Personal history of my engagement with cuprate superconductivity, 1986-2010

Six months ago I was asked to write a personal history of my engagement with the high-Tc problem of the cuprate superconductors, in rather informal and autobiographical style. As the work proceeded I realized that it was impossible and would have been dishonest to separate out my rather amusing but seminal early fumblings from the complete restructuring of the problem which I have achieved during the past decade. But the result became considerably too long, by over half, for its intended recipient. The assignment had left me with no obligation to deal with all the fascinating but irrelevant phenomenology which I had more or less instinctively ignored on my way, but that feature also fails to endear the article to any conceivable editorial board containing knowledgeable experts on the subject. Also, their purpose was for it to serve as a (quote) introduction to the more technical debates, but its message is that almost all of these are not relevant. They are not, on the whole, focused on achieving understanding of the crucial experimental anomalies, many, if not most, of which are now understood. The key to the problem is a new method of dealing with the constrained Hilbert space which follows from the necessity of Gutzwiller projection

Evolution of Hall coefficient in two-dimensional heavy fermion CeCoIn5_5

We report on the pressure dependence of the Hall coefficient $R_H$ in quasi-2D heavy fermion CeCoIn$_5$. At ambient pressure, below a temperature associated with the emergence of non-Fermi liquid properties, $R_H$ is anomalously enhanced. We found that the restoration of the Fermi liquid state with applied pressure leads to a gradual suppression of this dramatic enhancement. Moreover, the enhancement in $R_H$ was found to be confined to an intermediate temperature window, where inelastic electron-electron scattering is dominant. Our results strongly support the presence of cold and hot spots on the Fermi surface probably due to anisotropic scattering by antiferromagnetic fluctuations, which may also prove relevant for the debate on the anomalous normal-state properties of high-$T_c$ cuprates.Comment: 9 pages, 5 fiqures, to be published in J. Phys. Soc. Jp

Quasi-linear magnetoresistance in an almost 2D band structure

We present a theoretical study of the orbital magnetoresistance in a unixial anisotropic metal within the relaxation-time approximation. The appearance of a new dimensionless scale, delta=4t_perp/epsilon_F, allows the possibility of a new region at intermediate fields where the magnetoresistance is linear in applied magnetic field for currents flowing along the unixial direction. (Here, t_perp characterizes the bandwidth along the unixial direction.) In the limit of large anisotropy (small delta), corresponding to a quasi-two-dimensional metal made up of weakly coupled layers, we obtain an analytic expression for the magnetoresistance valid for all magnetic fields. We test our analytic results numerically and we compare our expressions with the c-axis magnetoresistance of Sr_2RuO_4.Comment: 7 pages Latex (revtex4 and epsf) 4 postscript figures included. Replaced with published version which includes more details and a fit to dat

Breakdown of Fermi-liquid theory in a cuprate superconductor

The behaviour of electrons in solids is remarkably well described by Landau's Fermi-liquid theory, which says that even though electrons in a metal interact they can still be treated as well-defined fermions, called ``quasiparticles''. At low temperature, the ability of quasiparticles to transport heat is strictly given by their ability to transport charge, via a universal relation known as the Wiedemann-Franz law, which no material in nature has been known to violate. High-temperature superconductors have long been thought to fall outside the realm of Fermi-liquid theory, as suggested by several anomalous properties, but this has yet to be shown conclusively. Here we report on the first experimental test of the Wiedemann-Franz law in a cuprate superconductor, (Pr,Ce)$_2$CuO$_4$. Our study reveals a clear departure from the universal law and provides compelling evidence for the breakdown of Fermi-liquid theory in high-temperature superconductors.Comment: 7 pages, 3 figure

Visual responsiveness in sensorimotor cortex is increased following amputation and reduced after mirror therapy

Phantom limb pain (PLP) following amputation, which is experienced by the vast majority of amputees, has been reported to be relieved with daily sessions of mirror therapy. During each session, a mirror is used to view the reflected image of the intact limb moving, providing visual feedback consistent with the movement of the missing/phantom limb. To investigate potential neural correlates of the treatment effect, we measured brain responses in volunteers with unilateral leg amputation using functional magnetic resonance imaging (fMRI) during a four-week course of mirror therapy. Mirror therapy commenced immediately following baseline scans, which were repeated after approximately two and four week intervals. We focused on responses in the region of sensorimotor cortex corresponding to primary somatosensory and motor representations of the missing leg. At baseline, prior to starting therapy, we found a strong and unexpected response in sensorimotor cortex of amputees to visually presented images of limbs. This response was stronger for images of feet compared to hands and there was no such response in matched controls. Further, this response to visually presented limbs was no longer present at the end of the four week mirror therapy treatment, when perceived phantom limb pain was also reduced. A similar pattern of results was also observed in extrastriate and parietal regions typically responsive to viewing hand actions, but not in regions corresponding to secondary somatosensory cortex. Finally, there was a significant correlation between initial visual responsiveness in sensorimotor cortex and reduction in PLP suggesting a potential marker for predicting efficacy of mirror therapy. Thus, enhanced visual responsiveness in sensorimotor cortex is associated with PLP and modulated over the course of mirror therapy

