Crystallization of bosonic quantum Hall states in a rotating quantum gas.

The dominance of interactions over kinetic energy lies at the heart of strongly correlated quantum matter, from fractional quantum Hall liquids1, to atoms in optical lattices2 and twisted bilayer graphene3. Crystalline phases often compete with correlated quantum liquids, and transitions between them occur when the energy cost of forming a density wave approaches zero. A prime example occurs for electrons in high-strength magnetic fields, where the instability of quantum Hall liquids towards a Wigner crystal4-9 is heralded by a roton-like softening of density modulations at the magnetic length7,10-12. Remarkably, interacting bosons in a gauge field are also expected to form analogous liquid and crystalline states13-21. However, combining interactions with strong synthetic magnetic fields has been a challenge for experiments on bosonic quantum gases18,21. Here we study the purely interaction-driven dynamics of a Landau gauge Bose-Einstein condensate22 in and near the lowest Landau level. We observe a spontaneous crystallization driven by condensation of magneto-rotons7,10, excitations visible as density modulations at the magnetic length. Increasing the cloud density smoothly connects this behaviour to a quantum version of the Kelvin-Helmholtz hydrodynamic instability, driven by the sheared internal flow profile of the rapidly rotating condensate. At long times the condensate self-organizes into a persistent array of droplets separated by vortex streets, which are stabilized by a balance of interactions and effective magnetic forces.

Spin-triplet superconductivity from excitonic effect in doped insulators.

SignificanceWe present a mechanism for unconventional superconductivity in doped band insulators, where short-ranged pairing interaction arises from Coulomb repulsion due to virtual interband or excitonic processes. Remarkably, electron pairing is found upon infinitesimal doping, giving rise to Bose-Einstein condensate (BEC)-Bardeen-Cooper-Schrieffer (BCS) crossover at low density. Our theory explains puzzling behaviors of superconductivity and predicts spin-triplet pairing in electron-doped ZrNCl and WTe2.

Keldysh Field Theory of Dynamical Exciton Condensation Transitions in Nonequilibrium Electron-Hole Bilayers.

Recent experiments have realized steady-state electrical injection of interlayer excitons in electron-hole bilayers subject to a large bias voltage. In the ideal case in which interlayer tunneling is negligibly weak, the system is in quasiequilibrium with a reduced effective band gap. Interlayer tunneling introduces a current and drives the system out of equilibrium. In this work we derive a nonequilibrium field theory description of interlayer excitons in biased electron-hole bilayers. In the large bias limit, we find that p-wave interlayer tunneling reduces the effective band gap and increases the effective temperature for intervalley excitons. We discuss possible experimental implications for InAs/GaSb quantum wells and transition metal dichalcogenide bilayers.

Sublattice Structure and Topology in Spontaneously Crystallized Electronic States.

The prediction and realization of the quantum anomalous Hall effect are often intimately connected to honeycomb lattices in which the sublattice degree of freedom plays a central role in the nontrivial topology. Two-dimensional Wigner crystals, on the other hand, form triangular lattices without sublattice degrees of freedom, resulting in a topologically trivial state. Here, we discuss the possibility of spontaneously formed honeycomb-lattice crystals that exhibit the quantum anomalous Hall effect. Starting from a single-band system with nontrivial quantum geometry, we derive the mean-field energy functional of a class of crystal states and express it as a model of sublattice pseudospins in momentum space. We find that nontrivial quantum geometry leads to extra terms in the pseudospin model that break an effective "time-reversal symmetry" and favor a topologically nontrivial pseudospin texture. When the effects of these extra terms dominate over the ferromagnetic exchange coupling between pseudospins, the anomalous Hall crystal state becomes energetically favorable over the trivial Wigner crystal state.

Topological Superconductivity in Doped Magnetic Moiré Semiconductors.

We show that topological superconductivity may emerge upon doping of transition metal dichalcogenide heterobilayers above an integer-filling magnetic state of the topmost valence moiré band. The effective attraction between charge carriers is generated by an electric p-wave Feshbach resonance arising from interlayer excitonic physics and has a tunable strength, which may be large. Together with the low moiré carrier densities reachable by gating, this robust attraction enables access to the long-sought p-wave BEC-BCS transition. The topological protection arises from an emergent time reversal symmetry occurring when the magnetic order and long wavelength magnetic fluctuations do not couple different valleys. The resulting topological superconductor features helical Majorana edge modes, leading to half-integer quantized spin-thermal Hall conductivity and to charge currents induced by circularly polarized light or other time-reversal symmetry-breaking fields.

