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In 1965 Kohn and Luttinger proposed a genuine electronic mechanism for superconductivity. Despite the bare electrostatic interaction between two electrons being repulsive, in a metal electron-hole fluctuations can give rise to Friedel oscillations of the screened Coulomb potential. Cooper pairing among the electrons then emerges when taking advantage of the attractive regions. The nature of the leading pairing mechanism in some two-dimensional transition metal dichalcogenides is still debated. Focusing on NbSe$_2$, we show that superconductivity can be induced by the Coulomb interaction when accounting for screening effects on the trigonal lattice with multiple orbitals. Using ab initio-based tight-binding parametrizations for the relevant low-energy d-bands, we evaluate the screened interaction microscopically, in a scheme that includes Bloch overlaps and Umklapp processes. In the direct space, we find long-range Friedel oscillations which alternate in sign. The momentum-resolved gap equations predict two quasi-degenerate nematic solutions near the critical temperature $T_c$, signaling the unconventional nature of the pairing. Their complex linear combination, i.e., a chiral gap with p-like symmetry, provides the ground state of the system. Our prediction of a fully gapped chiral phase well below $T_c$ is in agreement with the spectral function extracted from tunneling spectroscopy measurements of single-layer NbSe$_2$., Comment: 12 pages, 4 figures

When the period of an incommensurate charge density wave (ICDW) approaches an integer multiple of a lattice vector, the energy gain obtained from locking the period to the lattice can lead to a fascinating transition into a commensurate state. This transition actually occurs through an intermediate near-commensurate (NC) phase, with locally commensurate regions separated by an ordered array of phase slips of a complex CDW order parameter. TiSe2 is a paradigmatic CDW system where incommensuration is believed to be induced by carrier doping, yet its putative NC state has never been imaged or its nature established. Here we report the observation of a striking NC state in ultraclean, slightly doped monolayers of TiSe2, displaying an intricate network of coherent, unidirectional CDW domain walls over hundreds of nanometers. Detailed analysis reveals these are not phase slips of a complex CDW, but rather sign-changing Ising-type domain walls of two coupled real CDWs of previously known symmetry, consistent with the period doubling nature of the parent commensurate state. In addition, we observe an unexpected nematic modulation at the original lattice Bragg peaks which couples to the CDW order parameters. A Ginzburg-Landau analysis naturally explains the couplings and relative modulations of all order parameters, unveiling TiSe2 as a rare example of an NC-CDW of two intertwined real modulations and emergent nematicity.

Kondo lattices are ideal testbeds for the exploration of heavy-fermion quantum phases of matter. While our understanding of Kondo lattices has traditionally relied on complex bulk f-electron systems, transition metal dichalcogenide heterobilayers have recently emerged as simple, accessible and tunable 2D Kondo lattice platforms where, however, their ground state remains to be established. Here we present evidence of a coherent ground state in the 1T/1H-TaSe2 heterobilayer by means of scanning tunneling microscopy/spectroscopy at 340 mK. Our measurements reveal the existence of two symmetric electronic resonances around the Fermi energy, a hallmark of coherence in the spin lattice. Spectroscopic imaging locates both resonances at the central Ta atom of the charge density wave of the 1T phase, where the localized magnetic moment is held. Furthermore, the evolution of the electronic structure with the magnetic field reveals a non-linear increase of the energy separation between the electronic resonances. Aided by ab initio and auxiliary-fermion mean-field calculations, we demonstrate that this behavior is inconsistent with a fully screened Kondo lattice, and suggests a ground state with magnetic order mediated by conduction electrons. The manifestation of magnetic coherence in TMD-based 2D Kondo lattices enables the exploration of magnetic quantum criticality, Kondo breakdown transitions and unconventional superconductivity in the strict two-dimensional limit.

Transition metal dichalcogenides offer unprecedented versatility to engineer 2D materials with tailored properties to explore novel structural and electronic phase transitions. In this work, we present the atomic-scale evolution of the electronic ground state of a monolayer of Nb$_{1-\delta}$Mo$_{\delta}$Se$_2$ across the entire alloy composition range (0 < ${\delta}$ < 1) using low-temperature (300 mK) scanning tunneling microscopy and spectroscopy (STM/STS). In particular, we investigate the atomic and electronic structure of this 2D alloy throughout the metal to semiconductor transition (monolayer NbSe$_2$ to MoSe$_2$). Our measurements let us extract the effective doping of Mo atoms, the bandgap evolution and the band shifts, which are monotonic with ${\delta}$. Furthermore, we demonstrate that collective electronic phases (charge density wave and superconductivity) are remarkably robust against disorder. We further show that the superconducting TC changes non-monotonically with doping. This contrasting behavior in the normal and superconducting state is explained using first-principles calculations. We show that Mo doping decreases the density of states at the Fermi level and the magnitude of pair-breaking spin fluctuations as a function of Mo content. Our results paint a detailed picture of the electronic structure evolution in 2D TMD alloys, which is of utmost relevance for future 2D materials design.

