arXiv subjects

Shuqiu Wang

Publications and source records attributed to Shuqiu Wang.

7 recordsLinked to original sources

arXiv2026

Visualizing the Odd-parity Superconducting Order Parameter and its Quasiparticle Surface Band in UTe2

A distinctive identifier of nodal intrinsic topological superconductivity (ITS) would the appearance of an Andreev bound state on crystal surfaces parallel to the nodal axis, in the form of a topological quasiparticle surface band (QSB) appearing only for $T < T_C$. Moreover, theory shows that specific QSB characteristics observable in tunneling to an s-wave superconductor can distinguish between chiral and non-chiral ITS order parameter $Δ_k$. To search for such phenomena in $\text{UTe}_2$, s-wave superconductive scan-tip scanning tunneling microscopy (STM) imaging was employed. It reveals an intense zero-energy Andreev conductance maximum at the $\text{UTe}_2$ (0-11) crystal termination. Development of the zero-energy Andreev conductance peak into two finite-energy particle-hole symmetric conductance maxima as the tunnel barrier is reduced, then signifies that $\text{UTe}_2$ superconductivity is non-chiral. Quasiparticle interference imaging (QPI) for an ITS material should be dominated by the QSB for energies within the superconductive energy gap $|E| \le Δ$, so that bulk $Δ(k)$ characteristics of the ITS can only be detected excursively. Again using a superconducting scan-tip, the in-gap quasiparticle interference patterns of the QSB of $\text{UTe}_2$ were visualized. Specifically, a band of Bogoliubov quasiparticles appears as a characteristic sextet $q_i$ :$i = 1-6$ of interference wavevectors showing that QSB dispersions $k(E)$ occur only for energies $|E| \le Δ_{max}$ and only within the range of Fermi momenta projected onto the (0-11) crystal surface. In combination, these phenomena are consistent with a bulk $Δ(k)$ exhibiting spin triplet, time-reversal conserving, odd-parity, a-axis nodal, $B_{3u}$ symmetry in $\text{UTe}_2$.

cond-mat.supr-con↗

arXiv2025

Quasiparticle interference and spectral function of the UTe$_2$ superconductive surface band

We compute the (0-11) surface spectral function, the surface density of states (DOS), and the quasiparticle interference (QPI) patterns, both in the normal state and superconducting (SC) state of UTe$_2$. We consider all possible non-chiral and chiral order parameters (OPs) that could in principle describe the superconductivity in this compound. We describe the formation of surface states whose maximum intensity energy depends on the nature of the pairing. We study also the QPI patterns resulting from the scattering of these surface states. We show that the main feature distinguishing between various OPs is a QPI peak that is only observed experimentally in the superconducting state. The energy dispersion and the stability of this peak is consistent among the non-chiral OPs only with a $B_{3u}$ pairing. Moreover, $B_{3u}$ is the only non-chiral pairing that shows a peak at zero energy in the DOS, consistent with the experimental observations.

cond-mat.supr-con↗

arXiv2025

Odd-Parity Quasiparticle Interference in the Superconductive Surface State of UTe2

Although no known material exhibits intrinsic topological superconductivity, wherein spin-triplet odd-parity electron pairing occurs, UTe2 is now the leading representative of this class. Conventionally, the parity of the superconducting order parameter may be established by using Bogoliubov quasiparticle interference (QPI) imaging. However, odd-parity superconductors should support a topological quasiparticle surface band (QSB) at energies within the maximum superconducting energy gap. QPI would then be dominated by the electronic structure of the QSB and only reveal the characteristics of the bulk order parameter excursively. Here, we visualize quasiparticle interference patterns of UTe2 and find that, at the (0-11) cleave surface, a new band of Bogoliubov quasiparticles appears only in the superconducting state. QPI visualization then allows study of dispersion of states within this QSB, which we demonstrate exists only within the range of Fermi momenta projected onto the (0-11) surface. Finally, we develop a theoretical framework to predict the QPI signatures of such a QSB at the (0-11) surface of UTe2. Its predictions are most consistent with the experimental results if the bulk superconducting gap function exhibits time-reversal conserving, odd-parity, a-axis nodal, B3u symmetry.

