Direct observation of charge order in underdoped and optimally doped Bi${}_2$(Sr,La)${}_2$CuO${}_{6+\delta }$ by resonant inelastic x-ray scattering

Abstract

Charge order in underdoped and optimally doped high-$T_{\mathrm{c}}$ superconductors Bi${}_2$Sr${}_{2-x}$La${}_x$CuO${}_{6+\delta }$ (Bi2201) is investigated by Cu $L_3$ edge resonant inelastic x-ray scattering (RIXS). We have directly observed charge density modulation in the optimally doped Bi2201 at momentum transfer $Q_{\Vert }\simeq 0.23$ rlu, with smaller intensity and correlation length with respect to the underdoped sample. This demonstrates that short-range charge order in Bi2201 persists up to optimal doping, as in other hole-doped cuprates. We explored the nodal (diagonal) direction and found no charge order peak, confirming that charge order modulates only along the Cu-O bond directions. We measured the out-of-plane dependence of charge order, finding a flat response and no maxima at half integer \emph{L} values. This suggests there is no out-of-plane phase correlation in single layer Bi2201, at variance from YBa${}_2$Cu${}_3$O${}_{6+x}$ and La${}_{2-x}$(Ba,Sr)${}_x$CuO${}_4$. Combining our results with data from the literature we assess that charge order in Bi2201 exists in a large doping range across the phase diagram, i.e. $0.07\lesssim p\lesssim 0.16$, demonstrating thereby that it is intimately entangled with the antiferromagnetic background, the pseudogap and superconductivity.

9 pages, 7 figures

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• Evolution of Charge and Pair Density Modulations in Overdoped Bi2Sr2CuO6+delta
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• Strain-induced long-range charge-density wave order in the optimally doped Bi${}_2$Sr${}_{2-x}$La${}_x$CuO${}_6$ superconductor
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• Charge Order and Fluctuations in Bi${}_2$Sr${}_{2-x}$La${}_x$CuO${}_{6+\delta }$ Revealed by ${}^{63,65}$Cu-Nuclear Magnetic Resonance
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• Strong-coupling theory of bilayer plasmon excitations
• Persistence of vortexlike phase fluctuations in underdoped to heavily overdoped Bi-2201 cuprates
• $d_{x^2-y^2}$-wave density wave and $d_{x^2-y^2}$-wave superconducting gap on the extended Hubbard model on a square lattice
• Paring density waves as the origin of a ring-like RIXS profile in Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$
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