Carlo Castro - Academia.edu (original) (raw)
Papers by Carlo Castro
Advances in Condensed Matter Physics, 2010
Since the discovery of high-temperature superconductivity in 1986 by George Bednorz and Alex Müll... more Since the discovery of high-temperature superconductivity in 1986 by George Bednorz and Alex Müller, there has been a huge theoretical effort to understand the mechanism behind it. A lanthanum copper oxide, doped with barium, was the first compound displaying this phenomenon, and now many more high-temperature superconductors based on copper and oxygen have been discovered. These make up the cuprate family of superconductors. More recently fullerenes, MgB 2 , and in particular iron-based superconductors with high-transition temperatures have been discovered. Cuprates are different from conventional metallic superconductors in that they originate from the charge-doping of parent Mott insulators. The superconductivity arises in weakly coupled doped layers held together by ionic bonding. As well as their high-Tc, they display many unique properties. For instance, they exhibit two different energy scales: a "superconducting" gap (SG) that develops below the superconducting critical temperature which can be seen by extrinsic and intrinsic tunnelling experiments, as well as by high-resolution angleresolved photoemission experiments; and another gap-like feature, the so-called "pseudogap" (PG), that exists in the superconducting state and well above Tc, in the underdoped region with doping smaller than the optimal value at which the maximum Tc occurs. The PG phenomenon was first observed through spin response in underdoped YBa 2 Cu 3 O 7-δ . Many experiments have since detected this PG, including extrinsic and intrinsic tunnelling; photoemission, pump-probe spectroscopies, calorimetric, and many others. Initially this gap was interpreted as manifestation of preformed electron pairs existing above Tc called small bipolarons, bound together by a strong electron-phonon interaction (EPI). Since then many theoretical explanations have been proposed for the origin of the PG which can roughly be divided into two groups. The first of these groups argues that the PG originates from some competing order, either static or fluctuating, possibly also giving rise to inhomogeneous states. The second group interprets the pseudogap as a precursor of superconductivity and suggests the existence above Tc of preformed pairs with no coherence. Despite intensive research, a microscopic theory capable of describing unusual ARPES and tunnelling data has remained elusive and so the relationship between the SG and PG has remained a debated issue. A detailed and consistent interpretation of the SG, PG, and many other unusual properties could shed light on the key effective interactions in cuprate superconductors. In this regard, the interplay of EPI with correlations could be relevant.
Physical Review B, 1993
The low-energy properties of interacting Fermi systems are highly constrained by conservation law... more The low-energy properties of interacting Fermi systems are highly constrained by conservation laws. They generally simplify the structure of the underlying renormalization group by reducing the number of independent renormalization constants. In one dimension, all properties of normal metallic fixed points are uniquely determined by separate charge and spin conservation for states near the left and right Fermi points, respectively. We construct the general Luttinger-liquid theory of one-dimensional (1D) metals directly from these conservation laws. Luttinger-liquid parameters emerge naturally from the velocities associated with the conserved currents at the Luttinger-liquid fixed point. Instead of bosonization, one may thus use techniques familiar from Fermi-liquid theory, i.e., Feynman diagrams, equations of motion, and Ward identities. The choice of a technique comprising both Fermi- and Luttinger-liquid theory makes the similarities and differences of both theories particularly transparent, and sets the stage for constructing non-Fermi-liquid metallic fixed points in d>1. Several generic properties and asymptotic conservation laws of 2D non-Fermi-liquid metals are discussed.
Physical Review B, 2014
We show that in layered systems with electronic phase separation tendency, the long-range Coulomb... more We show that in layered systems with electronic phase separation tendency, the long-range Coulomb interaction can drive the spontaneous formation of unidirectional superlattices of electronic charge in a completely homogeneous crystalline background. In this self-organized electronic heterostructure, the ratio among the number of crystalline planes in the minority and majority electronic phases corresponds to Farey fractions with the superlattice period controlled by the background charge density and the frustrating Coulomb interaction strength. The phase diagram displays Arnold tongues obeying a modified Farey tree hierarchy and a devil's staircase, typical of systems with frustration among different scales. We further discuss the competition of these electronic superlattices, recently observed in iron-based superconductors and mixed valence compounds, with in-plane electronically modulated phases.
International Journal of Modern Physics B, 1996
We consider a one-dimensional system of electrons interacting via a shortrange repulsion and coup... more We consider a one-dimensional system of electrons interacting via a shortrange repulsion and coupled to phonons close to the metal-insulator transition at half filling. We argue that the metal-insulator transition can be described as a standard one dimensional incommensurate to commensurate transition, even if the electronic system is coupled to the lattice distortion. By making use of known results for this transition, we prove that low-momentum phonons do not play any relevant role close to half-filling, unless their coupling to the electrons is large in comparison with the other energy scales present in the problem. In other words the effective strength of the low-momentum transferred electron-phonon coupling does not increase close to the metalinsulator transition, even though the effective velocity of the mobile carriers is strongly diminished.
Localization and Metal-Insulator Transitions, 1985
ABSTRACT
Physical Review Letters, 1991
ABSTRACT
Physica A: Statistical Mechanics and its Applications, 1999
The standard description of metals is based on the Landau theory of Fermi systems (Fermi Liquid t... more The standard description of metals is based on the Landau theory of Fermi systems (Fermi Liquid theory). This picture breaks down in one dimensional systems, which are instead described by the Luttinger Liquid theory. Actually, experimental evidence indicates that Fermi Liquid theory breaks down in a variety of physical systems, including superconducting cuprates.
Journal of Superconductivity, 1996
Journal of Non-Crystalline Solids, 1985
The European Physical Journal H, 2014
Advances in Physics, 1998
Módulo número 2 1 2.1 El proceso de construcción de modelos de Programación Lineal.
