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We investigate superconducting gallium in its $\alpha$ phase using scanning tunneling microscopy and spectroscopy at temperatures down to about 100 mK. High-resolution tunneling spectroscopies using both superconducting and normal tips show that superconducting $\alpha$-Ga is accurately described by Bardeen-Cooper-Schrieffer theory, with a gap $\Delta_{\rm Ga}$ = 163 $\mu$eV on the $\alpha-$Ga(112) facet, with highly homogeneous spectra over the surface, including atomic defects and step edges. Using a superconducting Pb tip, we furthermore study the low-bias conductance features of the Josephson junction formed between tip and sample. The features are accurately described by dynamical Coulomb blockade theory, highlighting $\alpha-$Ga as a possible platform for surface science studies of mesoscopic superconductivity.

The study of moir\'e engineering started with the advent of van der Waals heterostructures in which stacking two-dimensional layers with different lattice constants leads to a moir\'e pattern controlling their electronic properties. The field entered a new era when it was found that adjusting the twist between two graphene layers led to strongly-correlated-electron physics and topological effects associated with atomic relaxation. Twist is now used routinely to adjust the properties of two-dimensional materials. Here, we investigate a new type of moir\'e superlattice in bilayer graphene when one layer is biaxially strained with respect to the other - so-called biaxial heterostrain. Scanning tunneling microscopy measurements uncover spiraling electronic states associated with a novel symmetry-breaking atomic reconstruction at small biaxial heterostrain. Atomistic calculations using experimental parameters as inputs reveal that a giant atomic swirl forms around regions of aligned stacking to reduce the mechanical energy of the bilayer. Tight-binding calculations performed on the relaxed structure show that the observed electronic states decorate spiraling domain wall solitons as required by topology. This study establishes biaxial heterostrain as an important parameter to be harnessed for the next step of moir\'e engineering in van der Waals multilayers.

Fractional charges are one of the wonders of the fractional quantum Hall effect, a liquid of strongly correlated electrons in a large magnetic field. Fractional excitations are also anticipated in two-dimensional crystals of non-interacting electrons under time-reversal symmetry, as bound states of a rotating bond order known as Kekul\'e vortex. However, the physical mechanisms inducing such topological defects remain elusive, preventing experimental realisations. Here, we report the observation of Kekul\'e vortices in the local density of states of graphene under time-reversal symmetry. The vortices result from intervalley scattering on chemisorbed hydrogen adatoms and have a purely electronic origin. Their 2{\pi} winding is reminiscent of the Berry phase {\pi} of the massless Dirac electrons. Remarkably, we observe that point scatterers with different symmetries such as divacancies can also induce a Kekul\'e bond order without vortex. Therefore, our local-probe study further confirms point defects as versatile building blocks for the control of graphene's electronic structure by kekul\'e order.

Terahertz (THz) Spintronic emitters based on ferromagnetic/metal junctions have become an important technology for the THz range, offering powerful and ultra-large spectral bandwidths. These developments have driven recent investigations of two-dimensional (2D) materials for new THz spintronic concepts. 2D materials, such as transition metal dichalcogenides (TMDs), are ideal platforms for SCC as they possess strong spin-orbit coupling (SOC) and reduced crystal symmetries. Moreover, SCC and the resulting THz emission can be tuned with the number of layers, electric field or strain. Here, epitaxially grown 1T-PtSe$_2$ and sputtered Ferromagnet (FM) heterostructures are presented as a novel THz emitter where the 1T crystal symmetry and strong SOC favor SCC. High quality of as-grown PtSe$_2$ layers is demonstrated and further FM deposition leaves the PtSe$_2$ unaffected, as evidenced with extensive characterization. Through this atomic growth control, the unique thickness dependent electronic structure of PtSe$_2$ allows the control of the THz emission by SCC. Indeed, we demonstrate the transition from the inverse Rashba-Edelstein effect in one monolayer to the inverse spin Hall effect in multilayers. This band structure flexibility makes PtSe$_2$ an ideal candidate as a THz spintronic 2D material and to explore the underlying mechanisms and engineering of the SCC for THz emission., Comment: 26 pages, 6 figures

