Dr Shuqiu Wang

Abstract:

Spin-triplet topological superconductors should exhibit many unprecedented electronic properties, including fractionalized electronic states relevant to quantum information processing. Although UTe₂ may embody such bulk topological superconductivity^{1,2,3,4,5,6,7,8,9,10,11}, its superconductive order parameter Δ(k) remains unknown¹². Many diverse forms for Δ(k) are physically possible¹² in such heavy fermion materials¹³. Moreover, intertwined^14,15 density waves of spin (SDW), charge (CDW) and pair (PDW) may interpose, with the latter exhibiting spatially modulating^14,15 superconductive order parameter Δ(r), electron-pair density^16,17,18,19 and pairing energy gap^{17,20,21,22,23}. Hence, the newly discovered CDW state²⁴ in UTe₂ motivates the prospect that a PDW state may exist in this material^24,25. To search for it, we visualize the pairing energy gap with μeV-scale energy resolution using superconductive scanning tunnelling microscopy (STM) tips^{26,27,28,29,30,31}. We detect three PDWs, each with peak-to-peak gap modulations of around 10 μeV and at incommensurate wavevectors P_i=1,2,3 that are indistinguishable from the wavevectors Q_i=1,2,3 of the prevenient²⁴ CDW. Concurrent visualization of the UTe₂ superconductive PDWs and the non-superconductive CDWs shows that every P_i:Q_i pair exhibits a relative spatial phase δϕ ≈ π. From these observations, and given UTe₂ as a spin-triplet superconductor¹², this PDW state should be a spin-triplet PDW^24,25. Although such states do exist³² in superfluid ³He, for superconductors, they are unprecedented.

Abstract:

Although nodal spin-triplet topological superconductivity appears probable in uranium ditelluride (UTe₂), its superconductive order parameter Δ_k remains unestablished. In theory, a distinctive identifier would be the existence of a superconductive topological surface band, which could facilitate zero-energy Andreev tunneling to an s-wave superconductor and also distinguish a chiral from a nonchiral Δ_k through enhanced s-wave proximity. In this study, we used s-wave superconductive scan tips and detected intense zero-energy Andreev conductance at the UTe₂ (0-11) termination surface. Imaging revealed subgap quasiparticle scattering interference signatures with a-axis orientation. The observed zero-energy Andreev peak splitting with enhanced s-wave proximity signifies that Δ_k of UTe₂ is a nonchiral state: B_1u, B_2u, or B_3u. However, if the quasiparticle scattering along the a axis is internodal, then a nonchiral B_3u state is the most consistent for UTe₂.

Abstract:

The primordial ingredient of cuprate superconductivity is the CuO₂ unit cell. Theories usually concentrate on the intra-atom Coulombic interactions dominating the 3d⁹ and 3d¹⁰ configurations of each copper ion. However, if Coulombic interactions also occur between electrons of the 2p⁶ orbitals of each planar oxygen atom, spontaneous orbital ordering may split their energy levels. This long-predicted intra-unit-cell symmetry breaking should generate an orbitally ordered phase, for which the charge transfer energy ε separating the 2p⁶ and 3d¹⁰ orbitals is distinct for the two oxygen atoms. Here we introduce sublattice-resolved ε(r) imaging to CuO₂ studies and discover intra-unit-cell rotational symmetry breaking of ε(r). Spatially, this state is arranged in disordered Ising domains of orthogonally oriented orbital order bounded by dopant ions, and within whose domain walls low-energy electronic quadrupolar two-level systems occur. Overall, these data reveal a Q = 0 orbitally ordered state that splits the oxygen energy levels by ~50 meV, in underdoped CuO₂.