There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This article reviews the physics of high-temperature superconductors from the point of view of the doping of a Mott insulator. The basic electronic structure of cuprates is reviewed, emphasizing the physics of strong correlation and establishing the model of a doped Mott insulator as a starting point. A variety of experiments are discussed, focusing on the region of the phase diagram close to the Mott insulator (the underdoped region) where the behavior is most anomalous. The normal state in this region exhibits pseudogap phenomenon. In contrast, the quasiparticles in the superconducting state are well defined and behave according to theory. This review introduces Anderson's idea of the resonating valence bond and argues that it gives a qualitative account of the data. The importance of phase fluctuations is discussed, leading to a theory of the transition temperature, which is driven by phase fluctuations and the thermal excitation of quasiparticles. However, an argument is made that phase fluctuations can only explain pseudogap phenomenology over a limited temperature range, and some additional physics is needed to explain the onset of singlet formation at very high temperatures. A description of the numerical method of the projected wave function is presented, which turns out to be a very useful technique for implementing the strong correlation constraint and leads to a number of predictions which are in agreement with experiments. The remainder of the paper deals with an analytic treatment of the $t\text{\ensuremath{-}}J$ model, with the goal of putting the resonating valence bond idea on a more formal footing. The slave boson is introduced to enforce the constraint againt double occupation and it is shown that the implementation of this local constraint leads naturally to gauge theories. This review follows the historical order by first examining the U(1) formulation of the gauge theory. Some inadequacies of this formulation for underdoping are discussed, leading to the SU(2) formulation. Here follows a rather thorough discussion of the role of gauge theory in describing the spin-liquid phase of the undoped Mott insulator. The difference between the high-energy gauge group in the formulation of the problem versus the low-energy gauge group, which is an emergent phenomenon, is emphasized. Several possible routes to deconfinement based on different emergent gauge groups are discussed, which leads to the physics of fractionalization and spin-charge separation. Next the extension of the SU(2) formulation to nonzero doping is described with a focus on a part of the mean-field phase diagram called the staggered flux liquid phase. It will be shown that inclusion of the gauge fluctuation provides a reasonable description of the pseudogap phase. It is emphasized that $d$-wave superconductivity can be considered as evolving from a stable U(1) spin liquid. These ideas are applied to the high-${T}_{c}$ cuprates, and their implications for the vortex structure and the phase diagram are discussed. A possible test of the topological structure of the pseudogap phase is described.

/pdf/doping-a-mott-insulator-physics-of-high-temperature-55r49vtp31.pdf

Doping a Mott insulator: Physics of high-temperature superconductivity

In the coming decade, the ability to sense and detect the state of biological systems and living organisms optically, electrically and magnetically will be radically transformed by developments in materials physics and chemistry. The emerging ability to control the patterns of matter on the nanometer length scale can be expected to lead to entirely new types of biological sensors. These new systems will be capable of sensing at the single-molecule level in living cells, and capable of parallel integration for detection of multiple signals, enabling a diversity of simultaneous experiments, as well as better crosschecks and controls.

/pdf/the-use-of-nanocrystals-in-biological-detection-3f8dgrg9fx.pdf

The use of nanocrystals in biological detection

MUCKE aims to mine a large volume of images, to structure them conceptually and to use this conceptual structuring in order to improve large-scale image retrieval. The last decade witnessed important progress concerning low-level image representations. However, there are a number problems which need to be solved in order to unleash the full potential of image mining in applications. The central problem with low-level representations is the mismatch between them and the human interpretation of image content. This problem can be instantiated, for instance, by the incapability of existing descriptors to capture spatial relationships between the concepts represented or by their incapability to convey an explanation of why two images are similar in a content-based image retrieval framework. We start by assessing existing local descriptors for image classification and by proposing to use co-occurrence matrices to better capture spatial relationships in images. The main focus in MUCKE is on cleaning large scale Web image corpora and on proposing image representations which are closer to the human interpretation of images. Consequently, we introduce methods which tackle these two problems and compare results to state of the art methods. Note: some aspects of this deliverable are withheld at this time as they are pending review. Please contact the authors for a preview.

http://ieeexplore.ieee.org/iel2/4524/12820/00592460.pdf

Image Processing

This article reviews the effort to understand the physics of high temperature superconductors from the point of view of doping a Mott insulator. The basic electronic structure of the cuprates is reviewed, emphasizing the physics of strong correlation and establishing the model of a doped Mott insulator as a starting point. A variety of experiments are discussed, focusing on the region of the phase diagram close to the Mott insulator (the underdoped region) where the behavior is most anomalous. We introduce Anderson's idea of the resonating valence bond (RVB) and argue that it gives a qualitative account of the data. The importance of phase fluctuation is discussed, leading to a theory of the transition temperature which is driven by phase fluctuation and thermal excitation of quasiparticles. We then describe the numerical method of projected wavefunction which turns out to be a very useful technique to implement the strong correlation constraint, and leads to a number of predictions which are in agreement with experiments. The remainder of the paper deals with an analytic treatment of the t-J model, with the goal of putting the RVB idea on a more formal footing. The slave-boson is introduced to enforce the constraint of no double occupation. The implementation of the local constraint leads naturally to gauge theories. We give a rather thorough discussion of the role of gauge theory in describing the spin liquid phase of the undoped Mott insulator. We next describe the extension of the SU(2) formulation to nonzero doping. We show that inclusion of gauge fluctuation provides a reasonable description of the pseudogap phase.

