In the quasi-2D electron systems of the layered transition metal dichalcogenides (TMD) there is still a controversy about the nature of the transitions to charge-density wave (CDW) phases, i.e. whether they are described by a Peierls-type mechanism or by a lattice-driven model. By performing scanning tunneling microscopy (STM) experiments on the canonical TMD-CDW systems, we have imaged the electronic modulation and the lattice distortion separately in 2H-TaS2, TaSe2, and NbSe2. Across the three materials, we found dominant lattice contributions instead of the electronic modulation expected from Peierls transitions, in contrast to the CDW states that show the hallmark of contrast inversion between filled and empty states. Our results imply that the periodic lattice distortion (PLD) plays a vital role in the formation of CDW phases in the TMDs and illustrate the importance of taking into account the more complicated lattice degree of freedom when studying correlated electron systems. PACS numbers: 71.45.Lr, 71.27.+a, 74.55.+v The transition metal dichalcogenides (TMD) have shown intriguing phenomena like the spin-valley physics [1, 2], superconductivity induced/enhanced by tuning various parameters [3][4][5][6][7][8][9], and charge-density waves (CDW) that coexist and compete with superconductivity (e.g. 2H-NbSe 2 , TaSe 2 , 1T-TaS 2 , and TiSe 2 ) [5-9]. Such competition between CDW and superconductivity is closely tied to the complicated interactions between the internal degrees of freedom, including charge, lattice and orbital. Differentiating which interactions are key requires knowing which of them are responsible for the different phases. The degree to which an electron-driven mechanism is the cause of CDWs in the trigonal prismatic structured (2H) TMDs is still under debate. Existing studies have proposed a variety of different mechanisms, including the Fermi surface nesting [10, 11], saddle band driven susceptibility divergence [12], f-wave gapping and marginal Fermi liquid [13], etc.These materials do show some evidence of the electronic nature of the CDW phases including the existence of incommensurate CDW phases [14,15], since 2k F is generally not expected to be a rational fraction of the lattice reciprocal vectors. Furthermore, the electronic origin is also supported by photoemission experiments which measured the Fermi surface of NbSe 2 and TaSe 2 and approximated the electronic susceptibility with an autocorrelation. This analysis showed peaks at wave vectors corresponding to those of the CDW [10,11]. However, inelastic X-ray scattering experiment in NbSe 2 [16] reveals that the lattice dynamics exhibit unconventional behavior and hence may be dominating the transition. Moreover, recent LDA calculations have shown the difficulties with Fermi surface nesting and have suggested that periodic lattice distortion (PLD), instead of eMod, is the essential ingredient [17,18]. In a recent real space study, Soumyanarayanan et al. [19] have shown that there is a close relationship between CDW formation and...

We present scanning tunneling microscopy and spectroscopy experiments on the novel J eff = 1/2 Mott insulator Sr 2 IrO 4. Local density of states (LDOS) measurements show an intrinsic insulating gap of 620 meV that is asymmetric about the Fermi level and is larger than previously reported values. The size of this gap suggests that Sr 2 IrO 4 is likely a Mott rather than Slater insulator. In addition, we found a small number of native defects which create in-gap spectral weight. Atomically resolved LDOS measurements on and off the defects show that this energy gap is quite fragile. Together the extended nature of the 5d electrons and poor screening of defects help explain the elusive nature of this gap.

We present a formulation for potential-density pairs to describe axisymmetric galaxies in the Newtonian limit of scalar-tensor theories of gravity. The scalar field is described by a modified Helmholtz equation with a source that is coupled to the standard Poisson equation of Newtonian gravity. The net gravitational force is given by two contributions: the standard Newtonian potential plus a term stemming from massive scalar fields. General solutions have been found for axisymmetric systems and the multipole expansion of the Yukawa potential is given. In particular, we have computed potential-density pairs of galactic disks for an exponential profile and their rotation curves.

We report the degree of order of twenty-two Jackson Pollock's paintings using Hausdorff-Besicovitch fractal dimension. Through the maximum value of each multi-fractal spectrum, the artworks are classify by the year in which they were painted. It has been reported that Pollock's paintings are fractal and it increased on his latest works. However our results show that fractal dimension of the paintings are on a range of fractal dimension with values close to two.We identify this behavior as a fractal-order transition. Based on the study of disorder-order transition in physical systems, we interpreted the fractal-order transition through its dark paint strokes in Pollocks' paintings, as structured lines following a power law measured by fractal dimension. We obtain selfsimilarity in some specific Pollock's paintings, that reveal an important dependence on the scale of observation. We also characterize by its fractal spectrum, the called Teri's Find. We obtained similar spectrums between Teri's Find and Number 5 from Pollock, suggesting that fractal dimension cannot be completely rejected as a quantitative parameter to authenticate this kind of artworks.

We demonstrate a general, computer automated procedure that inverts the reciprocal space scattering data (q-space) that are measured by spectroscopic imaging scanning tunnelling microscopy (SI-STM) in order to determine the momentum space (k-space) scattering structure. This allows a detailed examination of the k-space origins of the quasiparticle interference (QPI) pattern in Bi2Sr2CaCu2O8+x within the theoretical constraints of the joint density of states (JDOS). Our new method allows measurement of the differences between the positive and negative energy dispersions, the gap structure and an energy dependent scattering length scale. Furthermore, it resolves the transition between the dispersive QPI and the checkerboard ( excitation). We have measured the k-space scattering structure over a wide range of doping (p ∼ 0.22–0.08), including regions where the octet model is not applicable. Our technique allows the complete mapping of the k-space scattering origins of the spatial excitations in Bi2Sr2CaCu2O8+x, which allows for better comparisons between SI-STM and other experimental probes of the band structure. By applying our new technique to such a heavily studied compound, we can validate our new general approach for determining the k-space scattering origins from SI-STM data.