu, Hao Chen, Biao Lian, Entanglement Entropy in Timelike Slices: a Free Fermion Study, arXiv 2210.03134
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)