While condensed matter systems host both Fermionic and Bosonic quasi-particles, reliably predicting and empirically verifying topological states is only mature for Fermionic electronic structures, leaving topological Bosonic excitations sporadically explored. This is unfortunate, as Bosonic systems such a phonons offer the opportunity to assess spinless band structures where nodal lines can be realized without invoking special additional symetries to protect against spin-orbit coupling.Here we combine first-principles calculations and meV-resolution inelastic x-ray scattering to demonstrate the first realization of parity-time reversal (PT ) symmetry protected helical nodal lines in the phonon spectrum of MoB2. This structure is unique to phononic systems as the spin-orbit coupling present in electronic systems tends to lift the degeneracy away from high-symmetry locations. Our study establishes a protocol to accurately identify topological Bosonic excitations, opening a new route to explore exotic topological states in crystalline materials.
The magnetic excitations in electron doped (Sr1−xLax)2IrO4 with x = 0.03 were measured using resonant inelastic X-ray scattering at the Ir L3-edge. Although much broadened, well defined dispersive magnetic excitations were observed. Comparing with the magnetic dispersion from the undoped compound, the evolution of the magnetic excitations upon doping is highly anisotropic. Along the anti-nodal direction, the dispersion is almost intact. On the other hand, the magnetic excitations along the nodal direction show significant softening. These results establish the presence of strong magnetic correlations in electron doped (Sr1−xLax)2IrO4 with close analogies to the hole doped cuprates, further motivating the search for high temperature superconductivity in this system. PACS numbers: 71.27.+a, 74.25.Ha, 78.70.Dm Together with the tremendous research activity on the superconducting cuprates [1,2], efforts to compare the cuprates with other related systems have also been on-going for decades. Such comparison serves as a natural approach to clarify the roles of multiple emergent phenomena in the phase diagram of the cuprates, including magnetic fluctuations, superconductivity, pseudo gap and charge density waves etc. The 5d oxide Sr 2 IrO 4 is an excellent candidate for such study. This so called spin-orbit-coupling driven Mott insulator [3] is in close proximity to the single layered cuprate La 2 CuO 4 , both structure-wise [4] and electronically [5][6][7][8]. Sr 2 IrO 4 hosts a single hole in the t 2g manifold where a Mott gap is opened, assisted by strong spin-orbit coupling [3,9,10], and its magnetic excitation spectrum can be well described using a Heisenberg model of effective spin-1 2 moments on a square lattice [11,12]. With a minimum single band model, Sr 2 IrO 4 and La 2 CuO 4 are strikingly similar [13], leading to the proposal that this compound could also host unconventional high temperature superconductivity (HTS) upon doping [13,14]. Moreover, due to the opposite signs of the nextnearest-neighbor hopping integral in these two systems, theoretical work further suggests that the electron doped Sr 2 IrO 4 might be more closely analogous to those of hole (rather than electron) doped cuprates [13,14].Although the phase diagram of doped Sr 2 IrO 4 has not been fully explored, a large amount of experimental work supports the hypothesis that the Fermiology of the doped iridates is closely analogous to the cuprates. Upon doping with La up to 6%, Sr 2 IrO 4 evolves from an antiferromagnetically ordered insulator to a paramagnetic [15] or percolative [16] metal. A T-linear resistivity was observed with potassium substitution [15]. Further, angle-resolved photoemission spectroscopy (ARPES) data from several groups [5][6][7]17] has shown convincingly that doping indeed drives a similar low energy electron evolution as observed in the cuprates. An anisotropic pseudo gap opens on the Fermi surface, with the same symmetry as that of the cuprates. However, the related question of whether the magnetic correlations that ...
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