Doping a Mott Insulator: Physics of High Temperature Superconductivity

We have investigated spin pumping from ${\mathrm{Y}}_{3}{\mathrm{Fe}}_{5}{\mathrm{O}}_{12}$ thin films into Cu, Ag, Ta, W, Pt, and Au with varying spin-orbit coupling strengths. From measurements of Gilbert damping enhancement and inverse spin Hall signals spanning 3 orders of magnitude, we determine the spin Hall angles and interfacial spin mixing conductances for the six metals. The spin Hall angles largely vary as ${Z}^{4}$ ($Z$: atomic number), corroborating the role of spin-orbit coupling. Amongst the four 5d metals, the variation of the spin Hall angle is dominated by the sensitivity of the $d$-orbital moment to the $d$-electron count, confirming theoretical predictions.

Scaling of Spin Hall Angle in 3d, 4d, and 5d Metals from Y 3 Fe 5 O 12 /Metal Spin Pumping

The microscopic magnetic properties of the ${\mathrm{CuO}}_{2}$ planes in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{6.63}$ (${\mathit{T}}_{\mathit{c}}$=62 K) have been investigated in Cu and O NMR experiments. Unlike the fully oxygenated Y-Ba-Cu-${\mathrm{O}}_{7}$ (${\mathit{T}}_{\mathit{c}}$\ensuremath{\simeq}90 K), the various components of the Cu and O Knight-shift tensors show strong but identical temperature dependences in the normal state. This supports the picture that there is only one spin component in the ${\mathrm{CuO}}_{2}$ planes. The spin susceptibility deduced from Knight-shift results shows significant reduction with decreasing temperature in the normal state. The temperature dependences of the nuclear-spin-relaxation rates (1/${\mathit{T}}_{1}$) are very different for the Cu and the O sites. 1/(${\mathit{T}}_{1}$T) at the O sites is nearly proportional to the spin susceptibility. 1/(${\mathit{T}}_{1}$T) at the Cu sites shows a broad peak around 150 K. We discuss these relaxation behaviors based on a model of the dynamical spin susceptibility proposed by Millis, Monien, and Pines.

https://escholarship.org/content/qt2r91g6kk/qt2r91g6kk.pdf?t=ob117b

Cu and O NMR studies of the magnetic properties of YBa2Cu3O6.63 (Tc=62 K).

We report NMR measurements of the nuclear relaxation rate at all copper and oxygen sites in magnetically aligned powder samples of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ Comparison of the oxygen and copper relaxation reveals a characteristic temperature greater than ${T}_{c}$ The copper relaxation rate is enhanced by antiferromagnetic copper spin fluctuations which are undiminished in the superconducting state The absence of a coherence peak indicates that the superconductive pairing is not of the conventional BCS type

Spin dynamics at oxygen sites in YBa2Cu3O7.

We report the observation of a ferromagnetic resonance signal arising from a microscopic (∼20 μm×40 μm) particle of thin (3μm) yttrium iron garnet film using magnetic resonance force microscopy (MRFM). The large signal intensity in the resonance spectra suggests that MRFM could become a powerful microscopic ferromagnetic resonance technique with a micron or sub‐micron resolution. We also observe a very strong nonresonance signal which occurs in the field regime where the sample magnetization readily reorients in response to the modulation of the magnetic field. This signal will be the main noise source in applications where a magnet is mounted on the cantilever.

/pdf/observation-of-ferromagnetic-resonance-in-a-microscopic-19h68axb6x.pdf

Observation of ferromagnetic resonance in a microscopic sample using magnetic resonance force microscopy

Photoluminescence measurements show that the spin state of an $N\phantom{\rule{0}{0ex}}V$ center can be modified nonresonantly (i.e. at frequencies far from the $N\phantom{\rule{0}{0ex}}V$ Larmor frequencies) via coupling to the dynamic magnetization of a ferromagnet---an unexpected result that presents a new approach to transferring ferromagnetic spin information into a paramagnet.

P. C. Hammel

Papers

Scaling of Spin Hall Angle in 3d, 4d, and 5d Metals from Y 3 Fe 5 O 12 /Metal Spin Pumping

Cu and O NMR studies of the magnetic properties of YBa2Cu3O6.63 (Tc=62 K).

Spin dynamics at oxygen sites in YBa2Cu3O7.

Observation of ferromagnetic resonance in a microscopic sample using magnetic resonance force microscopy

Off-resonant manipulation of spins in diamond via precessing magnetization of a proximal ferromagnet