Antiferromagnetic stripe phase and large-gap insulating ground state of the correlated $\sqrt{3}\times\sqrt{3}$~R30$^{\circ}$-Sn/Si(111) single atomic layer

Abstract

The one-third monolayer Sn layer on Si(111) has long been considered a benchmark system for exploring two-dimensional Mott physics, owing to its narrow bandwidth and sizable on-site Coulomb repulsion. Previous experiments suggested the emergence of a low-temperature Mott insulating phase with an energy gap of only a few tens of meV, while theory predicted a possible antiferromagnetic ordering that remained experimentally elusive. Here, by combining low-temperature scanning tunneling microscopy/spectroscopy with first-principles calculations, we reveal that the $\sqrt{3}\times\sqrt{3}$~R30$^{\circ}$-Sn/Si(111) surface undergoes a transition below 30K into a robust insulating state characterized by a remarkably large gap of about 440 $\pm$ 120 meV at 4K, five to ten times larger than previously reported. Quasiparticle interference imaging uncovers a well-defined $2\sqrt{3}\times\sqrt{3}$~R30$^{\circ}$-Sn/Si(111) superstructure, providing direct evidence for a two-dimensional stripe-like antiferromagnetic order. Ab initio calculations reveal that the silicon substrate stabilizes this phase through strong nonlocal tin-tin interactions, highlighting the decisive role of substrate-driven correlations in the $\sqrt{3}\times\sqrt{3}$~R30$^{\circ}$-Sn/Si(111) system.

Figures (9)

• Figure 1: (color online) (a) Large scale STM topography of the $\sqrt{3}\times\sqrt{3}$ R30$^{\circ}$-Sn/Si(111) sample measured with $V_{bias}=-1.0~$V and $I=20~$pA. (b) Small scale area measured in the single $\sqrt{3}\times\sqrt{3}$ domain indicated by the yellow square in panel (a). All measurements were carried out at $T= 4.2$ K. (c) Top view of the $\sqrt{3}\times\sqrt{3}$ R30$^{\circ}$ and 2$\sqrt{3}\times\sqrt{3}$ R30$^{\circ}$-Sn/Si(111) structures (red and blue respectively) where yellow balls represent top Sn atoms, Si atoms are reported in gray scale from light (topmost layer) to dark (inner layer). The elementary Si(111) surface unit cell is shown in green. (d) Corresponding side view projected on the dashed line marked in panel (c). (e) Electronic wavefunctions at the $\Gamma$ point calculated in the HSE06-DFT framework at an energy closest to $\varepsilon_F$: the strong hybridization of Sn orbitals with neighboring Si orbitals leads to a spatial vertical extension up to the third Si(111) plane. g) Proposed magnetic ordering of the spin $1/2$ lattice at low temperature. The relative Brillouin zones are indicated.
• Figure 2: (color online) Temperature dependent $dI/dV(E=eV_{bias})$ spectra acquired by scanning tunneling spectroscopy in single $\sqrt{3}\times\sqrt{3}$ R30$^\circ$-Sn/Si(111) domains. (a) Comparison between tunneling spectra acquired at room temperature (RT), 77 K and 4 K. A large energy gap has set in at 4 K. These spectra are measured between [-1;1] V using a set-point at $I=200$ pA for $V_{bias}$=-1 V. (b) Temperature evolution of the $dI/dV(E)$ tunneling spectra between $37.6$ K and 6 K. The energy gap opening starts around 25-30K. These spectra are measured between [-2;2] V using a set-point at $I=200$ pA for $V_{bias}$=-2 V. (c) STM topography with atomic resolution measured in a $50\times50$ nm$^2$ area at $T=4.2$ K in $\sqrt{3}\times\sqrt{3}$ R30$^{\circ}$-Sn/Si(111) with $V_{bias}=-2.0~$V and $I=50~$pA. (d,e,f) $dI/dV(E,x,y)$ spectroscopic map recorded at $E=-1.30$ eV, $E=-1.10$ eV, $E=-0.65$ eV extracted from a $256\times256$ grid of spectroscopic maps measured in the energy range [-2;+2] eV. The Fourier transform of such $dI/dV(E,x,y)$ maps gives the QPI features presented in Fig. \ref{['QPI_mag_order']}. (g) Average spectrum of the whole $50\times50$ nm$^2$ area and individual spectra acquired above three typical defects indicated by the corresponding circles in images c-f: Si-substitution, Sn-vacancy and dopant-substitution, and in a location free of defects (labelled clean zone). We marked with Sn$_i$ and Si$_i$ the corresponding main tin and silicon states peaks in the density of states (see text).
• Figure 3: Top panel: electronic band structures for the antiferromagnetic $2\sqrt{3}\times\sqrt{3}$ R30$^\circ$-Sn/Si(111) system along the $\Gamma-X-M-Y-\Gamma$ path of the Brillouin zone (see Fig.\ref{['topos_structure']}) along with the corresponding density of states. Marked peaks in the density of states correspond to the measured ones (see Fig.\ref{['comp_dI_dV']}). The projected Si bulk band structure is indicated as gray-shaded areas. Bottom left panel: electronic band structures, same as top panel, as a function of the HSE screening parameter $\omega$, from $0.08$ (blue lines) to $0.55$ Bohr$^{-1}$ (ocher lines) (see text). Bottom right panel: direct (at $M$ point) and indirect band gap as a function of the screening parameter. Note that $\omega=0.11$ Bohr$^{-1}$ is the standard HSE06 value, used in the upper panel.
• Figure 4: (color online) Revealing signatures of the Sn, Si bandstructures and magnetic supercell. a) Energy dependent quasiparticle interferences (QPI) maps (black and white). The top row represents experimental QPI acquired under $B=0$ magnetic field while the bottom raw gives the theoretical calculated ones. Each top panel represents the numerical Fourier transform of a $dI/dV(E=eV)$ map acquired at the indicated energy at 4 K in the same $50\times50$ nm$^2$ area of a single $\sqrt{3}\times\sqrt{3}$ R30$^{\circ}$-Sn/Si(111) domain. The bottom row reports symmetrized joint density of states calculations obtained using the ab-initio electronic band structure shown in Fig.\ref{['el']}, top panel. The colored drawings are guide for the eyes. b) Experimental QPI maps acquired at $B=0$ and $B=6$ T perpendicular magnetic field. In addition to the usual Bragg peaks indicated by $q^1_{\sqrt{3}}$ and $q^2_{\sqrt{3}}$, sharp superlattice spots of weaker intensities are seen, indexed by the vector $q_{2\sqrt{3}}$, corresponding to the colinear antiferromagnetic ordering of the spin $1/2$ lattice.
• Figure 5: Optimizing the temperature growth: defects density. STM topographies of three different samples showing atomic resolution of a $100\times100$ nm$^2$ area of $\sqrt{3}\times\sqrt{3}~R30^{\circ}$-Sn/Si(111) measured at $T=4.2$ K with $V_{bias}=-2.0~$V and $I=50~$pA for 0.33 monolayer of Sn deposited on a n-doped $7\times7$-Si(111) substrate held at: a) 550$^{\circ}$C, b) 600$^{\circ}$C, c) 700$^{\circ}$C. The lowest point defects density is found at 600$^{\circ}$C.