Advances in Condensed Matter Physics, 2010
Since the discovery of high-temperature superconductivity in 1986 by George Bednorz and Alex Müll... more Since the discovery of high-temperature superconductivity in 1986 by George Bednorz and Alex Müller, there has been a huge theoretical effort to understand the mechanism behind it. A lanthanum copper oxide, doped with barium, was the first compound displaying this phenomenon, and now many more high-temperature superconductors based on copper and oxygen have been discovered. These make up the cuprate family of superconductors. More recently fullerenes, MgB 2 , and in particular iron-based superconductors with high-transition temperatures have been discovered. Cuprates are different from conventional metallic superconductors in that they originate from the charge-doping of parent Mott insulators. The superconductivity arises in weakly coupled doped layers held together by ionic bonding. As well as their high-Tc, they display many unique properties. For instance, they exhibit two different energy scales: a "superconducting" gap (SG) that develops below the superconducting critical temperature which can be seen by extrinsic and intrinsic tunnelling experiments, as well as by high-resolution angleresolved photoemission experiments; and another gap-like feature, the so-called "pseudogap" (PG), that exists in the superconducting state and well above Tc, in the underdoped region with doping smaller than the optimal value at which the maximum Tc occurs. The PG phenomenon was first observed through spin response in underdoped YBa 2 Cu 3 O 7-δ . Many experiments have since detected this PG, including extrinsic and intrinsic tunnelling; photoemission, pump-probe spectroscopies, calorimetric, and many others. Initially this gap was interpreted as manifestation of preformed electron pairs existing above Tc called small bipolarons, bound together by a strong electron-phonon interaction (EPI). Since then many theoretical explanations have been proposed for the origin of the PG which can roughly be divided into two groups. The first of these groups argues that the PG originates from some competing order, either static or fluctuating, possibly also giving rise to inhomogeneous states. The second group interprets the pseudogap as a precursor of superconductivity and suggests the existence above Tc of preformed pairs with no coherence. Despite intensive research, a microscopic theory capable of describing unusual ARPES and tunnelling data has remained elusive and so the relationship between the SG and PG has remained a debated issue. A detailed and consistent interpretation of the SG, PG, and many other unusual properties could shed light on the key effective interactions in cuprate superconductors. In this regard, the interplay of EPI with correlations could be relevant.
Physical Review B, 1993
The low-energy properties of interacting Fermi systems are highly constrained by conservation law... more The low-energy properties of interacting Fermi systems are highly constrained by conservation laws. They generally simplify the structure of the underlying renormalization group by reducing the number of independent renormalization constants. In one dimension, all properties of normal metallic fixed points are uniquely determined by separate charge and spin conservation for states near the left and right Fermi points, respectively. We construct the general Luttinger-liquid theory of one-dimensional (1D) metals directly from these conservation laws. Luttinger-liquid parameters emerge naturally from the velocities associated with the conserved currents at the Luttinger-liquid fixed point. Instead of bosonization, one may thus use techniques familiar from Fermi-liquid theory, i.e., Feynman diagrams, equations of motion, and Ward identities. The choice of a technique comprising both Fermi- and Luttinger-liquid theory makes the similarities and differences of both theories particularly transparent, and sets the stage for constructing non-Fermi-liquid metallic fixed points in d>1. Several generic properties and asymptotic conservation laws of 2D non-Fermi-liquid metals are discussed.
Physical Review B, 2014
We show that in layered systems with electronic phase separation tendency, the long-range Coulomb... more We show that in layered systems with electronic phase separation tendency, the long-range Coulomb interaction can drive the spontaneous formation of unidirectional superlattices of electronic charge in a completely homogeneous crystalline background. In this self-organized electronic heterostructure, the ratio among the number of crystalline planes in the minority and majority electronic phases corresponds to Farey fractions with the superlattice period controlled by the background charge density and the frustrating Coulomb interaction strength. The phase diagram displays Arnold tongues obeying a modified Farey tree hierarchy and a devil's staircase, typical of systems with frustration among different scales. We further discuss the competition of these electronic superlattices, recently observed in iron-based superconductors and mixed valence compounds, with in-plane electronically modulated phases.
International Journal of Modern Physics B, 1996
We consider a one-dimensional system of electrons interacting via a shortrange repulsion and coup... more We consider a one-dimensional system of electrons interacting via a shortrange repulsion and coupled to phonons close to the metal-insulator transition at half filling. We argue that the metal-insulator transition can be described as a standard one dimensional incommensurate to commensurate transition, even if the electronic system is coupled to the lattice distortion. By making use of known results for this transition, we prove that low-momentum phonons do not play any relevant role close to half-filling, unless their coupling to the electrons is large in comparison with the other energy scales present in the problem. In other words the effective strength of the low-momentum transferred electron-phonon coupling does not increase close to the metalinsulator transition, even though the effective velocity of the mobile carriers is strongly diminished.
Localization and Metal-Insulator Transitions, 1985
ABSTRACT
Physical Review Letters, 1991
ABSTRACT
Physica A: Statistical Mechanics and its Applications, 1999
The standard description of metals is based on the Landau theory of Fermi systems (Fermi Liquid t... more The standard description of metals is based on the Landau theory of Fermi systems (Fermi Liquid theory). This picture breaks down in one dimensional systems, which are instead described by the Luttinger Liquid theory. Actually, experimental evidence indicates that Fermi Liquid theory breaks down in a variety of physical systems, including superconducting cuprates.
Journal of Superconductivity, 1996
Journal of Non-Crystalline Solids, 1985
The European Physical Journal H, 2014
Advances in Physics, 1998
Módulo número 2 1 2.1 El proceso de construcción de modelos de Programación Lineal.