Moiré quantum matter
The moiré systems have become the most promising platform for exploring novel quantum phases because of their high tunability. My recent interest lies in the Kondo-driven phases in magic-angle twisted bilayer graphene. In the near future, I plan to develop a systematic framework for interacting magic-angle twisted bilayer graphene.
Kondo Lattice Model in Magic-Angle Twisted Bilayer Graphene
We construct Kondo lattice models for magic-angle twisted bilayer graphene (MATBG) and reveal the existence of a Kondo-driven fragile topological semimetal. We further investigate the stability of the Dirac Kondo semimetal by constructing a quantum phase diagram showing the interplay between Kondo hybridization and magnetic correlation. The destruction of Kondo hybridization suggests that the magic-angle twisted bilayer graphene may be on the verge of a solid-state quantum simulator for novel magnetic orders on a triangular lattice.
Phys. Rev. Lett. 131, 026501 (2023)
In addition, we investigate the renormalization of Kondo coupling and the competing Hund's rule interaction in the low-energy limit, providing a semi-quantitative estimate for several quantities that are crucial for the interaction-driven phases in MATBG.
Mott-moiré excitons
We develop a systematic theory for excitons subject to Fermi-Hubbard physics in moiré twisted transition metal dichalcogenides (TMDs). Specifically, we consider excitons from two moiré bands with a Mott-insulating valence band sustaining 120 ∘ spin order. These “Mott-moiré excitons,” which are achievable in twisted TMD heterobilayers, are bound states of a magnetic polaron in the valence band and a free electron in the conduction band. We find significantly narrower exciton bandwidths in the presence of Hubbard physics, serving as a potential experimental signature of strong correlations. We also demonstrate the high tunability of Mott-moiré excitons through the dependence of their binding energies, diameters, and bandwidths on the moiré period. In addition, we study bound states between charges outside of the strongly correlated moiré band and find that these as well exhibit signatures of spin correlation. Our work provides guidelines for future exploration of strongly correlated excitons in triangular Hubbard systems such as twisted TMD heterobilayers.
Band manipulation and spin texture in interacting moiré helical edges
We develop a theory for manipulating the effective band structure of interacting helical edge states realized on the boundary of two-dimensional time-reversal symmetric topological insulators. An interacting edge band gap develops for sufficiently strong interaction, spontaneously breaking time-reversal symmetry on edge. The resulting spin texture and the energy of the time-reversal breaking gaps can be tuned by an external moiré potential (i.e., a superlattice potential). Remarkably, we establish that by adjusting the strength and period of the potential, the interacting gaps can be entirely suppressed, and interacting Dirac points re-emerge. In addition, nearly flat bands can be created by the moiré potential with a sufficiently long period. Our theory provides a novel way to enhance the coherence length of interacting helical edges by suppressing the interacting gap. The implications of this finding for ongoing experiments on helical edge states are discussed.
Charge density wave and non-Fermi liquid behavior in minimally TBLG
We study phenomena driven by electron-electron interactions in the minimally twisted bilayer graphene (mTBLG) with a perpendicular electric field. The low-energy degrees of freedom in mTBLG are governed by a network of one-dimensional domain-wall states, described by two channels of one-dimensional linearly dispersing spin-1/2 fermions. We show that the interaction can realize a spin-gapped inter-channel charge density wave (CDW) state at low temperatures, forming a "Coulomb drag" between the channels and leaving only one charge conducting mode. Power-law-in-temperature resistivity emerges from the charge umklapp scatterings within a domain wall for sufficiently high temperatures. Remarkably, the presence of the CDW states can strengthen the charge umklapp scattering and induce a resistivity minimum at an intermediate temperature corresponding to the CDW correlation energy. We further discuss the conditions in which the domain walls dominate the resistivity of the network. In particular, the power-law-in-temperature resistivity results can apply to other systems that manifest topological domain-wall structures.
Floquet topological insulator and Hofstadter butterfly in minimally TBLG
We theoretically study the Hofstadter butterfly in minimally twisted bilayer graphene (mTBLG). We demonstrate that mTBLG with a large magnetic field realizes effective Floquet topological insulators (FTIs) carrying zero Chern number while hosting chiral edge states in bulk gaps. We identify the FTIs by analyzing the nontrivial spectral flow and explicitly computing the chiral edge states. Our theory paves the way for an effective realization of FTIs in equilibrium solid-state systems.
Single particle flat band driven by Quasiperiodicity
We point out that the nearly flat single-particle miniband can be realized in a broad class of systems with quasiperiodic modulations. We further study the deeper relations to the twisted bilayer graphene at the magic angle. Such systems are advantageous due to their simplicity. We demonstrate that the magic-angle region corresponds to novel critically delocalized wavefunctions in the momentum space (see the middle figure below). We also construct an effective Hubbard model and confirm the considerable interaction enhancement in the magic-angle region. Our work also suggests the possibility of studying strongly correlated physics in ultracold atom systems where quasiperiodic modulation can be implemented in a controlled fashion. With chiral symmetry (quasiperiodic hopping model), the miniband is much more flat (absolutely flat within the numerical accuracy) in the magic angle phase. The real-space wavefunctions are composed of topological zero modes (that require chiral symmetry) in the metallic phase (characterized by a finite density of states). The low-energy wavefunctions show a quantum-critical Chalker scaling in the pure quasiperiodic hopping limit.
npj Quantum Materials 5, 71 (2020)
Phys. Rev. B 101, 235121 (2020); Editors' suggestion
Superconductor versus insulator in twisted bilayer graphene
We present a simple model that captures the key aspects of the competition between superconducting and insulating states in twisted bilayer graphene. Within this model, the superconducting phase is primary and arises at generic fillings but is interrupted by the insulator at commensurate fillings. Notably, the insulator forms because of electron-electron interactions, but the model is agnostic as to the superconducting pairing mechanism, which need not originate with electron-electron interactions. The model comprises a collection of crossed one-dimensional quantum wires whose intersections form a superlattice. We place a locally superconducting puddle at each superlattice point that can exchange Cooper pairs with the quantum wires. We analyze this model assuming weak wire-puddle and wire-wire couplings. We show that for a range of repulsive intrawire interactions, the system is superconducting at `generic' incommensurate fillings, with the superconductivity being `interrupted' by an insulating phase at commensurate fillings. We further show that the gapped insulating states at commensurate fillings give way to gapless states upon application of external Zeeman fields. Despite the distinct microscopic details, these features are consistent with experimental observations in magic-angle twisted bilayer graphenes. We further study the complete phase diagram of this model and discover that it contains several distinct correlated insulating states, which we characterize herein.
