The family of edge-sharing tri-coordinated iridates and ruthenates has emerged in recent years as a major platform for Kitaev spin liquid physics, where spins fractionalize into emergent magnetic fluxes and Majorana fermions with Dirac-like dispersio
ns. While such exotic states are usually pre-empted by long-range magnetic order at low temperatures, signatures of Majorana fermions with long coherent times have been predicted to manifest at intermediate and higher energy scales, similar to the observation of spinons in quasi-1D spin chains. Here we present a Resonant Inelastic X-ray Scattering study of the magnetic excitations of the hyperhoneycomb iridate $beta$-Li$_2$IrO$_3$ under a magnetic field with a record-high-resolution spectrometer. At low-temperatures, dispersing spin waves can be resolved around the predicted intertwined incommensurate spiral and field-induced zigzag orders, whose excitation energy reaches a maximum of 16meV. A 2T magnetic field softens the dispersion around ${bf Q}=0$. The behavior of the spin waves under magnetic field is consistent with our semiclassical calculations for the ground state and the dynamical spin structure factor, which further predicts that the ensued intertwined uniform states remain robust up to very high fields (100 T). Most saliently, the low-energy magnon-like mode is superimposed by a broad continuum of excitations, centered around 35meV and extending up to 100meV. This high-energy continuum survives up to at least 300K -- well above the ordering temperature of 38K -- and gives evidence for pairs of long-lived Majorana fermions of the proximate Kitaev spin liquid.
Electrons confined to two dimensions display an unexpected diversity of behaviors as they are cooled to absolute zero. Noninteracting electrons are predicted to eventually localize into an insulating ground state, and it has long been supposed that e
lectron correlations stabilize only one other phase: superconductivity. However, many two-dimensional (2D) superconducting materials have shown surprising evidence for metallic behavior, where the electrical resistivity saturates in the zero-temperature limit, the nature of this unexpected metallic state remains under intense scrutiny. We report electrical transport properties for two disordered 2D superconductors, indium oxide and tantalum nitride, and observe a magnetic field-tuned transition from a true superconductor to a metallic phase with saturated resistivity. This metallic phase is characterized by a vanishing Hall resistivity, suggesting that it retains particle-hole symmetry from the disrupted superconducting state.
We study the two-dimensional superconductor-insulator transition (SIT) in thin films of tantalum nitride. At zero magnetic field, films can be disorder-tuned across the SIT by adjusting thickness and film stoichiometry; insulating films exhibit class
ical hopping transport. Superconducting films exhibit a magnetic field-tuned SIT, whose insulating ground state at high field appears to be a quantum-corrected metal. Scaling behavior at the field-tuned SIT shows classical percolation critical exponents $z u approx$ 1.3, with a corresponding critical field $H_c ll H_{c2}$. The Hall effect shows a crossing point near $H_c$, but with a non-universal critical value $rho_{xy}^c$ comparable to the normal state Hall resistivity. We propose that high-carrier density metals will always exhibit this pattern of behavior at the boundary between superconducting and (trivially) insulating ground states.
Honeycomb iridates are thought to have strongly spin-anisotropic exchange interactions that could lead to an extraordinary state of matter known as the Kitaev quantum spin liquid. The realization of this state requires almost perfectly frustrated int
eractions between the magnetic Ir$^{4+}$ ions, but small imbalances in energy make other ordered states more favorable. Indeed, the closeness in energy of these ordered states is itself a signature of the intrinsic frustration in the system. In this work, we illustrate that small magnetic fields can be employed to drive the frustrated quantum magnet $beta-$Li$_2$IrO$_3$,between different broken symmetry states, but without causing a true thermodynamic phase transition. This field-induced broken symmetry phase has all the signatures of a thermodynamic order parameter, but it is never truly formed in zero field. Rather, it is summoned when the scales of frustration are appropriately tipped, intertwined with other nearby quantum states.
