Long-Lived Topological Flatband Excitons in Semiconductor Moiré Heterostructures: A Bosonic Kane-Mele Model Platform.

Moiré superlattices based on two-dimensional transition metal dichalcogenides (TMDs) have emerged as a highly versatile and fruitful platform for exploring correlated topological electronic phases. One of the most remarkable examples is the recently discovered fractional quantum anomalous Hall effect (FQAHE) under zero magnetic field. Here, we propose a minimal structure that hosts long-lived excitons-a ubiquitous bosonic excitation in TMD semiconductors-with narrow topological bosonic bands.

Eliashberg Theory for Dynamical Screening in Bilayer Exciton Condensation.

We study the effect of dynamical screening of interactions on the transition temperatures (T_{c}) of exciton condensation in a symmetric bilayer of quadratically dispersing electrons and holes by solving the linearized Eliashberg equations for the anomalous interlayer Green's functions. We find that T_{c} is finite for the range of density and layer separations studied, decaying exponentially with interlayer separation. T_{c} is suppressed well below that predicted by a Hartree Fock mean field theory with unscreened Coulomb interaction, but is above the estimates from the statically screened Coulomb interaction.

Machine Learning the Disorder Landscape of Majorana Nanowires.

We develop a practical machine learning approach to determine the disorder landscape of Majorana nanowires by using training of the conductance matrix and inverting the conductance data in order to obtain the disorder details in the system. The inversion carried out through machine learning using different disorder parametrizations turns out to be unique in the sense that any input tunnel conductance as a function of chemical potential and Zeeman energy can indeed be inverted to provide the correct disorder landscape. Our work opens up a qualitatively new direction of directly determining the topological invariant and the Majorana wave-function structure corresponding to a transport profile of a device using simulations that quantitatively match the specific conductance profile.

Engineering the Kitaev Spin Liquid in a Quantum Dot System.

The Kitaev model on a honeycomb lattice may provide a robust topological quantum memory platform, but finding a material that realizes the unique spin-liquid phase remains a considerable challenge. We demonstrate that an effective Kitaev Hamiltonian can arise from a half-filled Fermi-Hubbard Hamiltonian where each site can experience a magnetic field in a different direction. As such, we provide a method for realizing the Kitaev spin liquid on a single hexagonal plaquette made up of 12 quantum dots.

Nematic Excitonic Insulator in Transition Metal Dichalcogenide Moiré Heterobilayers.

We study the effect of interelectron Coulomb interactions on the displacement field induced topological phase transition in transition metal dichalcogenide moiré heterobilayers. We find a nematic excitonic insulator phase that breaks the moiré superlattice's threefold rotational symmetry and preempts the topological phase transition in both AA and AB stacked heterobilayers when the interlayer tunneling is weak, or when the Coulomb interaction is not strongly screened. The nematicity originates from the frustration between the nontrivial spatial structure of the interlayer tunneling, which is crucial to the existence of the topological Chern band, and the interlayer coherence induced by the Coulomb interaction that favors uniformity in layer pseudospin orientations.

Kondo Lattice Model in Magic-Angle Twisted Bilayer Graphene.

We systematically study emergent Kondo lattice models from magic-angle twisted bilayer graphene using the topological heavy fermion representation. At the commensurate fillings, we demonstrate a series of symmetric strongly correlated metallic states driven by the hybridization between a triangular lattice of SU(8) local moments and delocalized fermions. In particular, a (fragile) topological Dirac Kondo semimetal can be realized, providing a potential explanation for the symmetry-preserving correlated state at ν=0.

Dissipative Prethermal Discrete Time Crystal.

An ergodic system subjected to an external periodic drive will be generically heated to infinite temperature. However, if the applied frequency is larger than the typical energy scale of the local Hamiltonian, this heating stops during a prethermal period that extends exponentially with the frequency. During this prethermal period, the system may manifest an emergent symmetry that, if spontaneously broken, will produce subharmonic oscillation of the discrete time crystal (DTC).

Topological Phases in AB-Stacked MoTe_{2}/WSe_{2}: Z_{2} Topological Insulators, Chern Insulators, and Topological Charge Density Waves.

We present a theory on the quantum phase diagram of AB-stacked MoTe_{2}/WSe_{2} using a self-consistent Hartree-Fock calculation performed in the plane-wave basis, motivated by the observation of topological states in this system. At filling factor ν=2 (two holes per moiré unit cell), Coulomb interaction can stabilize a Z_{2} topological insulator by opening a charge gap. At ν=1, the interaction induces three classes of competing states, spin density wave states, an in-plane ferromagnetic state, and a valley polarized state, which undergo first-order phase transitions tuned by an out-of-plane displacement field.

