Competing electronic phases in two-dimensional transition metal dichalcogenides constitute a fertile platform for uncovering emergent ground states and elucidating the control parameters that govern the correlated electron phases. Among these materials, vanadium diselenide is particularly compelling: while the bulk hosts a well-established charge density wave (CDW), monolayers exhibit markedly different electronic behavior. Here, we identify three distinct electronic regimes in mechanically exfoliated VSe_2 flakes on Au(111) substrates, where interfacial hybridization, charge transfer, and strain act as primary tuning parameters of electronic order. Monolayers strongly coupled to gold show complete suppression of the CDW, accompanied by the emergence of moiré modulations. In contrast, bilayers preserve the in-plane 4a × 4a CDW characteristic of the bulk limit. Strained, electronically decoupled monolayers formed in suspended membrane and bubble regions stabilize a √(3)a×√(7)a CDW phase, underscoring the reversible role of substrate interaction and hybridization.

Understanding how superconductivity competes with other electronic phases in cuprates requires direct access to the hidden non-superconducting low temperature phase, for which Abrikosov vortices provide a unique local probe. We map the doping- and field-dependent evolution of vortex-core states in Bi_2Sr_2CaCu_2O_8+δ across a broad doping range spanning the Fermi-surface Lifshitz transition. High-resolution scanning tunneling spectroscopy reveals a striking transformation of the vortex-core spectrum from unconventional, pseudogap-like signatures at moderate doping to more BCS-like behavior beyond a critical doping p^* ≈ 0.21. This crossover aligns with the pseudogap endpoint and the onset of Fermi-surface reconstruction, indicating a direct link between pseudogap physics and vortex electronic structure. Our findings highlight the vortex core as a sensitive local probe of the cuprate ground state.

Van der Waals semiconducting magnets exhibit a cornucopia of physical phenomena originating from the interplay of their semiconducting and magnetic properties. However, a comprehensive understanding of how semiconducting processes and magnetism are coupled is lacking. We address this question by performing scanning tunneling spectroscopy (STS) measurements on the magnetic semiconductor CrPS_4, and by comparing the results to photoluminescence experiments and density functional theory (DFT) calculations. Below the magnetic transition, STS exhibit multiple features absent in the paramagnetic state, caused by the proliferation of electronic bands due to spin splitting with a large (≃ 0.5 eV) exchange energy. The energetic differences between the band edges determined by STS match all observed photoluminescence transitions, which also proliferate in the magnetic state. DFT calculations quantitatively predict the relative positions of all detected bands, explain which pairs of bands lead to radiative transitions, and also reproduce the measured spatial dependence of electronic wavefunctions. Our results reveal how all basic optoelectronic processes observed in CrPS_4 can be understood in terms of the evolution of the electronic band structure when entering the magnetic state, and allow us to conclude that individual bands are fully spin-polarized over a broad energy interval.

Tunable electronic properties in transition metal dichalcogenides (TMDs) are essential to further their use in device applications. Here, we present a comprehensive scanning tunneling microscopy and spectroscopy study of a doping-induced charge density wave (CDW) in semiconducting bulk 1T-ZrSe2. We find that atomic impurities that locally shift the Fermi level (EF) into the conduction band trigger a CDW reconstruction concomitantly to the opening of a gap at EF. Our findings shed new light on earlier photoemission spectroscopy and theoretical studies of bulk 1T-ZrSe2 and provide local insight into the electron-doping-mediated CDW transition observed in semiconducting TMDs.

Scanning Tunneling Spectroscopy (STS) is a unique technique to probe the local density of states (LDOS) at the atomic scale by measuring the tunneling conductance between a sharp tip and a sample surface. However, the technique suffers of well-known limitations, the so-called set-point effect, which can potentially introduce artifacts in the measurements. We compare several STS imaging schemes applied to the LDOS modulations of the charge density wave state on atomically flat surfaces, and demonstrate that only constant-height STS is capable of mapping the intrinsic LDOS. In the constant-current STS, commonly used and easier-to-implement, the tip-sample distance variations imposed by the feedback loop result in set-point-dependent STS images and possibly mislead the identification of the CDW gap edges.

Geometric phase analysis (GPA) is a widely used technique for extracting displacement and strain fields from scanning probe images. Here, we demonstrate that GPA should be implemented with caution when several fundamental lattices contribute to the image, in particular in twisted heterostructures featuring moiré patterns. We find that in this case, GPA is likely to suggest the presence of chiral displacement and periodic strain fields, even if the structure is completely relaxed and without distortions. These delusive fields are subject to change with varying twist angles, which could mislead the interpretation of twist angle-dependent properties.

