The antiferromagnetic ground state of copper oxide Mott insulators is achieved by localizing an electron at each copper atom in real space (r-space). Removing a small fraction of these electrons (hole doping) transforms this system into a superconducting fluid of delocalized Cooper pairs in momentum space (k-space). During this transformation, two distinctive classes of electronic excitations appear. At high energies, the mysterious 'pseudogap' excitations are found, whereas, at lower energies, Bogoliubov quasi-particles-the excitations resulting from the breaking of Cooper pairs-should exist. To explore this transformation, and to identify the two excitation types, we have imaged the electronic structure of Bi(2)Sr(2)CaCu(2)O(8+delta) in r-space and k-space simultaneously. We find that although the low-energy excitations are indeed Bogoliubov quasi-particles, they occupy only a restricted region of k-space that shrinks rapidly with diminishing hole density. Concomitantly, spectral weight is transferred to higher energy r-space states that lack the characteristics of excitations from delocalized Cooper pairs. Instead, these states break translational and rotational symmetries locally at the atomic scale in an energy-independent way. We demonstrate that these unusual r-space excitations are, in fact, the pseudogap states. Thus, as the Mott insulating state is approached by decreasing the hole density, the delocalized Cooper pairs vanish from k-space, to be replaced by locally translational- and rotational-symmetry-breaking pseudogap states in r-space.

A complete knowledge of its excitation spectrum could greatly benefit efforts to understand the unusual form of superconductivity occurring in the lightly holedoped copper-oxides. Here we use tunnelling spectroscopy to measure the T→0 spectrum of electronic excitations N(E) over a wide range of hole-density p in superconducting Bi 2 Sr 2 CaCu 2 O 8+δ . We introduce a parameterization for N(E) based upon an anisotropic energy-gap ( ) ( ) 2 / ) ( ) ( 1 y x k Cos k Cos k − Δ = Δ r plus an effective scattering rate which varies linearly with energy E E α = Γ ) ( 2 . We demonstrate that this form of N(E) allows successful fitting of differential tunnelling conductance spectra throughout much of the Bi 2 Sr 2 CaCu 2 O 8+δ phase diagram. The resulting average Δ 1 values rise with falling p along the familiar trajectory of excitations to the 'pseudogap' energy, while the key scattering rate ) ( 1 2 * 2 Δ = Γ = Γ Eincreases from below ~1meV to a value approaching 25meV as the system is underdoped from 2 p~16% to p<10%. Thus, a single, particle-hole symmetric, anisotropic energy-gap, in combination with a strongly energy and doping dependent effective scattering rate, can describe the spectra without recourse to another ordered state.Nevertheless we also observe two distinct and diverging energy scales in the system: the energy-gap maximum Δ 1 and a lower energy scale Δ 0 separating the spatially homogeneous and heterogeneous electronic structures.Hole-doped copper-oxides have their highest superconducting critical temperature T c at hole-densities per CuO 2 of p~16%, and the superconductive state exhibits d-wave symmetry. By measuring STM tip-sample differential conductance dI/dV(r,V) ≡ g(r,V) at each location r and bias voltage V one can achieve energy resolved images of the localdensity-of-excitations N(E) because g(r,V) ∝ N(r,E=eV) (when the N(E) integrated to the junction formation bias is homogeneous 1 ). Near optimal doping, the g(V) spectra appear highly consistent with the theoretical N(E) of a d-wave superconductor; when superconductivity is suppressed by unitary scattering at a Zn atom 2,3 or at the center of a vortex core 3,4 , the two particle-hole symmetric peaks in g(V) are also suppressed as expected of the superconducting coherence peaks. Thus there can be little doubt that the measured N(E) near optimal doping is that of the d-wave superconducting state. But as p is reduced, the electronic excitations begin to exhibit 5,6,7 a 'pseudo' gap (PG) . This is a momentum-space anisotropic energy gap 5-9 in the excitation spectrum whose effects can be detected by numerous spectroscopic and thermodynamic techniques 6,7 far above the superconducting T c (which diminishes to zero as p→0). The PG energy scale increases linearly with diminishing p.Possible explanations for the PG include, for example, effects of hole-doping an antiferromagnetic Mott insulator 10 -14 . Different models for this situation yield an anisotropic energy-gap whose maximum diminishes linearly with increasing p (heuristically, one can view thi...

To probe the one-dimensional nature of single-wall carbon nanotubes (SWNTs) in bulk samples, we have devised a simple method for generating fibers of aligned SWNTs. We measured polarization-dependent Raman spectra on the oriented fibers. Contrary to what is expected from their theoretically assigned vibration-mode symmetries, all the Raman line intensities are observed to decrease in nearly equal amounts for the 647.1 nm laser excitation polarized perpendicular to the fiber axis versus that polarized parallel to the fiber axis. The effect is explained as a loss of resonance Raman scattering for the perpendicular polarization case.

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...