Coexisting electronic smectic liquid crystal and superconductivity in a Si square-net semimetal

Abstract

Electronic nematic and smectic liquid crystals are spontaneous symmetry-breaking phases that are seen to precede or coexist with enigmatic unconventional superconducting states in multiple classes of materials. In this Letter we describe scanning tunneling microscopy observations of a short ranged charge stripe (smectic) order in NaAlSi, whose superconductivity is speculated to have an unconventional origin. As well as this we resolve a clear spatial modulation of the superconducting gap amplitude, which arises due to the intertwined superconducting and smectic orders. Numerical calculations help to understand the possible driving mechanism as a suppression of kinetic energy on the Fermi surface formed in part by two large, flat-topped hole pockets of p-orbital character.

Figures (8)

• Figure 1: Overview of the NaAlSi surface as seen using STM. (a) Depiction of the layered crystal structure and (b) top-down view of its Na-terminated cleaved surface, which has $C_{4v}$ symmetry. Structures are depicted using VESTA VESTA. (c) $\frac{\mathrm{d}I}{\mathrm{d}V}(V)$ conductance curve showing overall semimetallic behavior with a 'v'-shaped minimum slightly above $E_{\mathrm{F}}$ ($V_{\mathrm{set}} = 480mV$, $I_{\mathrm{set}} = 100pA$, $V_{\mathrm{mod}} = 10mV$). (d) Conductance curve acquired around $E_{\mathrm{F}}$, with effective temperature $T_{\mathrm{eff}} \approx 350mK$, showing the superconducting gap ($V_{\mathrm{set}} = 50mV$, $I_{\mathrm{set}} = 250pA$, $V_{\mathrm{mod}} = 50\mu V$). (e) Typical STM topograph of the Na-terminated surface ($V_{\mathrm{set}} = 30mV$, $I_{\mathrm{set}} = 100pA$). The lattice vector orientations are marked with black arrows. (f) Image extracted at $V = 5mV$ from simultaneously acquired, normalized conductance ($V_{\mathrm{mod}} = 0.5mV$).
• Figure 2: Characterization of charge stripe order in $q$. (a) Fast Fourier transform (FFT) of $L(\mathbf{r}, V)$, written as $\mathcal{F} \left[ L(\mathbf{r}, V) \right]$ ($V_{\mathrm{set}} = 30mV$, $I_{\mathrm{set}} = 100pA$, $V_{\mathrm{mod}} = 0.5mV$). The Bragg peaks, at $\mathbf{q}_{a_{0}}$, are not visible simultaneously with the stripes. They become visible only at particular energies and after enhancement of their intensity [100-fold in panel (a)]. The pair of lobes, one of which is marked as $\mathbf{q}_{\mathrm{str}, a}$, describe the charge stripes. (The subscript $a$ denotes a direction parallel with the Bragg vector $\mathbf{q}_{a_{0}}$.) (b) A high-resolution view of the low-$q$ region. [The source $L(\mathbf{r})$ images for both (a) and (b) are shown in Appendix B.] (c) The magnitude of $\mathcal{F} \left[ L(\mathbf{r}, V=8mV) \right]$ sampled along linecut L0 in (b). The subsequent fitting procedure is described in Appendix C.
• Figure 3: Energy dependence of stripe intensity. (a) and (b) $\mathcal{F} \left[ L(\mathbf{r}) \right]$ images extracted above and below $E_{\mathrm{F}}$, respectively ($V_{\mathrm{set}} = 30mV$, $I_{\mathrm{set}} = 100pA$, $V_{\mathrm{mod}} = 0.5mV$). (Source $L(\mathbf{r})$ images are shown in Appendix B.) (c) Linecuts through $\mathcal{F} \left[ L(\mathbf{r}, V) \right]$ taken along the lines L1 and L2 marked in (a). Black arrows mark the features characterizing charge order. (d) The energy-dependence of total intensities under filters F1 and F2, located around the vector $\mathbf{q}_{\mathrm{str},a}$ obtained by 2D Gaussian fitting to the image in (a), and around its 90$^{\circ}$-rotated partner $\mathbf{q}_{\mathrm{str},b}$, respectively. The values near $E_{\mathrm{F}}$ are removed due to severe noise resulting from the vanishing denominator in the normalization.
• Figure 4: Observation of domains of charge stripe order. (a) Large field-of-view $L$ image exhibiting two domains of stripe order with differing orientations ($V_{\mathrm{set}} = 30mV$, $I_{\mathrm{set}} = 100pA$, $V_{\mathrm{mod}} = 0.5mV$). Fourier filtering is used to obtain amplitude maps for the Fourier components using filters similar to those in Fig. 3. The resulting maps are superimposed with separate color scales in (b). (c) Profiles through both amplitude maps [averaged over the short axis of the dashed rectangle in (b)], and (d) conductance measurement of the SC gap along the path L3 marked with a solid arrow ($V_{\mathrm{set}} = 50mV$, $I_{\mathrm{set}} = 250pA$, $V_{\mathrm{mod}} = 50\mu V$, $T_{\mathrm{eff}} \approx 350mK$). The approximate DW location is marked with a gray dashed line.
• Figure 5: Microscopic correspondence between charge stripe and SC orders. (a) A topograph ($V_{\mathrm{set}} = 50mV$, $I = 250pA$) and (b) simultaneous $L$ map in a small field of view. (c) and (d) Linecuts extracted from the simultaneous $\frac{\mathrm{d}I}{\mathrm{d}V}(V)$ conductance ($V_{\mathrm{mod}} = 50\mu V$, $T_{\mathrm{eff}} \approx 350mK$), along paths L4 and L5 marked in both (a) and (b) with dashed and solid lines, respectively. (e) $\frac{\mathrm{d}I}{\mathrm{d}V}(V)$ curves sampled at the peaks and troughs of the modulation in (c). (f) The value of the local SC order parameter $\Delta(\mathbf{r}) = \left[ \left| \Delta_{\mathrm{UCP}}(\mathbf{r}) \right| + \left| \Delta_{\mathrm{LCP}}(\mathbf{r}) \right| \right] /2$ (black circles) obtained using the fitting procedure described in Appendix E, and the corresponding variation of $L$ along path L2. The modulations of $\Delta(\mathbf{r})$ and $L(\mathbf{r})$ are in phase.