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The intermediate behavior near a quantum phase transition is crucial for understanding the quantum criticality of various competing phases and their separate origins, yet remains unexplored for the multiple Yu-Shiba-Rusinov (YSR) states. Here, we investigated the detailed spectroscopic change of the exchange coupling-dependent YSR states near a quantum phase transition. The initially developed one pair of YSR states, induced by the Fe vacancy in monolayer Fe(Te,Se) superconductor, are clearly resolved with high resolution showing an evolution into two pairs of YSR peaks yet with dichotomy in their spectral features. Interestingly, while the lower-energy YSR branch enters the quantum phase transition region, the higher-lying one remains rigidly away from the lower-energy counterpart with a constant energy difference. Spectral weight analysis of the higher-energy branch yields an exponential dependence on the exchange coupling, which can be well rationalized by taking the two pairs of YSR states as a result of field splitting by the magnetic anisotropy. Our results unveil the intermediate region of a quantum phase transition with a magnetic anisotropy-induced splitting of the YSR resonance, and highlight a prospect for developing functional electronics based on the flexibly controllable multiple quantum states., Comment: 8 pages, 3 figures

Polarons are entities of excess electrons dressed with local response of lattices, whose atomic-scale characterization is essential for understanding the many body physics arising from the electron-lattice entanglement, but yet difficult to achieve. Here, using scanning tunneling microscopy and spectroscopy (STM/STS), we show the visualization and manipulation of single polarons with different origin, i.e., electronic and conventional polarons, in monolayer CoCl2, that are grown on HOPG substrate via molecular beam epitaxy. Four types of polarons are identified, all inducing upward local band bending, but exhibiting distinct appearances, lattice occupations, polaronic states and local lattice distortions. First principles calculations unveil three types of polarons are stabilized by electron-electron interaction. The type-4 polaron, however, are driven by conventional lattice distortions. All the four types of polarons can be created, moved, erased, and moreover interconverted individually by the STM tip, allowing precise control of single polarons unprecedently. This finding identifies the rich category of polarons and their feasibility of manipulation in CoCl2, which can be generalized to other transition metal halides., Comment: 23 pages, 5 figures

Mott state in 1T-TaS2 is predicted to host quantum spin liquids (QSL). However, its insulating mechanism is controversial due to complications from interlayer coupling. Here, we study the Mott state in monolayer 1T-NbSe2, an electronic analogy to TaS2 exempt from interlayer coupling, using spectroscopic imaging scanning tunneling microscopy and first principles calculations. Monolayer NbSe2 surprisingly displays two types of Star-of-David (SD) motifs with different Mott gap sizes, that are interconvertible via temperature variation. And, bilayer 1T-NbSe2 shows Mott collapse by interlayer coupling. Our calculation unveils the two types of SDs possess distinct structural distortions, altering the effective Coulomb energies of the central Nb orbital. Our calculation suggests the Mott gap, the same parameter for determining the QSL regime, is tunable with strain. This finding offers a general strategy for manipulating the Mott state in 1T-NbSe2 and related systems via structural distortions, which may be tuned into the potential QSL regime., Comment: 20 pages, 5 figures

Intrinsic antiferromagnetism in van der Waals (vdW) monolayer (ML) crystals enriches the understanding regarding two-dimensional (2D) magnetic orders and holds special virtues over ferromagnetism in spintronic applications. However, the studies on intrinsic antiferromagnetism are sparse, owing to the lack of net magnetisation. In this study, by combining spin-polarised scanning tunnelling microscopy and first-principles calculations, we investigate the magnetism of vdW ML CrTe2, which has been successfully grown through molecular beam epitaxy. Surprisingly, we observe a stable antiferromagnetic (AFM) order at the atomic scale in the ML crystal, whose bulk is a strong ferromagnet, and correlate its imaged zigzag spin texture with the atomic lattice structure. The AFM order exhibits an intriguing noncollinear spin-flop transition under magnetic fields, consistent with its calculated moderate magnetic anisotropy. The findings of this study demonstrate the intricacy of 2D vdW magnetic materials and pave the way for their in-depth studies., Comment: 28 pages, 4 figures, Nature Communications, accepted