Effect of nonmagnetic dilution in honeycomb lattice iridates Na2_2IrO3_3 and Li2_2IrO3_3

We have synthesized single crystals of Na$_2$(Ir$_{1-x}$Ti$_x$)O$_3$ and polycrystals of Li$_2$(Ir$_{1-x}$Ti$_x$)O$_3$ and studied the effect of magnetic depletion on the magnetic properties by measurements of the magnetic susceptibility, specific heat and magnetocaloric effect at temperatures down to 0.1~K. In both systems, the non-magnetic substitution rapidly changes the magnetically ordered ground state into a spin glass, indicating strong frustration. While for the Li system the Weiss temperature $\Theta_{\rm W}$ remains unchanged up to $x=0.55$, a strong decrease $|\Theta_{\rm W}|$ is found for the Na system. This suggests that only for the former system magnetic exchange beyond nearest neighbors is dominating. This is also corroborated by the observation of a smeared quantum phase transition in Li$_2$(Ir$_{1-x}$Ti$_x$)O$_3$ near $x=0.5$, i.e. much beyond the site percolation threshold of the honeycomb lattice.Comment: 8 pages including supplemental, 12 figure

Origin of the insulating state in honeycomb iridates and rhodates

A burning question in the emerging field of spin-orbit driven insulating iridates, such as Na2IrO3 and Li2IrO3 is whether the observed insulating state should be classified as a Mott-Hubbard insulator derived from a half-filled relativistic j_eff=1/2 band or as a band insulator where the gap is assisted by spin-orbit interaction, or Coulomb correlations, or both. The difference between these two interpretations is that only for the former, strong spin-orbit coupling (lambda >~ W, where W is the band width) is essential. We have synthesized the isostructural and isoelectronic Li2RhO3 and report its electrical resistivity and magnetic susceptibility. Remarkably it shows insulating behavior together with fluctuating effective S=1/2 moments, similar to Na2IrO3 and Li2IrO3, although in Rh4+ (4d5) the spin-orbit coupling is greatly reduced. We show that this behavior has non-relativistic one-electron origin (although Coulomb correlations assist in opening the gap), and can be traced down to formation of quasi-molecular orbitals, similar to those in Na2IrO3.Comment: 7 pages, 7 figure

Investigation of unconventional reconstruction and electronic properties on the Na2IrO3 surface

Na2IrO3 is an intriguing material for which spin-orbit coupling plays a key role. Theoretical predictions, so far unverified, have been made that the surface of Na2IrO3 should exhibit a clear signature of the quantum spin Hall effect. We studied the surface of Na2IrO3 using scanning tunneling microscopy and density-functional theory calculations. We observed atomic level resolution of the surface and two types of terminations with different surface periodicity and Na content. By comparing bias-dependent experimental topographic images to simulated images, we determined the detailed atomistic structure of both observed surfaces. One of these reveals a strong relaxation to the surface of Na atoms from the subsurface region two atomic layers below. Such dramatic structural changes at the surface cast doubt on any prediction of surface properties based on bulk electronic structure. Indeed, using spatially resolved tunneling spectroscopy we found no indication of the predicted quantum spin Hall behavior

Unconventional magnetic order on the hyperhoneycomb Kitaev lattice in β\beta-Li2IrO3: full solution via magnetic resonant x-ray diffraction

The recently-synthesized iridate $\beta$-Li$_2$IrO$_3$ has been proposed as a candidate to display novel magnetic behavior stabilized by frustration effects from bond-dependent, anisotropic interactions (Kitaev model) on a three-dimensional "hyperhoneycomb" lattice. Here we report a combined study using neutron powder diffraction and magnetic resonant x-ray diffraction to solve the complete magnetic structure. We find a complex, incommensurate magnetic order with non-coplanar and counter-rotating Ir moments, which surprisingly shares many of its features with the related structural polytype "stripyhoneycomb" $\gamma$-Li$_2$IrO$_3$, where dominant Kitaev interactions have been invoked to explain the stability of the observed magnetic structure. The similarities of behavior between those two structural polytypes, which have different global lattice topologies but the same local connectivity, is strongly suggestive that the same magnetic interactions and the same underlying mechanism governs the stability of the magnetic order in both materials, indicating that both $\beta$- and $\gamma$-Li$_2$IrO$_3$ are strong candidates to realize dominant Kitaev interactions in a solid state material.Comment: 14 pages, 9 figure

Classical theta constants vs. lattice theta series, and super string partition functions

Recently, various possible expressions for the vacuum-to-vacuum superstring amplitudes has been proposed at genus $g=3,4,5$. To compare the different proposals, here we will present a careful analysis of the comparison between the two main technical tools adopted to realize the proposals: the classical theta constants and the lattice theta series. We compute the relevant Fourier coefficients in order to relate the two spaces. We will prove the equivalence up to genus 4. In genus five we will show that the solutions are equivalent modulo the Schottky form and coincide if we impose the vanishing of the cosmological constant.Comment: 21 page

Penrose-Onsager Criterion Validation in a One-Dimensional Polariton Condensate

We perform quantum tomography on one-dimensional polariton condensates, spontaneously occurring in linear disorder valleys in a CdTe planar microcavity sample. By the use of optical interferometric techniques, we determine the first-order coherence function and the amplitude and phase of the order parameter of the condensate, providing a full reconstruction of the single particle density matrix for the polariton system. The experimental data are used as input to theoretically test the consistency of Penrose-Onsager criterion for Bose-Einstein condensation in the framework of nonequilibrium polariton condensates. The results confirm the pertinence and validity of the criterion for a non equilibrium condensed gas.Comment: 5 pages, 4 figure

Effect of isoelectronic doping on honeycomb lattice iridate A_2IrO_3

We have investigated experimentally and theoretically the series (Na$_{1-x}$Li$_{x}$)$_{2}$IrO$_{3}$. Contrary to what has been believed so far, only for $x\leq0.25$ the system forms uniform solid solutions. For larger Li content, as evidenced by powder X-ray diffraction, scanning electron microscopy and density functional theory calculations, the system shows a miscibility gap and a phase separation into an ordered Na$_{3}$LiIr$_2$O$_{6}$ phase with alternating Na$_3$ and LiIr$_2$O$_6$ planes, and a Li-rich phase close to pure Li$_{2}$IrO$_{3}$. For $x\leq 0.25$ we observe (1) an increase of $c/a$ with Li doping up to $x=0.25$, despite the fact that $c/a$ in pure Li$_{2}$IrO$_{3}$ is smaller than in Na$_{2}$IrO$_{3}$, and (2) a gradual reduction of the antiferromagnetic ordering temperature $T_{N}$ and ordered moment. The previously proposed magnetic quantum phase transition at $x\approx 0.7$ may occur in a multiphase region and its nature needs to be re-evaluated.Comment: 8 pages, 9 figures including supplemental informatio