Moiré modulated quantum spin liquid candidate 1T-TaSe$_2$

Abstract

Quantum spin liquids are quantum phases of matter featuring collectively entangled states and emergent fractional many-body excitations. While methods exist to probe three-dimensional quantum spin liquids experimentally, these techniques lack the sensitivity to probe two-dimensional quantum spin liquids. This seriously hampers the study of potential monolayer quantum spin liquid candidates such as $α$-RuCl$_3$ and 1T-TaSe$_2$. Scanning tunneling microscopy (STM) and spectroscopy (STS) have recently been suggested as promising probes of the quantum spin liquid state, as they can access the spinon spectrum through inelastic tunneling spectroscopy (IETS). In this work, we employ this approach on the quantum spin liquid candidate material 1T-TaSe$_2$ and directly measure its low-energy inelastic excitations. We observe the emergence of a $\sqrt{3}\times\sqrt{3}$ reconstruction driven by the substrate, equivalent spectroscopy across all spin sites and coexistence of zero and finite energy excitations. We show that these observations are consistent with a modulated $\sqrt{3}\times\sqrt{3}$ spin liquid ground state. Our results demonstrate that IETS provides a powerful route to obtain atomic-scale insight into the magnetic excitations of two-dimensional materials, allowing to explore the effects of moiré modulations on potential quantum liquid phases.

Figures (4)

• Figure 1: CDW and Mott insulator state in monolayer 1T-TaSe$_2$ grown by MBE and characterized by STM at 5 K. a, Schematic of monolayer 1T-TaSe$_2$ crystal and the star-of-David structure. The red, blue and black atoms represent Ta, Se and carbon atoms. The angle between HOPG and 1T-TaSe$_2$ determines the moiré structure. b, A large-scale STM image of 1T-TaSe$_2$ monolayer islands on HOPG substrate. $V=1$ V, $I=20$ pA. c, A high-resolution STM topography image of the CDW superlattice. $V=-0.5$ V, $I=50$ pA. d, Representative tunnelling spectrum on 1T-TaSe$_2$. Arrows indicate the two lower Hubbard bands (LHB1 and LHB2) and the upper Hubbard band (UHB).
• Figure 2: Moiré modulation in 1T-TaSe$_2$ on HOPG substrate at different lattice orientations. a,d,g, d$I$/d$V$ maps (extracted from grid data, at biases around LHB1) on different 1T-TaSe$_2$ islands with atomic lattices rotated by $1^\circ$, $2^\circ$, and $3^\circ$ relative to the HOPG lattice. Besides CDW superlattices, new domain-like modulations are observed on $2^\circ$ and $3^\circ$ islands. b,e,h, FT images of the corresponding d$I$/d$V$ maps. The white circles highlight one of the CDW peaks and the hexagons highlight the CDW Brillouin zone. At or near the K and K' points of the CDW Brillouin zone, new sets of peaks highlighted by green circles correspond to the moiré pattern. c,f,i, Simulated FT images of moiré with relative angles around $1^\circ$, $2^\circ$, and $3^\circ$ from HOPG.
• Figure 3: Low energy inelastic excitations in 1T-TaSe$_2$. a, In-gap inelastic excitations of monolayer 1T-TaSe$_2$ (red line). Spectrum obtained with the same tip on HOPG as a comparison (blue line). b, STM image over serveral $\sqrt{3}$ moiré cells. $V= -0.5$ V, $I=100$ pA. c, d$I$/d$V$ at neighbouring CDW centers indicated in panel b. d, A detailed constant-height d$I$/d$V$ map of $\sqrt{3}$ moiré modulation. $V= -15$ mV, $I=400$ pA. Red triangles highlight the moiré trimerization. e, FT of the data in panel d showing the $\sqrt{3} \times \sqrt{3}$ reconstruction.
• Figure 4: Theoretical modeling of a moiré-modulated QSL state in 1T-TaSe$_2$. a, Sketch of the spinon and Heisenberg models considered for a moiré-modulated QSL. The grey stars represent localized spins 1/2. The moiré introduces an effective $\sqrt{3}\times\sqrt{3}$ modulation on the triangular lattice, creating a trimerization of the spins 1/2. Spinon and many-body models with two inequivalent coupling parameters in the TaSe$_2$ lattice. b,d Simulated dI/dV as a function of energy and trimerization strength values for the spinon and Heisenberg models. c,e Simulated dI/dV with $\tau_S = \tau_H = 0.5$ for spinon model and many-body models, respectively.