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

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.

💡 Research Summary

In this work the authors combine scanning tunneling microscopy (STM) and density‑functional theory (DFT) to reveal that the square‑net semimetal NaAlSi simultaneously hosts a short‑range electronic smectic liquid‑crystal order and bulk superconductivity with a critical temperature of about 7.2 K. High‑resolution STM on the Na‑terminated surface shows a pronounced one‑dimensional charge‑stripe pattern in the normalized conductance map L(r,V) at low bias (≈5 mV). Fourier analysis identifies an incommensurate wave vector q_str≈0.235 q_a0, corresponding to a stripe period of roughly 4.25 lattice constants, and indicates that the stripes are weakly pinned, fluctuate in amplitude and phase, and can reconfigure abruptly under tip perturbations. Energy‑dependent FFT maps reveal that the stripe intensity is strongest above the Fermi level for one orientation (q_str,a) and below the Fermi level for the orthogonal orientation (q_str,b), with the two intensity peaks separated by about 13 meV. Large‑area maps expose domains of stripe order rotated by 90°, separated by narrow domain walls; the superconducting gap measured across these walls does not change, suggesting that the smectic order neither competes strongly nor suppresses superconductivity.

Crucially, the superconducting coherence peaks display a spatial modulation that follows the stripe pattern. Line cuts perpendicular to the stripes show a periodic variation of the gap magnitude Δ(r) that is in phase with the local conductance L(r,V=5 mV), i.e., with the local charge density. This modulation is reminiscent of pair‑density‑wave phenomena observed in charge‑density‑wave superconductors, but here the primary order is a liquid‑crystal‑like smectic rather than a conventional CDW, leading the authors to propose a “pair smectic” as a secondary order.

DFT calculations of the surface electronic structure reproduce the known bulk bands: a Γ‑centered electron pocket of Al s‑character and two large, flat‑topped Si p‑derived hole pockets that extend along the Γ–X directions. The hole pockets are nearly degenerate in the pristine state, giving the crystal C4v symmetry. A lifting of the p_x/p_y degeneracy—interpreted as a band Jahn‑Teller effect—breaks rotational symmetry to C2v, producing a nematic precursor. The identified smectic wave vector q_str connects flat regions of one hole pocket to the electron pocket, providing a nesting condition that can open a small gap at the new Brillouin‑zone boundary. This reconstruction reduces kinetic energy (band dispersion) and stabilizes the stripe order without rendering the system insulating, because other parts of the Fermi surface remain metallic.

The authors therefore argue that the driving force for the smectic order is the suppression of kinetic energy on the flat portions of the p‑orbital hole bands. The coexistence of this electronic smectic with superconductivity, together with the observed gap modulation, suggests an intimate coupling: the smectic order modulates the local density of states, which in turn modulates the pairing strength. The lack of a gap change across domain walls indicates that the two orders are not in direct competition but rather coexist, possibly with the smectic acting as a scaffold for a spatially varying superconducting order parameter.

This study is significant for several reasons. First, it demonstrates that electronic liquid‑crystal phases, previously documented mainly in d‑orbital cuprate and iron‑based superconductors, can also emerge in p‑orbital square‑net semimetals where strong correlations are not obvious. Second, it provides a concrete example where flat band physics and kinetic‑energy frustration give rise to both nematic and smectic symmetry breaking, offering a new route to unconventional superconductivity. Third, the direct observation of a superconducting gap that follows the smectic modulation opens a fresh experimental window on pair‑density‑wave‑like phenomena in systems without a conventional charge‑density wave.

Overall, the paper establishes NaAlSi as a versatile platform for studying intertwined electronic orders in a low‑density, p‑orbital system, and it highlights the broader relevance of kinetic‑energy–driven instabilities in shaping the phase diagrams of quantum materials.