Evolution of the resistivity anisotropy in Bi_{2}Sr_{2-x}La_{x}CuO_{6+\delta} single crystals for a wide range of hole doping

To elucidate how the temperature dependence of the resistivity anisotropy of the cuprate superconductors changes with hole doping, both the in-plane and the out-of-plane resistivities (\rho_{ab} and \rho_{c}) are measured in a series of high-quality Bi_{2}Sr_{2-x}La_{x}CuO_{6+\delta} (BSLCO) single crystals for a wide range of x (x = 0.23 - 1.02), which corresponds to the hole doping per Cu, p, of 0.03 - 0.18. The anisotropy ratio, \rho_{c}/\rho_{ab}, shows a systematic increase with decreasing p at moderate temperatures, except for the most underdoped composition where the localization effect enhances \rho_{ab} and thus lowers \rho_{c}/\rho_{ab}. The exact p dependence of \rho_{c}/\rho_{ab} at a fixed temperature is found to be quite peculiar, which is discussed to be due to the effect of the pseudogap that causes \rho_{c}/\rho_{ab} to be increasingly more enhanced as p is reduced. The pseudogap also causes a rapid growth of \rho_{c}/\rho_{ab} with decreasing temperature, and, as a result, the \rho_{c}/\rho_{ab} value almost reaches 10^6 in underdoped samples just above T_c. Furthermore, it is found that the temperature dependence of \rho_{c} of underdoped samples show two distinct temperature regions in the pseudogap phase, which suggests that the divergence of \rho_{c} below the pseudogap temperature is governed by two different mechanisms.Comment: 10 pages, 10 figures, revised version. Discussions are expanded with a new analysis of the T-dependence of \rho_{c} and the resulting new phase diagra

Genomic catastrophes frequently arise in esophageal adenocarcinoma and drive tumorigenesis

Oesophageal adenocarcinoma (EAC) incidence is rapidly increasing in Western countries. A better understanding of EAC underpins efforts to improve early detection and treatment outcomes. While large EAC exome sequencing efforts to date have found recurrent loss-offunction mutations, oncogenic driving events have been underrepresented. Here we use a combination of whole-genome sequencing (WGS) and single-nucleotide polymorphism-array profiling to show that genomic catastrophes are frequent in EAC, with almost a third (32%, n¼40/123) undergoing chromothriptic events. WGS of 22 EAC cases show that catastrophes may lead to oncogene amplification through chromothripsis-derived double-minute chromosome formation (MYC and MDM2) or breakage-fusion-bridge (KRAS, MDM2 and RFC3). Telomere shortening is more prominent in EACs bearing localized complex rearrangements. Mutational signature analysis also confirms that extreme genomic instability in EAC can be driven by somatic BRCA2 mutations. These findings suggest that genomic catastrophes have a significant role in the malignant transformation of EAC

Comparison of coherent and weakly incoherent transport models for the interlayer magnetoresistance of layered Fermi liquids

The interlayer magnetoresistance of layered metals in a tilted magnetic field is calculated for two distinct models for the interlayer transport. The first model involves coherent interlayer transport and makes use of results of semi-classical or Bloch-Boltzmann transport theory. The second model involves weakly incoherent interlayer transport where the electron is scattered many times within a layer before tunneling into the next layer. The results are relevant to the interpretation of experiments on angular-dependent magnetoresistance oscillations (AMRO) in quasi-one- and quasi-two-dimensional metals. We find that the dependence of the magnetoresistance on the direction of the magnetic field is identical for both models except when the field is almost parallel to the layers. An important implication of this result is that a three-dimensional Fermi surface is not necessary for the observation of the Yamaji and Danner oscillations seen in quasi-two- and quasi-one-dimensional metals, respectively. A universal expression is given for the dependence of the resistance at AMRO maxima and minima on the magnetic field and scattering time (and thus the temperature). We point out three distinctive features of coherent interlayer transport: (i) a beat frequency in the magnetic oscillations of quasi-two-dimensional systems, (ii) a peak in the angular-dependent magnetoresistance when the field is sufficiently large and parallel to the layers, and (iii) a crossover from a linear to a quadratic field dependence for the magnetoresistance when the field is parallel to the layers. Properties (i) and (ii) are compared with published experimental data for a range of quasi-two-dimensional organic metals and for Sr2RuO4.Comment: 21 pages, RevTeX + epsf, 4 figures. Published version. Subsection added. References update

Measuring anisotropic scattering in the cuprates

A simple model of anisotropic scattering in a quasi two-dimensional metal is studied. Its simplicity allows an analytic calculation of transport properties using the Boltzmann equation and relaxation time approximation. We argue that the c-axis magnetoresistance provides the key test of this model of transport. We compare this model with experiments on overdoped Tl-2201 and find reasonable agreement using only weak scattering anisotropy. We argue that optimally doped Tl-2201 should show strong angular-dependent magnetoresistance within this model and would provide a robust way of determining the in-plane scattering anisotropy in the cuprates.Comment: 12 pages, 8 figures, typset in REVTeX 4. Version 2; added references and corrected typo