Honeycomb iridates such as $gamma$-Li$_2$IrO$_3$ are argued to realize Kitaev spin-anisotropic magnetic exchange, along with Heisenberg and possibly other couplings. While systems with pure Kitaev interactions are candidates to realize a quantum spin
liquid ground state, in $gamma$-Li$_2$IrO$_3$ it has been shown that the balance of magnetic interactions leads to the incommensurate spiral spin order at ambient pressure below 38 K. We study the fragility of this state in single crystals of $gamma$-Li$_2$IrO$_3$ using resonant x-ray scattering (RXS) under applied hydrostatic pressures of up to 3.0 GPa. RXS is a direct probe of the underlying electronic order, and we observe the abrupt disappearance of the $q$=(0.57, 0, 0) spiral order at a critical pressure $P_c = 1.5 $GPa with no accompanying change in the symmetry of the lattice. This dramatic disappearance is in stark contrast with recent studies of $beta$-Li$_2$IrO$_3$ that show continuous suppression of the spiral order in magnetic field; under pressure, a new and possibly nonmagnetic ground state emerges.
The complexity of the antiferromagnetic orders observed in the honeycomb iridates is a double-edged sword in the search for a quantum spin-liquid ground state: both attesting that the magnetic interactions provide many of the necessary ingredients, b
ut simultaneously impeding access. As a result, focus has been drawn to the unusual magnetic orders and the hints they provide to the underlying spin correlations. However, the study of any particular broken symmetry state generally provides little clue as to the possibilities of other nearby ground states cite{Anderson}. Here we use extreme magnetic fields to reveal the extent of the spin correlations in $gamma$-lithium iridate. We find that a magnetic field with a small component along the magnetic easy-axis melts long-range order, revealing a bistable, strongly correlated spin state. Far from the usual destruction of antiferromagnetism via spin polarization, the correlated spin state possesses only a small fraction of the total moment, without evidence for long-range order up to the highest attainable magnetic fields (>90 T).
We study magnetotransport properties of the electron-doped superconductor Pr$_{2-x}$Ce$_x$CuO$_{4pmdelta}$ with $x$ = 0.14 in magnetic fields up to 92~T, and observe Shubnikov de-Haas magnetic quantum oscillations. The oscillations display a single f
requency $F$=255$pm$10~T, indicating a small Fermi pocket that is $sim$~1% of the two-dimensional Brillouin zone and consistent with a Fermi surface reconstructed from the large hole-like cylinder predicted for these layered materials. Despite the low nominal doping, all electronic properties including the effective mass and Hall effect are consistent with overdoped compounds. Our study demonstrates that the exceptional chemical control afforded by high quality thin films will enable Fermi surface studies deep into the overdoped cuprate phase diagram.
For both electron- and hole-doped cuprates, superconductivity appears in the vicinity of suppressed broken symmetry order, suggesting that quantum criticality plays a vital role in the physics of these systems. A confounding factor in identifying the
role of quantum criticality in the electron-doped systems is the competing influence of chemical doping and oxygen stoichiometry. Using high quality thin films of Pr$_{2}$CuO$_{4pmdelta}$, we tune superconductivity and uncover the influence of quantum criticality without Ce substitution. We observe magnetic quantum oscillations that are consistent with the presence of small hole-like Fermi surface pockets, and a large mass enhancement near the suppression of superconductivity. Tuning these materials using only oxygen stoichiometry allows the observation of quantum oscillations and provides a new axis with which to explore the physics underlying the electron-doped side of the cuprate phase diagram.
In metals near a quantum critical point, the electrical resistance is thought to be determined by the lifetime of the carriers of current, rather than the scattering from defects. The observation of $T$-linear resistivity suggests that the lifetime o
nly depends on temperature, implying the vanishing of an intrinsic energy scale and the presence of a quantum critical point. Our data suggest that this concept extends to the magnetic field dependence of the resistivity in the unconventional superconductor BaFe$_2$(As$_{1-x}$P$_{x}$)$_2$ near its quantum critical point. We find that the lifetime depends on magnetic field in the same way as it depends on temperature, scaled by the ratio of two fundamental constants $mu_B/k_B$. These measurements imply that high magnetic fields probe the same quantum dynamics that give rise to the $T$-linear resistivity, revealing a novel kind of magnetoresistance that does not depend on details of the Fermi surface, but rather on the balance of thermal and magnetic energy scales. This opens new opportunities for the investigation of transport near a quantum critical point by using magnetic fields to couple selectively to charge, spin and spatial anisotropies.