Chemical substitution is a promising route for the exploration of a rich variety of doping- and/or disorder-dependent collective phenomena in low-dimensional quantum materials. Here we show that transition metal dichalcogenide alloys are ideal platforms to this purpose. In particular, we demonstrate the emergence of superconductivity in the otherwise metallic single-layer TaSe$_{2}$ by minute electron doping provided by substitutional W atoms. We investigate the temperature- and magnetic field-dependence of the superconducting state of Ta$_{1-\delta}$W$_\delta$Se$_2$ with electron doping ($\delta$) using variable temperature (0.34 K - 4.2 K) scanning tunneling spectroscopy (STS). We unveil the emergence of a superconducting dome spanning 0.003 < $\delta$ < 0.03 with a maximized critical temperature of 0.9 K, a significant increase from that of bulk TaSe$_{2}$ (T$_C$ = 0.14 K). Superconductivity emerges from an increase of the density of states (DOS) as the Fermi surface approaches a van Hove singularity due to doping. Once the singularity is reached, however, the DOS decreases with $\delta$, which gradually weakens the superconducting state, thus shaping the superconducting dome. Lastly, our doping-dependent measurements allow us to unambiguously track the development of a Coulomb glass phase triggered by disorder due to W dopants., Comment: This is the pre-peer reviewed version of an article that has been published in final form at npj 2D materials and applications [https://doi.org/10.1038/s41699-023-00401-4]

In certain unconventional superconductors with sizable electronic correlations, the availability of closely competing pairing channels leads to characteristic soft collective fluctuations of the order parameters, which leave fingerprints in many observables and allow to scrutinize the phase competition. Superconducting layered materials, where electron-electron interactions are enhanced with decreasing thickness, are promising candidates to display these correlation effects. In this work, we report the existence of a soft collective mode in single-layer NbSe$_2$, observed as a characteristic resonance excitation in high resolution tunneling spectra. This resonance is observed along with higher harmonics, its frequency $\Omega/2\Delta$ is anticorrelated with the local superconducting gap $\Delta$, and its amplitude gradually vanishes by increasing the temperature and upon applying a magnetic field up to the critical values (T$_C$ and H$_{C2}$), which sets an unambiguous link to the superconducting state. Aided by a microscopic model that captures the main experimental observations, we interpret this resonance as a collective Leggett mode that represents the fluctuation towards a proximate f-wave triplet state, due to subleading attraction in the triplet channel. Our findings demonstrate the fundamental role of correlations in superconducting 2D transition metal dichalcogenides, opening a path towards unconventional superconductivity in simple, scalable and transferable 2D superconductors., Comment: Advanced Materials (2022)

Two-dimensional transition metal dichalcogenides (TMDs) represent an ideal testbench for the search of materials by design, because their optoelectronic properties can be manipulated through surface engineering and molecular functionalization. However, the impact of molecules on intrinsic physical properties of TMDs, such as superconductivity, remains largely unexplored. In this work, the critical temperature (TC) of large-area NbSe2 monolayers is manipulated, employing ultrathin molecular adlayers. Spectroscopic evidence indicates that aligned molecular dipoles within the self-assembled layers act as a fixed gate terminal, collectively generating a macroscopic electrostatic field on NbSe2. This results in an \sim 55\% increase and a 70\% decrease in TC depending on the electric field polarity, which is controlled via molecular selection. The reported functionalization, which improves the air stability of NbSe2, is efficient, practical, up-scalable, and suited to functionalize large-area TMDs. Our results indicate the potential of hybrid 2D materials as a novel platform for tunable superconductivity.

Using ab initio methods based on density functional theory, the electronic and magnetic structure of layered hexagonal NbSe$_{2}$ is studied. In the case of single-layer NbSe$_{2}$ it is found that, for all the functionals considered, the magnetic solution is lower in energy than the non-magnetic solution. The magnetic ground-state is ferrimagnetic with a magnetic moment of 1.09 $\mu_{B}$ at the Nb atoms and a magnetic moment of 0.05 $\mu_{B}$, in the opposite direction, at the Se atoms. Our calculations show that single-layer NbSe$_{2}$ does not display a charge density wave instability unless a graphene layer is considered as a substrate. Then, two kinds of 3$\times$3 charge density waves are found, which are observed in our STM experiments. This suggest that the driving force of charge instabilities in NbSe$_{2}$ differ in bulk and in the single-layer limit. Our work sets magnetism into play in this highly-correlated 2D material, which is crucial to understand the formation mechanisms of 2D superconductivity and charge density wave order.