Moiré quantum matter

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.

Phys. Rev. B 104, L201113 (2021)

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.

Phys. Rev. B 104, 045146 (2021)

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.

Phys. Rev. Research 2, 033271 (2020)

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.

Phys. Rev. B 100, 115128 (2019)