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arXiv:1410.0153 · Advances in Condensed Matter Physics

Composite Operator Method Analysis of the Underdoped Cuprates Puzzle

Adolfo Avella

Published Jan 1, 2014• 21 citations

Abstract

The microscopical analysis of the unconventional and puzzling physics of the underdoped cuprates, as carried out lately by means of the composite operator method (COM) applied to the 2D Hubbard model, is reviewed and systematized. The 2D Hubbard model has been adopted as it has been considered the minimal model capable of describing the most peculiar features of cuprates held responsible for their anomalous behavior. COM is designed to endorse, since its foundation, the systematic emergence in any SCS of new elementary excitations described by composite operators obeying noncanonical algebras. In this case (underdoped cuprates—2D Hubbard model), the residual interactions—beyond a 2-pole approximation—between the new elementary electronic excitations, dictated by the strong local Coulomb repulsion and well described by the two Hubbard composite operators, have been treated within the noncrossing approximation. Given this recipe and exploiting the few unknowns to enforce the Pauli principle content in the solution, it is possible to qualitatively describe some of the anomalous features of high-Tc cuprate superconductors such as large versus small Fermi surface dichotomy, Fermi surface deconstruction (appearance of Fermi arcs), nodal versus antinodal physics, pseudogap(s), and kinks in the electronic dispersion. The resulting scenario envisages a smooth crossover between an ordinary weakly interacting metal sustaining weak, short-range antiferromagnetic correlations in the overdoped regime to an unconventional poor metal characterized by very strong, long-but-finite-range antiferromagnetic correlations leading to momentum-selective non-Fermi liquid features as well as to the opening of a pseudogap and to the striking differences between the nodal and the antinodal dynamics in the underdoped regime.

DOI: 10.1155/2014/515698

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The microscopical analysis of the unconventional and puzzling physics of the underdoped cuprates, as carried out lately by means of the composite operator method (COM) applied to the 2D Hubbard model, is reviewed and systematized. The 2D Hubbard model has been adopted as it has been considered the minimal model capable of describing the most peculiar features of cuprates held responsible for their anomalous behavior. COM is designed to endorse, since its foundation, the systematic emergence in any SCS of new elementary excitations described by composite operators obeying noncanonical algebras. In this case (underdoped cuprates—2D Hubbard model), the residual interactions—beyond a 2-pole approximation—between the new elementary electronic excitations, dictated by the strong local Coulomb repulsion and well described by the two Hubbard composite operators, have been treated within the noncrossing approximation. Given this recipe and exploiting the few unknowns to enforce the Pauli principle content in the solution, it is possible to qualitatively describe some of the anomalous features of high-Tc cuprate superconductors such as large versus small Fermi surface dichotomy, Fermi surface deconstruction (appearance of Fermi arcs), nodal versus antinodal physics, pseudogap(s), and kinks in the electronic dispersion. The resulting scenario envisages a smooth crossover between an ordinary weakly interacting metal sustaining weak, short-range antiferromagnetic correlations in the overdoped regime to an unconventional poor metal characterized by very strong, long-but-finite-range antiferromagnetic correlations leading to momentum-selective non-Fermi liquid features as well as to the opening of a pseudogap and to the striking differences between the nodal and the antinodal dynamics in the underdoped regime.

The two-dimensional Hubbard model is studied within the composite operator method (COM) with the self-energy computed in the self-consistent Born approximation (SCBA). The COM describes interacting electrons in terms of the new elementary excitations that appear in the system owing to strong correlations; residual interactions among these excitations are treated within the SCBA. On decreasing the doping (from the overdoped to underdoped region), anomalous features develop in the spectral function $A(\mathbf{k},\ensuremath{\omega})$, the Fermi surface, the momentum distribution function

n(\mathbf{k})

, the dispersion, and the density of states $N(\ensuremath{\omega})$ in the intermediate-coupling regime

(U=8)

at low temperatures

(T=0.01--0.02)

. At high doping

(n=0.7)

, the system resembles an ordinary weakly interacting metal. At low doping

(n=0.92)

, a pseudogap opens, hot and cold spots appear, and non-Fermi-liquid features develop. This behavior, together with the presence of kinks in the calculated electronic dispersion, is in agreement with angle-resolved photoemission spectroscopy data for high-

{T}_{c}

cuprates superconductors.

The two-dimensional Hubbard model is studied within the composite operator method (COM) with the electronic self-energy computed in the self-consistent Born approximation (SCBA). The main idea of the COM is to describe interacting electrons in terms of the composite elementary excitations appearing in the system owing to strong correlations; the residual interactions among these excitations are treated within the SCBA. By analysing the spectral function A(k,ω) on varying the filling, we find, at high doping, the ordinary Fermi-liquid behaviour of a weakly interacting metal and, at low doping, the opening of a pseudogap, as reported for cuprates superconductors.

In this review paper, we illustrate a possible route to obtain a reliable solution of the 2D Hubbard model and an explanation for some of the unconventional behaviours of underdoped high-T c cuprate superconductors within the framework of the composite operator method.The latter is described exhaustively in its fundamental philosophy, various ingredients and robust machinery to clarify the reasons behind its successful applications to many diverse strongly correlated systems, controversial phenomenologies and puzzling materials.

We present a novel solution of the 2D Hubbard model in the framework of the Composite Operator Method within a four-pole approximation. We adopt a basis of four fields: the two Hubbard operators plus two fields describing the Hubbard transitions dressed by nearest-neighbor spin fluctuations. We include these nonlocal operators because spin fluctuations play a dominant role in strongly correlated electronic systems with respect to other types of nonlocal charge, pair and double-occupancy fluctuations. The approximate solution performs very well once compared with advanced (semi-) numerical methods from the weak-to the strong-coupling regime, being by far less computational-resource demanding. We adopt this solution to study the single-particle properties of the model in the strong coupling regime, where the effects of strong short-range magnetic correlations are more relevant and could be responsible for anomalous features. In particular, we will focus on the characterization of the Fermi surface and of its evolution with doping.

A theoretical analysis of the thermodynamic response functions of the 2D single{band Hubbard model is carried out by means of the composite operator method.It is shown that all the features of these quantities can be explained by looking at the dependence of the thermodynamic variables on their conjugate ones.In this way, the electronic speci c heat and the entropy per site are determined in the paramagnetic phase.Also, for the electronic speci c heat and internal energy we present two dierent schemes of calculation.It is found that the numerical data from quantum Monte Carlo techniques for the internal energy and electronic speci c heat are well reproduced by determining them through the rst and second temperature derivatives of the chemical potential.The anomalous normal state properties in hole{doped cuprate high Tc superconductors are also well described.Finally, we obtain several characteristic crossing points for the response functions when plotted versus some thermodynamic variables.These peculiar features indicate the existence of more than one energy scale competing with thermal excitations and indicate, as already noted by Vollhardt, a crossover from a non{interacting to a highly correlated behaviour.

Strongly correlated electron systems with planar structure, like high{Tc superconductors, are currently under intensive study.In the search for a realistic model to describe the anomalous behaviors of these systems, we have studied the 2D Extended Hubbard model by means of the Composite Operator Method.The local properties, the density of states and the Fermi surface have been calculated as functions of the model parameters.Particular attention has been paid to the role played by the intersite interaction V which drives important changes in the electronic properties of the system.