Fig. 1. Phase tuning in Fe_5−δGeTe₂.

a Crystal structure of Fe₅GeTe₂ with atomic sites labeled. Fe(1) and Ge are modeled as split sites, marked by half-filled circles to represent 50% occupancy. b–d Schematic and procedures for tuning global symmetry via sublattice ordering. The two quantum phases can be switched by first annealing to above T_HT = 550 K and either quenching or slowly cooling to achieve the site-ordered phase or the site-disordered phase, respectively. The inset in d show the real steps of tuning phases. e–f Schematic model and STM topographic image of the $\sqrt{3}\times \sqrt{3}$ superstructure on Te termination. The right panels are Fourier transforms of the respective topographies with peaks corresponding to the lattice periodicity (white), a $\sqrt{3}\times \sqrt{3}$ superstructure periodicity (blue), and the second order of the $\sqrt{3}\times \sqrt{3}$ superstructure periodicity (pink). The inset scale bars are 17.3 nm⁻¹. The schematic lattice in e corresponds to an up–down–down (UDD) ordering of the Fe(1) atoms while that in f corresponds to a down–up–up (DUU) ordering of the Fe(1) sites. g–h The Fermi surfaces of the two phases were measured at 15 K using 114 eV LV photons, achieved by slow-cooling the crystal to room temperature from above T_HT (g) and quenching from above T_HT (h), respectively. The arrows indicate the photon polarization direction. i, j Polarization-resolved SHG intensity on slow-cooled and quenched crystals measured at 5K. In both figures, the crossed and parallel configurations correspond to E(2ω) ⊥ E(ω) and E(2ω) ∣∣ E(ω), respectively, while E(2ω) and E(ω) were simultaneously rotated in the crystal ab-plane. c.p.s. stands for counts per second. The dots are experimental data and the solid curves are the fits by a sixfold sinusoidal function.