Andrea Allais

Direct phase-sensitive identification of a d-form factor density wave in underdoped cuprates

Significance High-temperature superconductivity emerges when holes are introduced into the antiferromagnetic, insulating CuO2 plane of the cuprates. Intervening between the insulator and the superconductor is the mysterious pseudogap phase. Evidence has been accumulating that this phase supports an exotic density wave state that may be key to its existence. By introducing visualization techniques that discriminate the electronic structure at the two oxygen sites with each CuO2 unit cell, we demonstrate that this density wave consists of periodic modulations maintaining a phase difference of π between every such pair of oxygen sites. Therefore, the cuprate pseudogap phase contains a previously unknown electronic state—a density wave with a d-symmetry form factor. The identity of the fundamental broken symmetry (if any) in the underdoped cuprates is unresolved. However, evidence has been accumulating that this state may be an unconventional density wave. Here we carry out site-specific measurements within each CuO2 unit cell, segregating the results into three separate electronic structure images containing only the Cu sites [Cu(r)] and only the x/y axis O sites [Ox(r) and Oy(r)]. Phase-resolved Fourier analysis reveals directly that the modulations in the Ox(r) and Oy(r) sublattice images consistently exhibit a relative phase of π. We confirm this discovery on two highly distinct cuprate compounds, ruling out tunnel matrix-element and materials-specific systematics. These observations demonstrate by direct sublattice phase-resolved visualization that the density wave found in underdoped cuprates consists of modulations of the intraunit-cell states that exhibit a predominantly d-symmetry form factor.

Density wave instabilities in a correlated two-dimensional metal

Department of Physics, Harvard University, Cambridge MA 02138(Dated: February 26, 2014)Motivated by recent experimental evidence of charge order in the pseudogap phase of cuprates,we perform a variational analysis of charge-neutral, spin-singlet ordering in metals on the squarelattice, using a wavefunction with double occupancy projected out. We examine ordering with andwithout time-reversal symmetry, with arbitrary wavevector and tunable form factor. Depending onparameters, we nd d-wave bond density wave ordering with wavevector either parallel to the latticegenerators or diagonally oriented, or a ground state which carries a time reversal-breaking patternof spontaneous currents.

Connecting high-field quantum oscillations to zero-field electron spectral functions in the underdoped cuprates

The nature of the pseudogap regime of cuprate superconductors at low hole density remains unresolved. It has a number of seemingly distinct experimental signatures: a suppression of the paramagnetic spin susceptibility at high temperatures, low-energy electronic excitations that extend over arcs in the Brillouin zone, X-ray detection of charge-density wave order at intermediate temperatures and quantum oscillations at high magnetic fields and low temperatures. Here we show that a model of competing charge-density wave and superconducting orders provides a unified description of the intermediate and low-temperature regimes. We treat quantum oscillations at high field beyond semiclassical approximations, and find clear and robust signatures of an electron pocket compatible with existing observations; we also predict oscillations due to additional hole pockets. In the zero-field and intermediate temperature regime, we compute the electronic spectrum in the presence of thermally fluctuating charge-density and superconducting orders. Our results are compatible with experimental trends.

Quantum dimer model for the pseudogap metal

Significance The most interesting states of the copper oxide compounds are not the superconductors with high critical temperatures. Instead, the novelty lies primarily in the higher temperature metallic “normal” states from which the superconductors descend. Here, we develop a simple, intuitive model for the physics of the metal at low carrier density, in the “pseudogap” regime. This model describes an exotic metal that is similar in many respects to simple metals like silver. However, the simple metallic character coexists with “topological order” and long-range quantum entanglement previously observed only in exotic insulators or fractional quantum Hall states in very high magnetic fields. Our model is compatible with many recent observations, and we discuss more definitive experimental tests. We propose a quantum dimer model for the metallic state of the hole-doped cuprates at low hole density, p. The Hilbert space is spanned by spinless, neutral, bosonic dimers and spin S=1/2, charge +e fermionic dimers. The model realizes a “fractionalized Fermi liquid” with no symmetry breaking and small hole pocket Fermi surfaces enclosing a total area determined by p. Exact diagonalization, on lattices of sizes up to 8×8, shows anisotropic quasiparticle residue around the pocket Fermi surfaces. We discuss the relationship to experiments.

Spectral function of a localized fermion coupled to the Wilson-Fisher conformal field theory

We describe the dynamics of a single fermion in a dispersionless band coupled to the 2+1 dimensional conformal field theory (CFT) describing the quantum phase transition of a bosonic order parameter with N components. The fermionic spectral functions are expected to apply to the vicinity of quantum critical points in two-dimensional metals over an intermediate temperature regime where the Landau damping of the order parameter can be neglected. Some of our results are obtained by a mapping to an auxiliary problem of a CFT containing a defect line with an external field which locally breaks the global O(N) symmetry.

Confinement transition to density wave order in metallic doped spin liquids

Insulating quantum spin liquids can undergo a confinement transition to a valence bond solid state via the condensation of topological excitations of the associated gauge theory. We extend the theory of such transitions to fractionalized Fermi liquids (FL*): these are metallic doped spin liquids in which the Fermi surfaces only have gauge neutral quasiparticles. Using insights from a duality transform on a doped quantum dimer model for the U(1)-FL* state, we show that projective symmetry group of the theory of the topological excitations remains unmodified, but the Fermi surfaces can lead to additional frustrating interactions. We propose a theory for the confinement transition of

Loop current order andd-wave superconductivity: Some observable consequences

\mathbb{Z}_2

Auxiliary-boson and DMFT studies of bond ordering instabilities of \(t\)-\(J\)-\(V\) models on the square lattice

-FL* states via the condensation of visons. A variety of confining, incommensurate density wave states are possible, including some that are similar to the incommensurate

Connecting high-field quantum oscillations to the pseudogap in the underdoped cuprates

d

Comment on "Symmetry classification of bond order parameters in cuprates"

-form factor density wave order observed in several recent experiments on the cuprate superconductors.