No Arabic abstract
Stacked atomically thin transition metal dichalcogenides (TMDs) exhibit fundamentally new physical properties compared to those of the individual layers. The twist angle between the layers plays a crucial role in tuning these properties. Having a tool that provides highresolution, large area mapping of the twist angle, would be of great importance in the characterization of such 2D structures. Here we use polarization-resolved second harmonic generation (P-SHG) imaging microscopy to rapidly map the twist angle in large areas of overlapping WS2 stacked layers. The robustness of our methodology lies in the combination of both intensity and polarization measurements of SHG in the overlapping region. This allows the accurate measurement and consequent pixel-by-pixel mapping of the twist angle in this area. For the specific case of 30o twist angle, P-SHG enables imaging of individual layers.
The valley degeneracy of electron states in graphene stimulates intensive research of valley-related optical and transport phenomena. While many proposals on how to manipulate valley states have been put forward, experimental access to the valley polarization in graphene is still a challenge. Here, we develop a theory of the second optical harmonic generation in graphene and show that this effect can be used to measure the degree and sign of the valley polarization. We show that, at the normal incidence of radiation, the second harmonic generation stems from imbalance of carrier populations in the valleys. The effect has a specific polarization dependence reflecting the trigonal symmetry of electron valley and is resonantly enhanced if the energy of incident photons is close to the Fermi energy.
Second harmonic generation (SHG) spectroscopy ubiquitously enables the investigation of surface chemistry, interfacial chemistry as well as symmetry properties in solids. Polarization-resolved SHG spectroscopy in the visible to infrared regime is regularly used to investigate electronic and magnetic orders through their angular anisotropies within the crystal structure. However, the increasing complexity of novel materials and emerging phenomena hamper the interpretation of experiments solely based on the investigation of hybridized valence states. Here, polarization-resolved SHG in the extreme ultraviolet (XUV-SHG) is demonstrated for the first time, enabling element-resolved angular anisotropy investigations. In non-centrosymmetric LiNbO$_3$, elemental contributions by lithium and niobium are clearly distinguished by energy dependent XUV-SHG measurements. This element-resolved and symmetry-sensitive experiment suggests that the displacement of Li ions in LiNbO$_3$, which is known to lead to ferroelectricity, is accompanied by distortions to the Nb ion environment that breaks the inversion symmetry of the NbO$_{6}$ octahedron as well. Our simulations show that the measured second harmonic spectrum is consistent with Li ion displacements from the centrosymmetric position by $sim$0.5 Angstrom while the Nb-O bonds are elongated/contracted by displacements of the O atoms by $sim$0.1 Angstrom. In addition, the polarization-resolved measurement of XUV-SHG shows excellent agreement with numerical predictions based on dipole-induced SHG commonly used in the optical wavelengths. This constitutes the first verification of the dipole-based SHG model in the XUV regime. The findings of this work pave the way for future angle and time-resolved XUV-SHG studies with elemental specificity in condensed matter systems.
Valley polarization in graphene breaks inversion symmetry and therefore leads to second-harmonic generation. We present a complete theory of this effect within a single-particle approximation. It is shown that this may be a sensitive tool to measure the valley polarization created, e.g., by polarized light and, thus, can be used for a development of ultrafast valleytronics in graphene.
Two-dimensional (2D) layered semiconductors with both ultrawide bandgap and strong second harmonic generation (SHG) are essential for expanding the nonlinear optical (NLO) applications to deep-ultraviolet (DUV) region in nanoscale. Unfortunately, these materials are rare in nature and have not been discovered until now. In this Letter, we predict the B2S2O9 (BSO), an existing layered oxide, can exhibit both DUV bandgap and strong SHG effects, comparable to the best known DUV NLO bulks. The strong SHG intensities in BSO, originated from the ordered arrangement of polar SO4 and BO4 tetrahedra forming planar structure, are linearly tunable by the layer thickness. Surprisingly, the spontaneous rotations of rigid tetrahedra under strains can induce the (nearly) zero Poissons ratios in BSO, which simultaneously result in the robust SHG effects against large strains, fundamentally differing from other known 2D NLO semiconductors. The discovery of BSO may provide an unprecedented opportunity to explore DUV NLO physics and applications in 2D limit.
The emergence of flat electronic bands and of the recently discovered strongly correlated and superconducting phases in twisted bilayer graphene crucially depends on the interlayer twist angle upon approaching the magic angle $theta_M approx 1.1deg$. Although advanced fabrication methods allow alignment of graphene layers with global twist angle control of about 0.1$deg$, little information is currently available on the distribution of the local twist angles in actual magic angle twisted bilayer graphene (MATBG) transport devices. Here we map the local $theta$ variations in hBN encapsulated devices with relative precision better than 0.002$deg$ and spatial resolution of a few moir$e$ periods. Utilizing a scanning nanoSQUID-on-tip, we attain tomographic imaging of the Landau levels in the quantum Hall state in MATBG, which provides a highly sensitive probe of the charge disorder and of the local band structure determined by the local $theta$. We find that even state-of-the-art devices, exhibiting high-quality global MATBG features including superconductivity, display significant variations in the local $theta$ with a span close to 0.1$deg$. Devices may even have substantial areas where no local MATBG behavior is detected, yet still display global MATBG characteristics in transport, highlighting the importance of percolation physics. The derived $theta$ maps reveal substantial gradients and a network of jumps. We show that the twist angle gradients generate large unscreened electric fields that drastically change the quantum Hall state by forming edge states in the bulk of the sample, and may also significantly affect the phase diagram of correlated and superconducting states. The findings call for exploration of band structure engineering utilizing twist-angle gradients and gate-tunable built-in planar electric fields for novel correlated phenomena and applications.