Frieze charge-stripes in a correlated kagome superconductor CsCr$_3$Sb$_5$

TL;DR

The paper addresses how electronic density waves organize in CsCr$_3$Sb$_5$, a strongly correlated kagome superconductor. It uses spectroscopic-imaging STM to resolve two orthogonal unidirectional density waves, Q1 and Q2, with distinct symmetry properties and a four-sublattice intracell model that explains the frieze-phase order. The main finding is that Q2 forms a frieze charge-stripe phase breaking all in-plane mirror symmetries but preserving a mirror-glide, with sublattice interference shaping its Fourier features; Q1 accompanies a structural density wave. Together, these results link electronic frieze symmetry to superconductivity under pressure and establish frieze symmetry as a productive lens for discovering new electronic states in quantum materials.

Abstract

Kagome metals have developed into a vibrant playground for materials physics, where geometric frustration, electronic correlations and band topology come together to create a variety of exotic phenomena. Recently synthesized CsCr$_3$Sb$_5$ has provided a rare opportunity to explore unconventional superconductivity in a strongly correlated kagome system with hints of frustrated magnetism and quantum criticality. Using spectroscopic imaging scanning tunneling microscopy, we reveal a cascade of density wave transitions with different symmetries in bulk single crystals of CsCr$_3$Sb$_5$. In particular, we discover a new electronic state $-$ a unidirectional density wave that breaks all mirror symmetries akin to a chiral density wave, but in contrast retains a mirror-glide symmetry. We term this state a frieze charge-stripe order phase, because its symmetry properties agree with one of the fundamental frieze symmetry groups. A combination of high-resolution imaging, Fourier analysis and theoretical simulations uncovers the crucial role of sublattice degrees of freedom in forming this phase, with internal chiral textures of opposite handedness. Our experiments reveal that superconductivity in CsCr$_3$Sb$_5$ develops from a new type of a unidirectional density wave, and set the foundation for exploring electronic states with frieze symmetry groups in quantum materials.

Figures (13)

• Figure 1: Crystal structure and surface identification of CsCr$_3$Sb$_5$ - a 3D ball model of the CsCr$_3$Sb$_5$ crystal structure (top panel) and the atomic structure in the $ab$-plane (bottom panel). b STM topograph across a step edge between two terraces: the Sb (lower) and the Cs (higher). c Apparent topographic height along the dashed red line in (b) showing a 6.9 $\mathring{\text{A}}$ height difference between the Cs and the Sb termination, consistent with the expected bulk structure. d,e Representative STM topographs of the Cs surface and the Sb surface termination, respectively. STM setup conditions: b, $V_{sample}$ = 1 V, $I_{set}$ = 10 pA; d, $V_{sample}$ = 100 mV, $I_{set}$ = 400 pA; e, $V_{sample}$ =300 mV, $I_{set}$ = 500 pA.
• Figure 1: Fourier transform linecuts along Q$_1$ direction. Fourier transform linecuts, offset for clarity, along the Q$_1$ direction, same as those plotted in Fig. 2g, but in a different visual representation. STM setup conditions: $I_{set}$ = 300 pA.
• Figure 2: Identifying different types of charge modulations at low temperature.(a) STM topograph of the Sb surface showing stripe-like modulations in a single domain, and (b) associated Fourier transform (FT). Atomic Bragg peaks Q$^i_{Bragg}$ ($i$=$a,b,c$) are enclosed in black diamonds. Two main wave vectors Q$_1$ and Q$_2$ and enclosed in red and blue circles, respectively. Higher order harmonics and satellite peaks are enclosed in dashed circles. Both Q$_1$ and Q$_2$ are unidirectional and perpendicular to one another. (c) Smaller STM topographs showing the modulations at different STM biases. FT linecuts from panel (b) along: (d) dashed line showing Q$_1$ and associated peaks, (e) dashed blue line showing Q$_2$ and higher harmonics, and (f) dashed black line showing all the Q$_2$ Bragg satellite peaks. (g) Waterfall plot of FT linecuts of STM topographs along the red dashed line in (b) showing the absence of dispersion of Q$_1$-related peaks. (h) Waterfall plot of FT linecuts of STM topographs along the blue dashed line in (b) showing the absence of the dispersion of Q$_2$-related peaks. (i) Waterfall plot of FT linecuts of d$I$/d$V$ maps along the blue dashed line in (b) showing the absence of dispersion of Q$_2$-related peaks. STM setup conditions: a, $V_{sample}$ = -500 mV, $I_{set}$ = 200 pA; c, $I_{set}$ = 50 pA; g,h, $I_{set}$ = 300pA; i, $V_{sample}$ = 100mV, $I_{set}$ = 300pA, $V_{exc}$ = 2mV.
• Figure 2: Reproducibility of observations of different density waves.(a,b) STM topograph and corresponding Fourier transform obtained on sample 1, also from main text. (c,d) STM topograph and corresponding Fourier transform obtained on sample 2. Data on the two samples was obtained using two different STM tip wires. STM setup conditions: a, $V_{sample}$ = -500 mV, $I_{set}$ = 200 pA; b, $V_{sample}$ = 300 mV, $I_{set}$ = 200 pA.
• Figure 3: Imaging of domains with different charge-stripe orientation.(a) STM topograph encompassing multiple domains, two of which are enclosed by dashed green and orange squares. This rules out that unidirectionality observed is a consequence of an aniostropic STM tip. (b,c) Zoom-ins on the two domains denoted by the squares in (a), and (d,e) their associated Fourier transforms (FTs). Atomic Bragg peaks Q$^i_{Bragg}$ ($i$=$a,b,c$) are enclosed in black diamonds. Two main wave vectors Q$_1$ and Q$_2$ and enclosed in red and blue solid circles, respectively. Higher order harmonics and satellite peaks are enclosed in dashed circles. It can be seen that both Q$_1$ and Q$_2$ rotate together, and are orthogonal to one another in different domains. STM setup conditions: a,b,c, $V_{sample}$ = -500 mV, $I_{set}$ = 300 pA.