We discuss fluctuating order in a quantum disordered phase proximate to a quantum critical point, with particular emphasis on fluctuating stripe order. Optimal strategies for extracting information concerning such local order from experiments are derived with emphasis on neutron scattering and scanning tunneling microscopy. These ideas are tested by application to two model systemsthe exactly solvable one dimensional electron gas with an impurity, and a weakly-interacting 2D electron gas. We extensively review experiments on the cuprate high-temperature superconductors which can be analyzed using these strategies. We adduce evidence that stripe correlations are widespread in the cuprates. Finally, we compare and contrast the advantages of two limiting perspectives on the high-temperature superconductor: weak coupling, in which correlation effects are treated as a perturbation on an underlying metallic (although renormalized) Fermi liquid state, and strong coupling, in which the magnetism is associated with well defined localized spins, and stripes are viewed as a form of micro-phase separation. We present quantitative indicators that the latter view better accounts for the observed stripe phenomena in the cuprates.

Angle-resolved photoemission experiments reveal evidence of an energy gap in the normal state excitation spectrum of the cuprate superconductor Bi2Sr2CaCu2O8+delta. This gap exists only in underdoped samples and closes around the doping level at which the superconducting transition temperature Tc is a maximum. The momentum dependence and magnitude of the gap closely resemble those of the dx2-y2 gap observed in the superconducting state. This observation is consistent with results from several other experimental techniques, which also indicate the presence of a gap in the normal state. Some possible theoretical explanations for this effect are reviewed.

Polar Kerr effect in the spin-triplet superconductor Sr2RuO4 was measured with high precision using a Sagnac interferometer with a zero-area Sagnac loop. We observed non-zero Kerr rotations as big as 65 nanorad appearing below Tc in large domains. Our results imply a broken time reversal symmetry state in the superconducting state of Sr2RuO4, similar to 3 He-A.PACS numbers: 74.25. Gz,74.70.Pq,74.25.Ha,78.20.Ls Soon after the discovery of the layered-perovskite superconductor Sr 2 RuO 4 [1], it was predicted to be an oddparity superconductor [2,3]. Subsequently, a large body of experimental results in support of odd-parity superconductivity has been obtained [4], with the most recent one being a phase-sensitive measurement [5]. The symmetry of the superconducting state is related simply to the relative orbital angular momentum of the electrons in each Cooper pair. Odd parity corresponds to odd orbital angular momentum and symmetric spin-triplet pairing. While a priori the angular momentum state can be p (i.e. L = 1), f ( i.e. L = 3), or even higher order [6,7], theoretical analyses of superconductivity in Sr 2 RuO 4 favor the p-wave order parameter symmetry [2,8]. There are many allowed p-wave states that satisfy the cylindrical Fermi surface for a tetragonal crystal which is the case of Sr 2 RuO 4 (see e.g. table IV in [4]). Some of these states break time-reversal symmetry (TRS), since the condensate has an overall magnetic moment because of either the spin or orbital (or both) parts of the pair wave function. While an ideal sample will not exhibit a net magnetic moment, surfaces and defects at which the Meissner screening of the TRS-breaking moment is not perfect can result in a small magnetic signal [7]. Indeed, muon spin relaxation (µSR) measurements on good quality single crystals of Sr 2 RuO 4 showed excess relaxation that spontaneously appear at the superconducting transition temperature. The exponential nature of the increased relaxation suggested that its source is a broad distribution of internal fields, of strength ∼ 0.5 Oe, from a dilute array of sources [9,10]. While TRS breaking is not the only explanation for the µSR observations, it was accepted as the most likely one [4]. However, since the existence of TRS breaking has considerable implications for understanding the superconductivity of Sr 2 RuO 4 , establishing the existence of this effect, and in particular in the bulk without relying on imperfections and defects is of utmost importance. The challenge is therefore to couple to the TRS-breaking part of the order parameter to demonstrate the effect unambiguously.In this paper we show results of polar Kerr effect (PKE) measurements on high quality single crystals of Sr 2 RuO 4 . In these measurements we are searching for an effect analogous to the magneto-optic Kerr effect (MOKE) which would cause a rotation of the direction of polarization of the reflected linearly polarized light normally incident to the superconducting planes. PKE is sensitive to TRS breaking since it measures the existenc...

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Scanning tunneling spectroscopy studies on high-quality Bi2Te3 crystals exhibit perfect correspondence to ARPES data, hence enabling identification of different regimes measured in the local density of states (LDOS). Oscillations of LDOS near a step are analyzed. Within the main part of the surface band oscillations are strongly damped, supporting the hypothesis of topological protection. At higher energies, as the surface band becomes concave, oscillations appear which disperse with a particular wave-vector that may result from an unconventional hexagonal warping term.PACS numbers: 71.18.+y, 71.20.Nr, A new type of three-dimensional (3D) bulk insulating materials with surface Quantum Spin Hall Effect states protected by time reversal symmetry has been recently predicted [1], and soon afterwards observed experimentally in BiSb bulk crystals [2]. Subsequently, Bi 2 Te 3 has been argued to be a similar three-dimensional topological insulator (TI), exhibiting a bulk gap and a single, non-degenerate Dirac fermion band on the surface [3]. Indeed, recent angle resolved photoemission spectroscopy (ARPES) confirmed that prediction [4]. In particular, with appropriate hole-doping, the Fermi level could be tuned to intersect only the surface states, indicating fully gapped bulk states as is expected from a three-dimensional TI. While ARPES could confirm the nature of the band, it is still a challenge to demonstrate unambiguously the topologically "protected" nature of the surface state in Bi 2 Te 3 , or any other 3D TI system.In this paper we present scanning tunneling microscopy (STM) and spectroscopy (STS) studies on high-quality doped Bi 2 Te 3 crystals. First we show that the STS spectra exhibit remarkable correspondence to ARPES data, hence enabling us to identify each region of the local density of states (LDOS) measured. Second, by analyzing the electron-waves (Friedel-oscillations) observed near cleavage steps, we show that within the main part of the surface state band oscillations are strongly damped, a hallmark of the strong supression of backscattering, hence supporting the hypothesis of a protected band. Finally, we show that in the region in which the surface band is warped, pronounced oscillations appear, with a distinct nesting wave-vector. Possible influence of the bulk conduction band on the oscillations is also proposed.For the present study we used Sn and Cd doped single crystals of Bi 2 Te 3 (see Fig. 1a for crystal structure and Fig. 1b,c for ARPES data). Nominal doping levels between 0 and 0.27% for Sn, and up to 1% for Cd were incorporated to compensate n-type doping from vacancy and anti-site defects that are common in the Bi 2 Te 3 system. Actual doping was determined separately using chemical and Hall-effect methods and were shown by ARPES [4] to be in excellent agreement with the relative position of the Dirac point with respect to the Fermi energy. For example, undoped crystals exhibit a Dirac point at ∼ −335 meV, 0.27% Sn doping yielded a Dirac point at ∼ −300 meV, while for a typical ∼ 1% Cd...