Henri Alloul

Bio: Henri Alloul is an academic researcher from University of Paris-Sud. The author has contributed to research in topics: Superconductivity & Antiferromagnetism. The author has an hindex of 39, co-authored 193 publications receiving 5659 citations. Previous affiliations of Henri Alloul include Centre national de la recherche scientifique & École Polytechnique.

Introduction to Superconductivity

Abstract: We have seen how the conductivity of a metal is limited by collisions, which determine the electron mean free path. After a collision, an electron completely loses all memory of its quantum state as specified by its quasi-momentum k. It is thus impossible to follow a Bloch state over any distance much greater than the mean free path. To understand the microscopic origin of these collisions, one had to measure the conductivity of very pure metals at low temperatures. This was made possible by the work of the physicist Kammerlingh Onnes, who specialised in the liquefaction of gases and opened the way to the use of cryogenic fluids. In 1911, he succeeded in liquefying 4He, at a temperature of 4.2 K. He then suggested using the low temperatures created in this way to study the low temperature conductivity of pure metals. Quite unexpectedly, he discovered that the conductivity of mercury increased by several orders of magnitude at temperatures below 4.18 K. This discovery of superconductivity remained a mystery for more than 40 years. With hindsight, it is clear that the prerequisites of quantum mechanics had not yet been established. Of course, this did not prevent the physicists of the first half of the twentieth century from gradually getting a hold on the fundamental manifestations of this phenomenon through ideas based entirely on experimental observations.

89Y NMR evidence for a Fermi-liquid behavior in YBa2Cu3O6+x

Abstract: We report NMR shift \ensuremath{\Delta}K and ${T}_{1}$ data of $^{89}\mathrm{Y}$ taken from 77 to 300 K in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{6+\mathrm{x}}$ for 0.35lxl1, from the insulating to the metallic state. A Korringa law and therefore a Fermi-liqud picture is found to apply for the spin part ${K}_{s}$ of \ensuremath{\Delta}K. The spin contribution ${\ensuremath{\chi}}_{s}$(x,T) to ${\ensuremath{\chi}}_{m}$ is singled out, as the T variation of \ensuremath{\Delta}K scales linearly with the macroscopic susceptibility ${\ensuremath{\chi}}_{m}$. This implies that Cu(3d) and O(2p) holes do not have independent degrees of freedom. Their hybridization, which has a \ensuremath{\sigma} character, hardly varies with doping. These results put severe constraints on theoretical models of high-${T}_{c}$ cuprates.

Defects in correlated metals and superconductors

Abstract: In materials with strong local Coulomb interactions, simple defects such as atomic substitutions strongly affect both macroscopic and local properties of the system. A nonmagnetic impurity, for instance, is seen to induce magnetism nearby. Even without disorder, models of such correlated systems are generally not soluble in 2 or 3 dimensions, and so few exact results are known for the properties of such impurities. Nevertheless, some simple physical ideas have emerged from experiments and approximate theories. Here, we first review what we can learn about this problem from 1D antiferromagnetically correlated systems. We then discuss experiments on the high Tc cuprate normal state which probe the effect of impurities on local charge and spin degrees of freedom, and compare with theories of single impurities in correlated hosts, as well as phenomenological effective Kondo descriptions. Subsequently, we review theories of impurities in d-wave superconductors including residual quasiparticle interactions, and compare with experiments in the superconducting state. We argue that existing data exhibit a remarkable similarity to impurity-induced magnetism in the 1D case, implying the importance of electronic correlations for the understanding of these phenomena, and suggesting that impurities may provide excellent probes of the still poorly understood ground state of the cuprates.

Correlations between magnetic and superconducting properties of Zn-substituted YBa2Cu3O6+x.

Abstract: ${\mathit{T}}_{\mathit{c}}$ and ${\mathit{T}}_{\mathit{N}}$ (N\'eel) have been measured for a series of ${\mathrm{YBa}}_{2}$(${\mathrm{Cu}}_{0.96}$${\mathrm{Zn}}_{0.04}$${)}_{3}$${\mathrm{O}}_{6+\mathit{x}}$ samples. The T variations of the homogeneous susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathit{s}}$ of the ${\mathrm{CuO}}_{2}$ planes, given by the shift of the $^{89}\mathrm{Y}$ NMR line, are found to be nearly unchanged with respect to pure samples for xg0.5, which implies that the charge transfer is negligibly modified by Zn, and that the magentic pseudo-gap is not associated with superconducting pairing. Detection of an unusual Curie contribution to the $^{89}\mathrm{Y}$ NMR width for x\ensuremath{\ge}0.5 provides evidence that Zn induces magnetic moments in the ${\mathrm{CuO}}_{2}$ planes, which play a role in the depression of ${\mathit{T}}_{\mathit{c}}$.

Unconventional superconductivity in magic-angle graphene superlattices

Abstract: The behaviour of strongly correlated materials, and in particular unconventional superconductors, has been studied extensively for decades, but is still not well understood. This lack of theoretical understanding has motivated the development of experimental techniques for studying such behaviour, such as using ultracold atom lattices to simulate quantum materials. Here we report the realization of intrinsic unconventional superconductivity-which cannot be explained by weak electron-phonon interactions-in a two-dimensional superlattice created by stacking two sheets of graphene that are twisted relative to each other by a small angle. For twist angles of about 1.1°-the first 'magic' angle-the electronic band structure of this 'twisted bilayer graphene' exhibits flat bands near zero Fermi energy, resulting in correlated insulating states at half-filling. Upon electrostatic doping of the material away from these correlated insulating states, we observe tunable zero-resistance states with a critical temperature of up to 1.7 kelvin. The temperature-carrier-density phase diagram of twisted bilayer graphene is similar to that of copper oxides (or cuprates), and includes dome-shaped regions that correspond to superconductivity. Moreover, quantum oscillations in the longitudinal resistance of the material indicate the presence of small Fermi surfaces near the correlated insulating states, in analogy with underdoped cuprates. The relatively high superconducting critical temperature of twisted bilayer graphene, given such a small Fermi surface (which corresponds to a carrier density of about 1011 per square centimetre), puts it among the superconductors with the strongest pairing strength between electrons. Twisted bilayer graphene is a precisely tunable, purely carbon-based, two-dimensional superconductor. It is therefore an ideal material for investigations of strongly correlated phenomena, which could lead to insights into the physics of high-critical-temperature superconductors and quantum spin liquids.

Spin glasses: Experimental facts, theoretical concepts, and open questions

Abstract: This review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data. The most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned. The Edwards-Anderson model of spin glasses and its treatment within the replica method and mean-field theory are outlined, and concepts such as "frustration," "broken replica symmetry," "broken ergodicity," etc., are discussed. The dynamic approach to describing the spin glass transition is emphasized. Monte Carlo simulations of spin glasses and the insight gained by them are described. Other topics discussed include site-disorder models, phenomenological theories for the frozen phase and its excitations, phase diagrams in which spin glass order and ferromagnetism or antiferromagnetism compete, the Ne\'el model of superparamagnetism and related approaches, and possible connections between spin glasses and other topics in the theory of disordered condensed-matter systems.

Doping a Mott insulator: Physics of high-temperature superconductivity

Abstract: 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.