Shubhayu Chatterjee

Topological order in the pseudogap metal

Significance The copper oxide-based high-temperature superconductors display a mysterious “pseudogap” metal phase at temperatures just above the critical temperature in a regime of low hole density. Extensive experimental and numerical studies have yielded much information on the nature of the electron corrections, but a fundamental theoretical understanding has been lacking. We show that a theory of a metal with topological order and emergent gauge fields can model much of the numerical data. Our study opens up a route to a deeper understanding of the long-range quantum entanglement in these superconductors and to the direct detection of the topological characteristics of the many-body quantum state. We compute the electronic Green’s function of the topologically ordered Higgs phase of a SU(2) gauge theory of fluctuating antiferromagnetism on the square lattice. The results are compared with cluster extensions of dynamical mean field theory, and quantum Monte Carlo calculations, on the pseudogap phase of the strongly interacting hole-doped Hubbard model. Good agreement is found in the momentum, frequency, hopping, and doping dependencies of the spectral function and electronic self-energy. We show that lines of (approximate) zeros of the zero-frequency electronic Green’s function are signs of the underlying topological order of the gauge theory and describe how these lines of zeros appear in our theory of the Hubbard model. We also derive a modified, nonperturbative version of the Luttinger theorem that holds in the Higgs phase.

Insulators and metals with topological order and discrete symmetry breaking

Numerous experiments have reported discrete symmetry breaking in the high temperature pseudogap phase of the hole-doped cuprates, including breaking of one or more of lattice rotation, inversion, or time-reversal symmetries. In the absence of translational symmetry breaking or topological order, these conventional order parameters cannot explain the gap in the charged fermion excitation spectrum in the anti-nodal region. Zhao et al. (1601.01688) and Jeong et al. (arXiv:1701.06485) have also reported inversion and time-reversal symmetry breaking in insulating Sr2IrO4 similar to that in the metallic cuprates, but co-existing with Neel order. We extend an earlier theory of topological order in insulators and metals, in which the topological order combines naturally with the breaking of these conventional discrete symmetries. We find translationally-invariant states with topological order co-existing with both Ising-nematic order and spontaneous charge currents. The link between the discrete broken symmetries and the topological-order-induced pseudogap explains why the broken symmetries do not survive in the confining phases without a pseudogap at large doping. Our theory also connects to the O(3) non-linear sigma model and CP1 descriptions of quantum fluctuations of the Neel order. In this framework, the optimal doping criticality of the cuprates is primarily associated with the loss of topological order.

Superconductivity from a confinement transition out of a fractionalized Fermi liquid with Z2 topological and Ising-nematic orders

The Schwinger-boson theory of the frustrated square lattice antiferromagnet yields a stable, gapped

Probing excitations in insulators via injection of spin currents

\mathbb{Z}_2

Thermal and electrical transport in metals and superconductors across antiferromagnetic and topological quantum transitions

spin liquid ground state with time-reversal symmetry, incommensurate spin correlations and long-range Ising-nematic order. We obtain an equivalent description of this state using fermionic spinons (the fermionic spinons can be considered to be bound states of the bosonic spinons and the visons). Upon doping, the

Intertwining Topological Order and Broken Symmetry in a Theory of Fluctuating Spin-Density Waves

\mathbb{Z}_2

Spin density wave order, topological order, and Fermi surface reconstruction

spin liquid can lead to a fractionalized Fermi liquid (FL*) with small Fermi pockets of electron-like quasiparticles, while preserving the

Fractionalized Fermi liquid with bosonic chargons as a candidate for the pseudogap metal

\mathbb{Z}_2

Pseudogap and Fermi-Surface Topology in the Two-Dimensional Hubbard Model

topological and Ising-nematic orders. We describe a Higgs transition out of this deconfined metallic state into a confining superconducting state which is usually of the Fulde-Ferrell-Larkin-Ovchinnikov type, with spatial modulation of the superconducting order.

Diagnosing phases of magnetic insulators via noise magnetometry with spin qubits.

We propose a spin transport experiment to measure the low-energy excitations in insulators with spin degrees of freedom, with a focus on detecting ground states that lack magnetic order. A general formalism to compute the spin-current from a metal with a non-equilibrium distribution of spins to an insulator is developed. It is applied to insulating states with and without long range magnetic order, and salient features in the spin-conductance are noted.