Intrinsic Topological Superconductivity
Imaging P-Wave Scattering Interference in Superconductive Surface State of UTe2
Essence: Scattering interference of the quasiparticles in the superconductive topological surface band to UTe2 is visualized and linked quantitatively to the projection of B3u intrinsic topological superconductivity onto the (0-11) cleave surface of the crystal.
Top left: Density of electronic states N(r,V=0) and its FT N(q,V=0) in normal state of UTe2. Bottom left: Andreev tunnel conductance a(r,V=0) and its FT a(q,V=0) in superconductive state of UTe2. Comparison of their intensities is at right.
Although no known material definitely exhibits intrinsic topological superconductivity in which a spin-triplet electron pairing potential Δ(k) has odd parity, UTe2 is now the leading candidate. Ideally, the parity of Δ(k) might be established by using Bogoliubov quasiparticle interference (QPI) imaging. However, odd-parity superconductors should support a topological quasiparticle surface band (QSB) on crystal termination surfaces only for energies within the superconductive energy gap. The QPI should then be dominated by the QSB electronic structure and only reveal bulk Δ(k) characteristics excursively.
By using a superconducting scan-tips QPI we discover and visualize the in-gap quasiparticle interference patterns of its QSB. QPI visualization then yields a characteristic sextet qi:i=1-6 of interference wavevectors from which we establish QSB dispersions, and their existence only for energies |E| ≤ Δmax within the range of Fermi momenta projected onto the (0-11) crystal surface. Quantitative evaluation of this sextet qi then demonstrates precisely how the QSB is projected from the subtending bulk Fermi surface. Finally, a novel theoretical framework has been developed to predict the QPI signatures of a topological QSB at this (0-11) surface with results demonstrably consistent with the experimental data - if the bulk Δ(k) exhibits time-reversal conserving, odd-parity, a-axis nodal, B3u symmetry.
Pair Wavefunction Symmetry in UTe2 from Zero-Energy Surface State Visualization.
arXiv:2501.16636 Science in press (2025)
Essence: The zero-energy Andreev surface state expected if UTe2 is an odd-parity spin-triplet topological superconductor, is detected and visualized by using a novel configuration of s-wave superconductive scan-tip, tunneling through the superconductive topological surface state, into the bulk intrinsic topological superconductor. The characteristic of theses Andreev spectra on UTe2 are highly consistent with it being a B3u symmetry spin-triplet superconductor.
Schematic diagram of scanned Andreev tunneling microscope setup for studies of intrinsic topological superconductivity . The superconductive topological surface band of quasiparticles intervenes inside the junction between an s-wave scan tip and a p-wave intrinsic topological superconductor.
While nodal spin-triplet topological superconductivity appears highly probable in UTe2, its superconductive order-parameter Δk remains unestablished. In theory, a distinctive identifier would be the existence of a superconductive topological surface band (TSB), which could facilitate zero-energy Andreev tunneling to an s-wave superconductor, and also distinguish a chiral from non-chiral Δk via enhanced s-wave proximity. We employ s-wave superconductive scan-tips and detect intense zero-energy Andreev conductance at the UTe2 (0-11) termination surface. Imaging reveals sub-gap quasiparticle scattering interference signatures with a-axis orientation. The observed zero-energy Andreev peak splitting with enhanced s-wave proximity, signifies that Δk of UTe2 is a non-chiral state: B1u, B2u or B3u. However, if the quasiparticle scattering along the a-axis is internodal, then a non-chiral B3u state is the most consistent for UTe2.
Detection of a Pair Density Wave State in UTe2
Essence: Three pair density wave (PDW) states, coincident in their wavevectors with the three charge density wave (CDW) states observed previously, were discovered and visualized in spin-triplet superconductor UTe2.
Schematic diagram of PDW visualization in UTe2: Left is the (0-11) termination crystal surface. Middle is the measured energy gap modulation. Right: simultaneous visualization of the preexisting CDW state.
Spin-triplet topological superconductors should exhibit many unprecedented electronic properties and, although UTe2 may embody such bulk topological superconductivity, its superconductive order-parameter Δ(k) was unknown. Many diverse forms for Δ(k) are physically possible including intertwined density waves of spin (SDW), charge (CDW) and pairs (PDW). The latter state exhibits spatially modulating superconductive order-parameter Δ(r), electron pair density and pairing energy-gap. To search for a PDW state in UTe2, we visualize the pairing energy-gap with μeV-scale energy-resolution using superconductive STM tips. We detect three PDWs, each with peak-peak gap modulations circa 10 μeV and at incommensurate wavevectors Pi=1,2,3 that are indistinguishable from the wavevectors Qi=1,2,3 of the prevenient CDW. Concurrent visualization of the UTe2 superconductive PDWs and the non-superconductive CDWs reveals that every Pi : Qi pair exhibits a relative phase δϕ≈π. From these observations, and given UTe2 as a spin-triplet superconductor, this PDW state is a spin-triplet pair density wave.
Momentum Resolved Energy Gaps of Sr2RuO4 from Bogoliubov QPI
Essence: Bogoliubov QPI in superconducting Sr2RuO4 at 90mK reveals characteristics of the momentum-space structure of the superconducting energy gaps. They are nodal along (±1,±1) crystal axes on both the α and β bands. These results are most consistent with this material being a dx2-y2 symmetry superconductor – and thus not topological.
Left: the tunneling spectrum of Sr2RuO4 at T=90mK; middle is the Bogoliubov QPI signature inside the gap shown at left. Right is the best fit Sr2RuO4 energy gap structure from Bogoliubov QPI studies.
Sr2RuO4 has long been the focus of intense research interest because of conjectures that it is a p-wave topological superconductor. It is the momentum space (k-space) structure of the superconducting energy gap Δi(k) on each band i that encodes its unknown superconducting order-parameter. But, because the energy scales are so low, it was not possible to directly measure the Δi(k) of Sr2RuO4. We implemented Bogoliubov quasiparticle interference (BQPI) imaging at T=90 mK to visualize the set of Bogoliubov scattering interference wavevectors qj:j=1−5 consistent with eight gap nodes/minima, that are all closely aligned to the (±1,±1) crystal-lattice directions on both the α-and β-bands. Taking these observations in combination with other recent advances, the BQPI signature of Sr2RuO4 appears most consistent with Δi(k) having dx2−y2 (B1g) symmetry.