cond-mat.supr-con↗

arXiv2025

Pair Wavefunction Symmetry in UTe2 from Zero-Energy Surface State Visualization

Although nodal spin-triplet topological superconductivity appears probable in UTe2, its superconductive order-parameter $Δ_k$ 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 $Δ_k$ via enhanced s-wave proximity. Here 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 $Δ_k$ 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.

cond-mat.supr-con↗

arXiv2023

Discovery of Orbital Ordering in Bi2Sr2CaCu2O8+x

The primordial ingredient of cuprate superconductivity is the CuO2 unit cell. Here, theoretical attention usually concentrates on the intra-atom Coulombic interactions dominating the 3d^9 and 3d^10 configurations of each copper ion. However, if Coulombic interactions also occur between electrons of the 2p^6 orbitals of each planar oxygen atom, spontaneous orbital ordering may split their energy levels. This long predicted intra-unit cell symmetry breaking should then generate an orbital ordered phase, for which the charge-transfer energy E separating the 2p^6 and 3d^10orbitals is distinct for the two oxygen atoms. Here we introduce sublattice resolved E(r) imaging techniques to CuO2 studies and discover intra-unit-cell rotational symmetry breaking of E(r), with energy-level splitting between the two oxygen atoms on the 50 meV scale. Spatially, this state is arranged in disordered Ising domains of orthogonally oriented orbital order that appear 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 energy levels of the oxygen orbitals by ~50 meV, in underdoped CuO2.

cond-mat.supr-con↗

arXiv2023

Detection of a Pair Density Wave State in UTe$_2$

Spin-triplet topological superconductors should exhibit many unprecedented electronic properties including fractionalized electronic states relevant to quantum information processing. Although UTe$_2$ may embody such bulk topological superconductivity, its superconductive order-parameter $Δ(\mathbf{k})$ remains unknown. Many diverse forms for $Δ(\mathbf{k})$ are physically possible in such heavy fermion materials. Moreover, intertwined density waves of spin (SDW), charge (CDW) and pairs (PDW) may interpose, with the latter state exhibiting spatially modulating superconductive order-parameter $Δ(\mathbf{r})$, electron pair density and pairing energy-gap. Hence, the newly discovered CDW state in UTe$_2$ motivates the prospect that a PDW state may exist in this material. To search for it, we visualize the pairing energy-gap with $μ$$eV$-scale energy-resolution using superconductive STM tips. We detect three PDWs, each with peak-peak gap modulations circa 10 $μ$$eV$ and at incommensurate wavevectors $\mathbf{P}_{i=1,2,3}$ that are indistinguishable from the wavevectors $\mathbf{Q}_{i=1,2,3}$ of the prevenient CDW. Concurrent visualization of the UTe$_2$ superconductive PDWs and the non-superconductive CDWs reveals that every $\mathbf{P}_i$ : $\mathbf{Q}_i$ pair exhibits a relative phase $δϕ\approx π$. From these observations, and given UTe$_2$ as a spin-triplet superconductor, this PDW state should be a spin-triplet pair density wave. While such states do exist in superfluid $^{3}$He, for superconductors they are unprecedented.

cond-mat.supr-con↗

arXiv2021

Scattering Interference Signature of a Pair Density Wave State in the Cuprate Pseudogap Phase

An unidentified quantum fluid designated as the pseudogap (PG) phase is produced by electron-density depletion in the CuO$_2$ antiferromagnetic insulator. Current theories suggest that the PG phase may be a pair density wave (PDW) state characterized by a spatially modulating density of electron pairs. Such a state should exhibit a periodically modulating energy gap $Δ_P(\pmb r)$ in real-space, and a characteristic quasiparticle scattering interference (QPI) signature $Λ_P(\pmb q)$ in wavevector space. By studying strongly underdoped Bi$_2$Sr$_2$CaDyCu$_2$O$_8$ at hole-density ~0.08 in the superconductive phase, we detect the $8a_0$-periodic $Δ_P(\pmb r)$ modulations signifying a PDW coexisting with superconductivity. Then, by visualizing the temperature dependence of this electronic structure from the superconducting into the pseudogap phase, we find evolution of the scattering interference signature $Λ(\pmb q)$ that is predicted specifically for the temperature dependence of an $8a_0$-periodic PDW. These observations are consistent with theory for the transition from a PDW state coexisting with d-wave superconductivity to a pure PDW state in the Bi$_2$Sr$_2$CaDyCu$_2$O$_8$ pseudogap phase.

cond-mat.supr-con↗