Strain is attracting much interest as a mean to tune the properties of thin exfoliated two-dimensional materials and their heterostructures. Numerous devices to apply tunable uniaxial strain are proposed in the literature, but only few for biaxial strain, often with a trade-off between maximum strain and uniformity, reversibility, and device size. We present a compact device that allows for the controlled application of uniform in-plane biaxial strain, with maximum deformation and uniformity comparable to those found in much larger devices. Its performance and strain uniformity over the sample area are modeled using finite element analysis and demonstrated by measuring the response of exfoliated 2H-MoS2 to strain by Raman spectroscopy.

Synthetic materials and heterostructures obtained by the controlled stacking of exfoliated monolayers are emerging as attractive functional materials owing to their highly tunable properties. We present a detailed scanning tunneling microscopy and spectroscopy study of single layer MoS2-on-gold heterostructures as a function of the twist angle. We find that their electronic properties are determined by the hybridization of the constituent layers and are modulated at the moiré period. The hybridization depends on the layer alignment, and the modulation amplitude vanishes with increasing twist angle. We explain our observations in terms of a hybridization between the nearest sulfur and gold atoms, which becomes spatially more homogeneous and weaker as the moiré periodicity decreases with increasing twist angle, unveiling the possibility of tunable hybridization of electronic states via twist angle engineering.

Inducing and controlling spin-orbit coupling (SOC) in graphene is key to create topological states of matter, and for the realization of spintronic devices. Placing graphene onto a transition metal dichalcogenide is currently the most successful strategy to achieve this goal, but there is no consensus as to the nature and the magnitude of the induced SOC. Here, we show that the presence of backscattering in graphene-on-WSe2 heterostructures can be used to probe SOC and to determine its strength quantitatively, by imaging quasiparticle interference with a scanning tunneling microscope. A detailed theoretical analysis of the Fourier transform of quasiparticle interference images reveals that the induced SOC consists of a valley-Zeeman (λvZ ≈ 2 meV) and a Rashba (λR ≈ 15 meV) term, one order of magnitude larger than what theory predicts, but in excellent agreement with earlier transport experiments. The validity of our analysis is confirmed by measurements on a 30 degree twist angle heterostructure that exhibits no backscattering, as expected from symmetry considerations. Our results demonstrate a viable strategy to determine SOC quantitatively by imaging quasiparticle interference.

The mechanism of high-temperature superconductivity remains one of the great challenges of contemporary physics. Here, we review efforts to image the vortex lattice in copper oxide-based high-temperature superconductors and to measure the characteristic electronic structure of the vortex core of a d-wave superconductor using scanning tunneling spectroscopy.

We report experimental coupling of chiral magnetism and superconductivity in [IrFeCoPt]/Nb heterostructures. The stray field of skyrmions with radius ≈50  nm is sufficient to nucleate antivortices in a 25 nm Nb film, with unique signatures in the magnetization, critical current, and flux dynamics, corroborated via simulations. We also detect a thermally tunable Rashba-Edelstein exchange coupling in the isolated skyrmion phase. This realization of a strongly interacting skyrmion-(anti)vortex system opens a path toward controllable topological hybrid materials, unattainable to date.

Low magnetic field scanning tunneling spectroscopy of individual Abrikosov vortices in heavily overdoped Bi_2Sr_2CaCu_2O_8+δ unveils a clear d-wave electronic structure of the vortex core, with a zero-bias conductance peak at the vortex center that splits with increasing distance from the core. We show that previously reported unconventional electronic structures, including the low energy checkerboard charge order in the vortex halo and the absence of a zero-bias conductance peak at the vortex center, are direct consequences of short inter-vortex distance and consequent vortex-vortex interactions prevailing in earlier experiments.

In the presence of multiple bands, well-known electronic instabilities may acquire new complexity. While multiband superconductivity is the subject of extensive studies, the possibility of multiband charge density waves (CDWs) has been largely ignored so far. Here, combining energy dependent scanning tunnelling microscopy (STM) topography with a simple model of the charge modulations and a self-consistent calculation of the CDW gap, we find evidence for a multiband CDW in 2H-NbSe2. This CDW not only involves the opening of a gap on the inner band around the K-point, but also on the outer band. This leads to spatially out-of-phase charge modulations from electrons on these two bands, which we detect through a characteristic energy dependence of the CDW contrast in STM images.

We present a very-compact bicomponent-permanent-magnet design capable of generating 1.25 T in a small volume, significantly above the 0.6 T available from a single uniformly magnetized permanent magnet. In addition to the enhanced maximum field, our design drastically limits the stray field present around a standard permanent magnet. These features make it suitable for retrofitting existing experiments with a substantial magnetic field, in particular, scanning probes and optical, Raman, and photoemission spectroscopy, in diverse environments, from ambient to ultrahigh vacuum and over a wide temperature range.

