Surface charge density wave in UTe2

Abstract

The spatially uniform electronic density characteristic of a metal can become unstable at low temperatures, leading to the formation of charge density waves (CDWs). These CDWs, observed in dichalcogenides, cuprates, and pnictides arise from features in the atomic lattice and its interaction with the electronic band structure that facilitate charge ordering. However, CDWs are rarely observed in presence of Kondo screening and heavy fermion quasiparticles. The heavy fermion topological superconductor candidate UTe$_2$ presents a notable exception, exhibiting a CDW whose origin remains elusive. Here we report high resolution Scanning Tunneling Microscopy (STM) experiments that reveal the primitive wavevectors of the CDW in UTe$_2$. This allows for a refined identification of the nesting wavevectors in the electronic bandstructure. Although these wavevectors have no specific influence on the bulk properties, for example on antiferromagnetic fluctuations, they cause the interactions leading to the CDW at the surface. The heavy fermion hybridization pattern is spatially modulated specifically at the nesting wavevectors, suggesting that surface induced modifications in the U 5f electron valence enable a novel form of purely electron-driven charge ordering.

Figures (12)

• Figure 1: | Crystal structure and CDW of UTe$_2$.a Atomic lattice of UTe$_2$. Violet, red and green spheres depict Te(1), Te(2) and U atoms, respectively. The cleaved (011) plane is given in grey. b Atomic resolution topographic image of the UTe$_2$ surface. The atomic lattice positions are marked by dots, with colors corresponding to those in a. The white scale bar represents 1 nm. Te(2) atoms form chains along the crystallographic a-direction. The rectangle shown with solid blue lines defines the surface unit cell, while the primitive crystal unit cell is indicated by dashed blue lines. c Schematic phase diagram of UTe$_2$, adapted from Refs.Ran2019Lewin_2023. Phases are labelled as field polarized (FP), superconducting in the FP phase (SC$_{FP}$) and superconducting in the paramagnetic phase (SC$_{PM}$). The black dashed line indicates the direction of the applied magnetic field, perpendicular to the cleaved (011) surface. d-f Black lines schematically represent the bulk Brillouin zone. Reciprocal space axes are shown in the bottom left corner of each panel. Blue dots denote selected high symmetry points of the bulk Brillouin zone. The complete set of high-symmetry points for the bulk and the surface Brillouin zones is presented in Extended Data Fig. \ref{['FigBZs']} and discussed in Supplementary Information, Section 1. Orange dots provide the positions of the Bragg peaks previously reported in Refs.Aishwarya2023Gu2023Aishwarya2024LaFleur2024. Yellow dots denote the position of the Bragg peaks of the CDW identified in this study, and the green arrows represent the corresponding wavevectors $Q_{CDW1}$ and $Q_{CDW2}$.
• Figure 1: | Surface (011) and bulk Brillouin zones of UTe$_2$.a The bulk Brillouin zone of UTe$_2$ is delineated by black lines. The zone center, designated as the $\Gamma$ point, is indicated by a blue star. Additional high-symmetry points are also marked. The positions of the $\Gamma$ points in all 14 adjacent bulk Brillouin zones are also represented by blue stars. b The bulk Brillouin zone, as in a, projected into the (011) surface plane is shown by black lines. The surface Brillouin zone, delineated by red lines, corresponds to the Wigner-Seitz cell of the surface reciprocal lattice, defined by projected bulk $\Gamma$ (blue stars). High symmetry points of the surface Brillouin zone are indicated by blue points and labeled as $\overline{\Gamma}$, $\overline{X}$, $\overline{Y}$ and $\overline{Y}'$. The two-dimensional surface surface point group is $D_1$.
• Figure 2: | Tunneling conductance maps of the CDW. Tunneling conductance maps of UTe$_2$ at 10 T a, 15 T b, and 20 T c, acquired from three distinct fields of view, and their corresponding Fourier transforms d,e,f. The white scale bars are 5 nm long. The bias voltage for all three maps is close to zero. For tunneling conductance maps as a function of the bias voltage, refer to Extended Data Fig. \ref{['FigureBias']} and Supplementary videos. The white scale bar in the Fourier transforms d-f represents 1 nm$^{-1}$. The color scale for each map is indicated by the bars on the left. Bragg peaks associated with the atomic lattice are marked by white circles in d,e,f. The surface Brillouin zone is delineated by red lines in d,e,f (see also Extended Data Fig. \ref{['FigBZs']} and Supplementary Infomation, Section 1). Bragg peaks corresponding to charge modulations reported in previous experiments are located slightly outside the surface Brillouin zone boundary and are marked by orange circles. The newly identified CDW wavevectors are indicated by yellow circles in d,e,f.
• Figure 2: | Conductance maps and their Fourier transforms. We present representative tunneling conductance maps (left panels) and their corresponding Fourier transforms (right panels) for a few bias voltages (indicated in each panel), acquired at magnetic fields of a 10 T, b 15 T and c 20 T. The full bias voltage dependence is provided as Supplementary videos.
• Figure 3: | Bulk Fermi surface and Fermi contours at the surface of UTe$_2$.a The Fermi surface is represented as a colored contour, with blue indicating electron-like bands and orange indicating hole-like bands. The bulk Brillouin zone is delineated by black lines. Reciprocal space planes perpendicular to ${\bm k}_{\perp}$, specifically at $k_{\perp}=0$ and $k_{\perp}=|\Gamma-S|$, are shown in grey. As shown in the Extended Data Fig.\ref{['FigBandstructure']} b, the whole Fermi surface has a pronounced U 5f character, which dominates in the features shown in b,c,d. b Fermi surface contour at the reciprocal space plane $k_{\perp}=|\Gamma-S|$. The ${\bm k}_{\parallel}$ axis is perpendicular to ${\bm k}_x$ within the (011) surface plane in reciprocal space (depicted in grey in a). The surface Brillouin zone is delineated by a red line (see also Extended Data Fig. \ref{['FigBZs']}). The wavevector $\bm{Q}_{CDW1}$, indicated by a light green arrow, is very close to the nesting wavevector of the electron-like band. c Normalized density of states of the Fermi surface contour $g_{Norm,\nu}({\bm k}_{\perp})=\frac{1}{L}\int_L\frac{dL}{\vert \nabla_{\bm{k}} E\vert }$, where $L$ is the length of the Fermi surface contour in reciprocal space and $\nu$ is the band index. Blue and orange colors correspond to the respective band, as in a. Top axis indicates the high symmetry points that the plane passes through. d We depict the atomic Bragg lattice as black points within the reciprocal space surface plane ${\bf k}_{\perp}=0$. The first Brillouin zone of the surface is delineated by red lines and is repeated into adjacent reciprocal space regions. The Fermi contour of the hole band is represented by orange lines. The surface Brillouin zone order is numbered from $1-5$ and the zones are distinguished by different colors. The Fermi contours in higher-order surface Brillouin zones are folded into the first surface Brillouin zone by vector addition of a reciprocal lattice wavevector of the surface $\overline{{\bm G_S}}$. Dark green arrows indicate the experimentally determined wavevector $\bm{Q}_{CDW2}$.