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

TL;DR

This work develops a surface Green-function framework for UTe$_2$ on the (0-11) plane to compute surface spectral functions and QPI patterns across normal and superconducting states for all triplet pairing possibilities. Using a four-orbital tight-binding model and $T$-matrix formalism, it shows that surface-state signatures—and particularly a zero-energy DOS peak and a robust ${f q}_1$ QPI feature—distinguish the non-chiral $B_{3u}$ pairing as most consistent with STM experiments. The analysis highlights how spin-polarized surface states and interference effects shape QPI, enabling discrimination among $A_u$, $B_{1u}$, $B_{2u}$, $B_{3u}$ and mixed chiral states. Overall, the results provide a concrete, symmetry-protected diagnostic for identifying the superconducting order parameter in UTe$_2$, with significant implications for understanding its topological and pairing properties.

Abstract

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.

Figures (34)

• Figure 1: Schematic picture of the UTe$_2$ lattice. The 4-orbital tight-binding model used in this work includes nearest-neighbor hopping between U atoms, nearest-neighbor hopping between blue color Te atoms, as gray color Te atoms weakly affect the Fermi surfacetheuss2024single, and hybridization $\delta$ between U and Te energy bands.
• Figure 2: Top view and 3D view of Fermi surface in the 4-orbital model in the presence of hybridization $\delta$.
• Figure 3: UTe$_2$ in the normal state at $E=0$: the surface spectral functions $A_s(E,k_\#,k_x)$ and its "bulk" component $A_b(E,k_\#,k_x)$ (upper row), and the JDOS $J(E,q_\#,q_x)$ and QPI $\delta\rho(E,q_\#,q_x)$ (lower row). The first Brillouin zone in the (0-11) plane is marked by the white rectangle.
• Figure 4: Density of states for non-chiral pairings. The black curve represents the bulk density of states, while the red curve corresponds to the surface density of states in the presence of a (0-11) impurity plane which mimics a surface in a 3D sample. The horizontal gray line corresponds to the DOS in the normal state. At low energies, the bulk density of states for all non-chiral pairings exhibits a characteristic U-shaped profile, consistent with either gapped or nodal superconductivity in three dimensions. The $B_{3u}$ pairing is showing a pronounced zero-energy peak in the surface DOS in contrast with the other pairings still exhibiting a U-shaped profile. We have $\Delta_0=0.3$ meV and $\eta=0.1$ meV.
• Figure 5: Density of states for chiral pairings. The black curve represents the bulk density of states, while the red curve corresponds to the surface density of states in the presence of a (0-11) impurity plane which mimics a surface in a 3D sample. The horizontal gray line corresponds to the DOS in the normal state. At low energies, the bulk density of states for all chiral pairings exhibits a characteristic U-shaped profile, consistent with either gapped or nodal superconductivity in three dimensions. We take $\Delta_0=0.3$ meV and $\eta=0.1$ meV.