Correlation-Induced Triplet Pairing Superconductivity in Graphene-Based Moiré Systems.

Motivated by the possible non-spin-singlet superconductivity in the magic-angle twisted trilayer graphene experiment, we investigate the triplet-pairing superconductivity arising from a correlation-induced spin-fermion model of Dirac fermions with spin, valley, and sublattice degrees of freedom. We find that the f-wave pairing is favored due to the valley-sublattice structure, and the superconducting state is time-reversal symmetric, fully gapped, and nontopological. With a small in-plane magnetic field, the superconducting state becomes partially polarized, and the transition temperature can be slightly enhanced.

Acoustic-Phonon-Mediated Superconductivity in Rhombohedral Trilayer Graphene.

Motivated by the observation of two distinct superconducting phases in the moiréless ABC-stacked rhombohedral trilayer graphene, we investigate the electron-acoustic-phonon coupling as a possible pairing mechanism. We predict the existence of superconductivity with the highest T_{c}∼3  K near the Van Hove singularity. Away from the Van Hove singularity, T_{c} remains finite in a wide range of doping.

Interaction-Driven Filling-Induced Metal-Insulator Transitions in 2D Moiré Lattices.

Using a realistic band structure for twisted WSe_{2} materials, we develop a theory for the interaction-driven correlated insulators to conducting metals transitions through the tuning of the filling factor around commensurate fractional fillings of the moiré unit cell in the 2D honeycomb lattice, focusing on the dominant half-filled Mott insulating state, which exists for both long- and short-range interactions. We find metallic states slightly away from half-filling, as have recently been observed experimentally. We discuss the stabilities and the magnetic properties of the resulting insulating and metallic phases, and comment on their experimental signatures.

Observation of Many-Body Localization in a One-Dimensional System with a Single-Particle Mobility Edge.

We experimentally study many-body localization (MBL) with ultracold atoms in a weak one-dimensional quasiperiodic potential, which in the noninteracting limit exhibits an intermediate phase that is characterized by a mobility edge. We measure the time evolution of an initial charge density wave after a quench and analyze the corresponding relaxation exponents. We find clear signatures of MBL when the corresponding noninteracting model is deep in the localized phase.

Universal optical conductivity of a disordered Weyl semimetal.

Topological Weyl semimetals, besides manifesting chiral anomaly, can also accommodate a disorder-driven unconventional quantum phase transition into a metallic phase. A fundamentally and practically important question in this regard concerns an experimentally measurable quantity that can clearly distinguish these two phases. We show that the optical conductivity while serving this purpose can also play the role of a bonafide order parameter across such disorder-driven semimetal-metal quantum phase transition by virtue of displaying distinct scaling behavior in the semimetallic and metallic phases, as well as inside the quantum critical fan supporting a non-Fermi liquid.

Interacting Hofstadter spectrum of atoms in an artificial gauge field.

Motivated by experimental advances in the synthesis of gauge potentials for ultracold atoms, we consider the superfluid phase of interacting bosons on a square lattice in the presence of a magnetic field. We show that superfluid order implies spatial symmetry breaking, and predict clear signatures of many-body effects in time-of-flight measurements. By developing a Bogoliubov expansion based on the exact Hofstadter spectrum, we find the dispersion of the quasiparticle modes within the superfluid phase, and describe the consequences for Bragg spectroscopy measurements.

Quantum stripe ordering in optical lattices.

We predict the robust existence of a novel quantum orbital stripe order in the p-band Bose-Hubbard model of two-dimensional triangular optical lattices with cold bosonic atoms. An orbital angular momentum moment is formed on each site exhibiting a stripe order both in the superfluid and Mott-insulating phases. The stripe order spontaneously breaks time-reversal, lattice translation, and rotation symmetries.

Topologically protected qubits from a possible non-Abelian fractional quantum Hall state.

The Pfaffian state is an attractive candidate for the observed quantized Hall plateau at a Landau-level filling fraction nu=5/2. This is particularly intriguing because this state has unusual topological properties, including quasiparticle excitations with non-Abelian braiding statistics. In order to determine the nature of the nu=5/2 state, one must measure the quasiparticle braiding statistics.