Charge density waves (CDWs) are understood in great detail in one dimension, but they remain largely enigmatic in two-dimensional systems. In particular, numerous aspects of the associated energy gap and the formation mechanism are not fully understood. Two long-standing riddles are the amplitude and position of the CDW gap with respect to the Fermi level (E-F) and the frequent absence of CDW contrast inversion (CI) between opposite bias scanning tunneling microscopy (STM) images. Here, we find compelling evidence that these two issues are intimately related. Combining density functional theory and STM to analyze the CDW pattern and modulation amplitude in 1T-TiSe2, we find that CI takes place at an unexpected negative sample bias because the CDW gap opens away from E-F, deep inside the valence band. This bias becomes increasingly negative as the CDW gap shifts to higher binding energy with electron doping. This study shows the importance of CI in STM images to identify periodic modulations with a CDW and to gain valuable insight into the CDW gap, whose measurement is notoriously controversial.

The surface diffusion potential landscape plays an essential role in a number of physical and chemical processes such as self-assembly and catalysis. Diffusion energy barriers can be calculated theoretically for simple systems, but there is currently no experimental technique to systematically measure them on the relevant atomic length scale. Here, we introduce an atomic force microscopy based method to semiquantitatively map the surface diffusion potential on an atomic length scale. In this proof of concept experiment, we show that the atomic force microscope damping signal at constant frequency-shift can be linked to nonconservative processes associated with the lowering of energy barriers and compared with calculated single-atom diffusion energy barriers.

Scanning tunneling microscopy (STM) reveals unusual sharp features in otherwise defect-free Bi nanolines self-assembled on Si(001). They appear as subatomic thin lines perpendicular to the Bi nanoline at positive biases and as atomic size beads at negative biases. Density functional theory (DFT) simulations show that these features can be attributed to buckled Si dimers substituting for Bi dimers in the nanoline, where the sharp feature is the counterintuitive signature of these dimers flipping during scanning. The perfect correspondence between the STM data and the DFT simulation demonstrated in this paper highlights the detailed understanding we have of the complex Bi-Si(001) Haiku system. This discovery has applications in the patterning of Si dangling bonds for nanoscale electronics. KIRKHAM, C. J., et al. Subatomic electronic feature from dynamic motion of Si dimer defects in Bi nanolines on Si(001). Physical Review. B, Condensed Matter, 2017, vol. 96, no. 7, p.

We report a detailed study of the microscopic effects of Cu intercalation on the charge density wave (CDW) in 1\textit{T}-Cu$_x$TiSe$_2$. Scanning tunneling microscopy and spectroscopy (STM/STS) reveal a unique, Cu driven spatial texturing of the charge ordered phase, with the appearance of energy dependent CDW patches and sharp $\pi$-phase shift domain walls ($\pi$DWs). The energy and doping dependencies of the patchwork are directly linked to the inhomogeneous potential landscape due to the Cu intercalants. They imply a CDW gap with unusual features, including a large amplitude, the opening below the Fermi level and a shift to higher binding energy with electron doping. Unlike the patchwork, the $\pi$DWs occur independently of the intercalated Cu distribution. They remain atomically sharp throughout the investigated phase diagram and occur both in superconducting and non-superconducting specimen. These results provide unique atomic-scale insight on the CDW ground state, questioning the existence of incommensurate CDW domain walls and contributing to understand its formation mechanism and interplay with superconductivity.

The charge density wave (CDW) in solids is a collective ground state combining lattice distortions and charge ordering. It is defined by a complex order parameter with an amplitude and a phase. The amplitude and wavelength of the charge modulation are readily accessible to experiment. However, accurate measurements of the corresponding phase are significantly more challenging. Here we combine reciprocal and real space information to map the full complex order parameter based on topographic scanning tunneling microscopy (STM) images. Our technique overcomes limitations of Fourier space based techniques to achieve distinct amplitude and phase images with high spatial resolution. Applying this analysis to transition metal dichalcogenides provides striking evidence that their CDWs consist of three individual unidirectional charge modulations whose ordering vectors are connected by the fundamental rotational symmetry of the crystalline lattice. Spatial variations in the relative phases of these three modulations account for the different CDW contrasts often observed in STM topographic images. Phase images further reveal topological defects and discommensurations, a singularity predicted by theory for a nearly commensurate CDW. Such precise real space mapping of the complex order parameter provides a powerful tool for a deeper understanding of the CDW ground state whose formation mechanisms remain largely unclear.

Contrast inversion (CI) between opposite polarity scanning tunneling microscopy (STM) images, although seen as a hallmark of the charge density wave (CDW) ground state, is only rarely observed. Combining density functional theory and STM on pristine 1T-TiSe2, we show that CI takes place at increasingly negative sample bias as the CDW gap shifts to higher binding energy with electron doping. There is a point where the gap is shifted so far below the Fermi level (EF) that CI disappears altogether. Contrast inversion thus gives a different insight into the CDW gap, whose measurement by scanning tunneling spectroscopy is notoriously controversial. It provides unique evidence that the CDW gap is not bound to EF and that it can develop deep inside the valence band, an explicit constraint on any model description of the CDW phase transition.