Probing d-wave superconducting gap of high-$T_{\mathrm{c}}$ cuprate ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{10+\delta }$ by resonant inelastic X-ray scattering

Abstract

The superconducting gap is a characteristic feature of high-T${}_c$ superconductors and provides crucial information on the pairing mechanism underlying high-temperature superconductivity. Here, we employ high-resolution resonant inelastic X-ray scattering (RIXS) at the Cu $L_3$-edge to investigate the superconducting gap in the overdoped cuprate ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{10+\delta }$ ($T_{\mathrm{c}}$ = 107 K). By analyzing antisymmetrized, temperature-dependent RIXS spectra over a range of in-plane momentum transfers, we observe a clear suppression of low-energy spectral weight below T${}_c$, indicative of superconducting gap formation. This suppression is most pronounced at small momentum transfers ($|{\mathbf{q}}_{\parallel }|\le 0.18$ r.l.u.) and corresponds to a gap size of approximately 2${\Delta }_0\sim$ 130 meV. Comparison with theoretical calculations of the momentum-dependent charge susceptibility supports a d-wave symmetry of the superconducting gap, while an isotropic s-wave gap fails to reproduce key experimental features. These findings establish RIXS as a powerful, bulk-sensitive probe of superconducting gap symmetry and highlight its utility for studying materials beyond the reach of surface-sensitive techniques such as ARPES and STM.

11 pages, 10 figures

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