Lucile Savary

Quantum Excitations in Quantum Spin Ice

Recent work has highlighted remarkable effects of classical thermal fluctuations in the dipolar spin ice compounds, such as ‘‘artificial magnetostatics,’’ manifesting as Coulombic power-law spin correlations and particles behaving as diffusive ‘‘magnetic monopoles.’’ In this paper, we address quantum spin ice, giving a unifying framework for the study of magnetism of a large class of magnetic compounds with the pyrochlore structure, and, in particular, discuss Yb2Ti2O7, and extract its full set of Hamiltonian parameters from high-field inelastic neutron scattering experiments. We show that fluctuations in Yb2Ti2O7 are strong, and that the Hamiltonian may support a Coulombic ‘‘quantum spin liquid’’ ground state in low magnetic fields and host an unusual quantum critical point at larger fields. This appears consistent with puzzling features seen in prior experiments on Yb2Ti2O7. Thus, Yb2Ti2O7 is the first quantum spin liquid candidate for which the Hamiltonian is quantitatively known.

Coulombic Quantum Liquids in Spin-1/2 Pyrochlores

We develop a nonperturbative gauge mean field theory (gMFT) method to study a general effective spin-1/2 model for magnetism in rare earth pyrochlores. gMFT is based on a novel exact slave-particle formulation, and matches both the perturbative regime near the classical spin ice limit and the semiclassical approximation far from it. We show that the full phase diagram contains two exotic phases: a quantum spin liquid and a Coulombic ferromagnet, both of which support deconfined spinon excitations and emergent quantum electrodynamics. Phenomenological properties of these phases are discussed.

Order by Quantum Disorder in Er2Ti2O7

Here we establish the systematic existence of a U(1) degeneracy of all symmetry-allowed Hamiltonians quadratic in the spins on the pyrochlore lattice, at the mean-field level. By extracting the Hamiltonian of Er(2)Ti(2)O(7) from inelastic neutron scattering measurements, we then show that the U(1)-degenerate states of Er(2)Ti(2)O(7) are its classical ground states, and unambiguously show that quantum fluctuations break the degeneracy in a way which is confirmed by experiment. The degree of symmetry protection of the classical U(1) degeneracy in Er(2)Ti(2)O(7) is unprecedented in other materials. As a consequence, our observation of order by disorder is unusually definitive. We provide further verifiable consequences of this phenomenon, and several additional comparisons between theory and experiment.

Superconductivity in Three-Dimensional Spin-Orbit Coupled Semimetals

Motivated by the experimental detection of superconductivity in the low-carrier density half-Heusler compound YPtBi, we study the pairing instabilities of three-dimensional strongly spin-orbit coupled semimetals with a quadratic band touching point. In these semimetals the electronic structure at the Fermi energy is described by spin j=3/2 quasiparticles, which are fundamentally different from those in ordinary metals with spin j=1/2. We develop a general approach to analyzing pairing instabilities in j=3/2 materials by decomposing the pair scattering interaction into irreducible channels, projecting them to the Fermi surface and deriving the corresponding Eliashberg theory. Applying our method to a generic density-density interaction in YPtBi we establish the following results: (i) The pairing strength in each channel uniquely encodes the j=3/2 nature of the Fermi surface band structure--a manifestation of the fundamental difference with ordinary metals. In particular, this implies that Andersons theorem, which addresses the effect of spin-orbit coupling and disorder on pairing states of spin-1/2 electrons, cannot be applied in this case. (ii) The leading pairing instabilities are different for electron and hole doping. This implies that superconductivity depends on carrier type. (iii) In the case of hole doping--relevant to YPtBi, we find two odd-parity channels in close competition with s-wave pairing. One of these two channels is a multicomponent pairing channel, allowing for the possibility of time-reversal symmetry breaking. (iv) In the case of Coulomb interactions mediated by the long-ranged electric polarization of optical phonon modes, a significant coupling strength is generated in spite of the extremely low density of carriers. Furthermore, non-linear response and Fermi liquid corrections can favor non-s-wave pairing and potentially account for the experimentally-observed Tc.

New Type of Quantum Criticality in the Pyrochlore Iridates

Magnetic fluctuations and electrons couple in intriguing ways in the vicinity of zero temperature phase transitions - quantum critical points - in conducting materials. Quantum criticality is implicated in non-Fermi liquid behavior of diverse materials, and in the formation of unconventional superconductors. Here we uncover an entirely new type of quantum critical point describing the onset of antiferromagnetism in a nodal semimetal engendered by the combination of strong spin-orbit coupling and electron correlations, and which is predicted to occur in the iridium oxide pyrochlores. We formulate and solve a field theory for this quantum critical point by renormalization group techniques, show that electrons and antiferromagnetic fluctuations are strongly coupled, and that both these excitations are modified in an essential way. This quantum critical point has many novel features, including strong emergent spatial anisotropy, a vital role for Coulomb interactions, and highly unconventional critical exponents. Our theory motivates and informs experiments on pyrochlore iridates, and constitutes a singular realistic example of a non-trivial quantum critical point with gapless fermions in three dimensions.

Impurity effects in highly frustrated diamond-lattice antiferromagnets

We consider the effects of local impurities in highly frustrated diamond-lattice antiferromagnets, which exhibit large but nonextensive ground-state degeneracies. Such models are appropriate to many A-site magnetic spinels. We argue very generally that sufficiently dilute impurities induce an ordered magnetic ground state and provide a mechanism of degeneracy breaking. The states that are selected can be determined by a “swiss cheese model” analysis, which we demonstrate numerically for a particular impurity model in this case. Moreover, we present criteria for estimating the stability of the resulting ordered phase to a competing frozen (spin glass) one. The results may explain the contrasting finding of frozen and ordered ground states in CoAl_2O_4 and MnSc_2S_4, respectively.

Pairing States of Spin-3/2 Fermions: Symmetry-Enforced Topological Gap Functions

A new theoretical analysis provides a classification for the pairing states of spin-3/2 quasiparticles in bismuth-based half-Heusler materials, which show signatures of unconventional and possibly topological superconductivity.

Quantum spin ice on the breathing pyrochlore lattice

The Coulombic quantum spin liquid in quantum spin ice is an exotic quantum phase of matter that emerges on the pyrochlore lattice and is currently actively searched for. Motivated by recent experiments on the Yb-based breathing pyrochlore material

Signatures of the helical phase in the critical fields at twin boundaries of noncentrosymmetric superconductors

{\mathrm{Ba}}_{3}{\mathrm{Yb}}_{2}{\mathrm{Zn}}_{5}{\mathrm{O}}_{11}

Quantum spin liquids: a review

, we theoretically study the phase diagram and magnetic properties of the relevant spin model. The latter takes the form of a quantum spin ice Hamiltonian on a breathing pyrochlore lattice, and we analyze the stability of the quantum spin liquid phase in the absence of the inversion symmetry which the lattice breaks explicitly at lattice sites. Using a gauge mean-field approach, we show that the quantum spin liquid occupies a finite region in parameter space. Moreover, there exists a direct quantum phase transition between the quantum spin liquid phase and featureless paramagnets, even though none of theses phases break any symmetry. At nonzero temperature, we show that breathing pyrochlores provide a much broader finite-temperature spin liquid regime than their regular counterparts. We discuss the implications of the results for current experiments and make predictions for future experiments on breathing pyrochlores.