Spontaneous Lattice Distortion in the Spin-Triplet Superconductor CuxBi2Se3

The doped topological insulator ${\mathrm{Cu}}_{x}{\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ has attracted considerable attention as a new platform for studying novel properties of spin-triplet and topological superconductivity. In this work, we performed synchrotron x-ray diffraction measurements on ${\mathrm{Cu}}_{x}{\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ ($0.24\ensuremath{\le}x\ensuremath{\le}0.46$) to investigate the coupling between the superconducting order parameter and crystal lattice. In the crystals in which the vector order parameter ($\mathbit{d}$ vector) is tilted from the crystal high-symmetry directions as evidenced by nematic diamagnetic susceptibility, we find a sizable lattice distortion ($\ensuremath{\sim}100\text{ }\text{ }\mathrm{pp}\mathrm{m}$) associated with the onset of superconductivity. In contrast, in crystals with the $\mathbit{d}$ vector aligned along the high-symmetry directions, we find no appreciable change in lattice constant. Together with a pronounced vestigial behavior of the distortion, the results are clear evidence for an odd-parity ${E}_{u}$ order parameter that couples with trigonal lattice. Furthermore, in the crystal with $x=0.46$ where diamagnetic susceptibility is isotropic in the plane, no lattice distortion accompanying the superconducting transition is found, which is in line with a chiral superconducting state in the highly doped region. Our work shows that lattice distortion can be a powerful diagnosing quantity for nematic superconductivity with two-component order parameter.