Variational Ansatz for an Abelian to Non-Abelian Topological Phase Transition in ν=1/2+1/2 Bilayers.

We propose a one-parameter variational ansatz to describe the tunneling-driven Abelian to non-Abelian transition in bosonic ν=1/2+1/2 fractional quantum Hall bilayers. This ansatz, based on exact matrix product states, captures the low-energy physics all along the transition and allows us to probe its characteristic features. The transition is continuous, characterized by the decoupling of antisymmetric degrees of freedom. We futhermore determine the tunneling strength above which non-Abelian statistics should be observed experimentally. Finally, we propose to engineer the interlayer tunneling to create an interface trapping a neutral chiral Majorana fermion. We microscopically characterize such an interface using a slightly modified model wave function.

New mechanism and exact theory of superconductivity from strong repulsive interaction.

We introduce a general mechanism for superconductivity in Fermi systems with strong repulsive interaction. Because kinetic terms are small compared to the bare repulsion, the dynamics of charge carriers is constrained by the presence of other nearby carriers. By treating kinetic terms as a perturbation around the atomic limit, we show that pairing can be induced by correlated multiparticle tunneling processes that favor two itinerant carriers to be close together. Our analytically controlled theory provides a quantitative formula relating Tc to microscopic parameters, with maximum Tc reaching about 10% of the Fermi temperature. Our work demonstrates a powerful method for studying strong coupling superconductivity with unconventional pairing symmetry. It also offers a realistic new route to realizing finite angular momentum superfluidity of spin-polarized fermions in optical lattice.

Magic in twisted transition metal dichalcogenide bilayers.

The long-wavelength moiré superlattices in twisted 2D structures have emerged as a highly tunable platform for strongly correlated electron physics. We study the moiré bands in twisted transition metal dichalcogenide homobilayers, focusing on WSe2, at small twist angles using a combination of first principles density functional theory, continuum modeling, and Hartree-Fock approximation. We reveal the rich physics at small twist angles θ < 4∘, and identify a particular magic angle at which the top valence moiré band achieves almost perfect flatness. In the vicinity of this magic angle, we predict the realization of a generalized Kane-Mele model with a topological flat band, interaction-driven Haldane insulator, and Mott insulators at the filling of one hole per moiré unit cell. The combination of flat dispersion and uniformity of Berry curvature near the magic angle holds promise for realizing fractional quantum anomalous Hall effect at fractional filling. We also identify twist angles favorable for quantum spin Hall insulators and interaction-induced quantum anomalous Hall insulators at other integer fillings.

Geometric squeezing into the lowest Landau level.

The equivalence between particles under rotation and charged particles in a magnetic field relates phenomena as diverse as spinning atomic nuclei, weather patterns, and the quantum Hall effect. For such systems, quantum mechanics dictates that translations along different directions do not commute, implying a Heisenberg uncertainty relation between spatial coordinates. We implement squeezing of this geometric quantum uncertainty, resulting in a rotating Bose-Einstein condensate occupying a single Landau gauge wave function. We resolve the extent of zero-point cyclotron orbits and demonstrate geometric squeezing of the orbits' centers 7 decibels below the standard quantum limit. The condensate attains an angular momentum exceeding 1000 quanta per particle and an interatomic distance comparable to the cyclotron orbit. This offers an alternative route toward strongly correlated bosonic fluids.

Creation of a Bose-condensed gas of 87Rb by laser cooling.

Protocols for attaining quantum degeneracy in atomic gases almost exclusively rely on evaporative cooling, a time-consuming final step associated with substantial atom loss. We demonstrate direct laser cooling of a gas of rubidium-87 (87Rb) atoms to quantum degeneracy. The method is fast and induces little atom loss. The atoms are trapped in a two-dimensional optical lattice that enables cycles of compression to increase the density, followed by Raman sideband cooling to decrease the temperature. From a starting number of 2000 atoms, 1400 atoms reach quantum degeneracy in 300 milliseconds, as confirmed by a bimodal velocity distribution. The method should be broadly applicable to many bosonic and fermionic species and to systems where evaporative cooling is not possible.