The moir\'e of twisted graphene bilayers can generate flat bands in which charge carriers do not posses enough kinetic energy to escape Coulomb interactions with each other leading to the formation of novel strongly correlated electronic states. This exceptionally rich physics relies on the precise arrangement between the layers.We survey published Scanning Tunnelling Microscope (STM) measurements to prove that near the magic angle, native heterostrain, the relative deformations between the layers, dominates twist in determining the flat bands. This is demonstrated at large doping where electronic correlations have a weak effect and where we also show that tip-induced strain can have a strong influence. In the opposite situation of low doping, we find that electronic correlation further normalize the flat bands in a way that strongly depends on experimental details., Comment: Supplementary information available on request

Electronic band structures dictate the mechanical, optical and electrical properties of crystalline solids. Their experimental determination is therefore of crucial importance for technological applications. While the spectral distribution in energy bands is routinely measured by various techniques, it is more difficult to access the topological properties of band structures such as the Berry phase {\gamma}. It is usually thought that measuring the Berry phase requires applying external electromagnetic forces because these allow realizing the adiabatic transport on closed trajectories along which quantum mechanical wave-functions pick up the Berry phase. In graphene, the anomalous quantum Hall effect results from the Berry phase {\gamma} = {\pi} picked up by massless relativistic electrons along cyclotron orbits and proves the existence of Dirac cones. Contradicting this belief, we demonstrate that the Berry phase of graphene can be measured in absence of any external magnetic field. We observe edge dislocations in the Friedel oscillations formed at hydrogen atoms chemisorbed on graphene. Following Nye and Berry in describing these topological defects as phase singularities of complex fields, we show that the number of additional wave-fronts in the dislocation is a real space measurement of the pseudo spin winding, i.e. graphene's Berry phase. Since the electronic dispersion can also be retrieved from Friedel oscillations, our study establishes the electronic density as a powerful observable to determine both the dispersion relation and topological properties of wavefunctions. This could have profound consequences for the study of the band-structure topology of relativistic and gapped phases in solids., Comment: Supplementary information available at Nature's web site

We demonstrate that stacking layered materials allows a novel type of strain engineering where each layer is strained independently, which we call heterostrain. We combine detailed structural and spectroscopic measurements with tight-binding calculations to show that small uniaxial heterostrain suppresses Dirac cones and leads to the emergence of flat bands in twisted graphene layers (TGLs). Moreover, we demonstrate that heterostrain reconstructs much more severely the energy spectrum of TGLs than homostrain for which both layers are strained identically ; a result which should apply to virtually all van der Waals structure opening exciting possibilities for straintronics with 2D materials., Comment: Main text + supplementary information

Establishing good electrical contacts to nanoscale devices is a major issue for modern technology and contacting 2D materials is no exception to the rule. One-dimensional edge-contacts to graphene were recently shown to outperform surface contacts but the method remains difficult to scale up. We report a resist-free and scalable method to fabricate few graphene layers with electrical contacts in a single growth step. This method derives from the discovery reported here of the growth of few graphene layers on a metallic carbide by thermal annealing of a carbide forming metallic film on SiC in high vacuum. We exploit the combined effect of edge-contact and partially-covalent surface epitaxy between graphene and the metallic carbide to fabricate devices in which low contact-resistance and Josephson effect are observed. Implementing this approach could significantly simplify the realization of large-scale graphene circuits., Comment: supplementary information available at the publisher's site

