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Register a new userComposite Operator Method analysis of the underdoped cuprates puzzle
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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 to describe the most peculiar features of cuprates held responsible for their anomalous behavior. COM is designed to endorse, since its foundations, the systematic emergence in any SCS of new elementary excitations described by composite operators obeying non-canonical 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 Non Crossing 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 vs. small Fermi surface dichotomy, Fermi surface deconstruction (appearance of Fermi arcs), nodal vs. anti-nodal physics, pseudogap(s), 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 anti-nodal dynamics in the underdoped regime.
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The underdoped cuprates have a number of interesting and unusual properties that often seem hard to reconcile with one another. In this paper we show how many of these diverse phenomena can be synthesized into a single coherent theoretical picture. Specifically we present a description where a pseudogap and gapless Fermi arcs exist in the normal state above the superconducting transition temperature ($T_c$), but give way to the observed quantum oscillations and other phenomena at low temperature when the superconductivity is suppressed by a magnetic field. We show the consistency between these phenomena and observations of enhanced Nernst and diamagnetic signals above $T_c$. We also develop a description of the vortex core inside the superconducting state and discuss its relation with the high field phenomena.
The enigmatic cuprate superconductors have attracted resurgent interest with several recent reports and discussions of competing orders in the underdoped side. Motivated by this, here we address the natural question of fragility of the d-wave superconducting state in underdoped cuprates. Using a combination of theoretical approaches we study t-J like models, and discover an - as yet unexplored - instability that is brought about by an internal (anti-symmetric mode) fluctuation of the d-wave state. This new theoretical result is in good agreement with recent STM and ARPES studies of cuprates. We also suggest experimental directions to uncover this physics.
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-$T_text{c}$ 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.
The one-particle spectral function of a state formed by superconducting (SC) clusters is studied via Monte Carlo techniques. The clusters have similar SC amplitudes but randomly distributed phases. This state is stabilized by the competition with anti-ferromagnetism, after quenched disorder is introduced. Fermi arcs between the critical temperature Tc and the cluster formation temperature scale T* are observed, similarly as in the pseudo-gap state of the cuprates. The arcs originate at metallic regions in between the neighboring clusters that present large SC phase differences.
Several experimental and theoretical studies indicate the existence of a critical point separating the underdoped and overdoped regions of the high-T_c cuprates phase diagram. There are at least two distinct proposals on the critical concentration and its physical origin. First one is associated with the pseudogap formation for p<p*, with p~0.2. Another one relies on the Hall effect measurements and suggests that the critical point and the quantum phase transition (QPT) take place at optimal doping, p_{opt}~0.16. Here we have performed a precise density of states calculation and found that there are two QPTs and the corresponding critical concentrations associated with the change of the Fermi surface topology upon doping.
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