The fundamental properties of valleys are recently attracting growing attention due to electrons in new and topical materials possessing this degree-of-freedom and recent proposals for val-leytronics devices. In silicon MOSFETs, the interest has a longer history since the valley degree of freedom had been identified as a key parameter in the observation of the controversial "metallic behaviour" in two dimensions. However, while it has been recently demonstrated that lifting valley degeneracy can destroy the metallic behaviour, little is known about the role of intervalley scattering. Here, we show that the metallic behaviour can be observed in the presence of strong interval-ley scattering in silicon on insulator (SOI) quantum wells. Analysis of the conductivity in terms of quantum corrections reveals that interactions are much stronger in SOI than in conventional MOSFETs, leading to the metallic behaviour despite the strong intervalley scattering. The prospect of manipulating the valley degree of freedom in materials like AlAs, 1 silicon 2--4 graphene, Comment: Supplementary code for the calculation of WL with intervalley scattering available at the publisher's site

Valleytronics is rapidly emerging as an exciting area of basic and applied research. In two dimensional systems, valley polarisation can dramatically modify physical properties through electron-electron interactions as demonstrated by such phenomena as the fractional quantum Hall effect and the metal-insulator transition. Here, we address the electrons' spin alignment in a magnetic field in silicon-on-insulator quantum wells under valley polarisation. In stark contrast to expectations from a non-interacting model, we show experimentally that less magnetic field can be required to fully spin polarise a valley-polarised system than a valley-degenerate one. Furthermore, we show that these observations are quantitatively described by parameter free ab initio quantum Monte Carlo simulations. We interpret the results as a manifestation of the greater stability of the spin and valley degenerate system against ferromagnetic instability and Wigner crystalisation which in turn suggests the existence of a new strongly correlated electron liquid at low electron densities., Comment: Main manuscript + supplementary information

The electron tunneling is experimentally studied between two-dimensional electron gases (2DEGs) formed in a single-doped-barrier heterostructure in the magnetic fields directed perpendicular to the 2DEGs planes. It is well known that the quantizing magnetic field induces the Coulomb pseudogap suppressing the electron tunneling at Fermi level. In this paper we firstly present the experimental results revealing the pseudogap in the electron tunneling assisted by elastic electron scattering on disorder., Comment: 5 pages, 2 figures, Proc. of the ICPS-2008

We report an experimental study of quantum conductivity corrections in a low mobility, high density two-dimensional electron gas in a AlGaAs/GaAs/AlGaAs quantum well in a wide temperature range (1.5K - 110K). This temperature range covers both the diffusive and the ballistic interaction regimes for our samples. It has been therefore possible to study the crossover between these regimes for both the longitudinal conductivity and the Hall effect. We perform a parameter free comparison of our experimental data for the longitudinal conductivity at zero magnetic field, the Hall coefficient, and the magnetoresistivity to the recent theories of interaction-induced corrections to the transport coefficients. A quantitative agreement between these theories and our experimental results has been found., Comment: extended version of cond-mat/0412463

We report the observation of a metal-insulator transition (MIT) in a two- dimensional electron gas (2DEG) in a Si/SiGe heterostructure at zero magnetic field. On going through the MIT we observe the corresponding evolution of the magnetic field induced transition between the insulating phase and the quantum Hall (QH) liquid state in the QH regime. Similar to the previous reports for a GaAs sample, we find that the critical magnetic field needed to produce the transition becomes zero at the critical electron density corresponding to the zero field MIT. The temperature dependence of the conductivity in a metallic-like state at zero field is compared with the theory of the interaction corrections at intermediate and ballistic regimes $k_{B}T\tau/\hbar\geq1$. The theory yields a good fit for the linear part of the curve. However the slope of that part of $\sigma_{xx}(T)$ is about two times smaller than that reported in other 2D systems with similar values of $r_s$. At the same time, the recent theory of magnetoresistance due to electron-electron interaction in the case of arbitrary $k_{B}T\tau/\hbar$, smooth disorder and classically strong fields does not seem to be quite adequate for the description of the parabolic magnetoresistance observed in our samples. We attribute these results to the fact that neither of these theories deals with the whole scattering potential in a sample but leaves either its long range or its short range component out of consideration., Comment: 8 pages, 5 figures