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Ponto crítico quântico supercondutor em sistemas multi-bandas

Aline Ramires

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

The study of quantum phase transitions provides a new route to ¯nd and understand unconventional phases in Condensed Matter Physics. The past decades have seen a sub- stantial rejuvenation of interest in this area of study, driven by experiments on the cuprate superconductors, heavy fermions' materials, organic conductors and related compounds. Nevertheless, the transitions involving superconducting phases are not as well explored theoretically as transitions involving magnetic phases. Thus, the study of superconduct- ing systems with treatments beyond mean ¯eld theories seems to be necessary to verify the behavior of °uctuations in the normal phase near the transition to the superconductor state. We propose a generalization of the equation of motion method for equilibrium Green's functions to handle systems with time-dependent perturbations. This generalization is based on the properties of Green's functions and in the adiabatic application of the disturbance. We study a two band s-wave superconductor with hybridization, based on an attractive Hubbard model. We consider the system under the action of a fictitious field, time and wave vector dependent, which couples to the superconducting order parameter. We calculate the zero order propagators in the field, using the conventional equation of motion method, and the first order ones, using the generalized equation of motion. The response to the field is given by a generalized susceptibility, which in the one-band case reduces to the one obtained by Thouless. We associate the emergence of superconductivity with the divergence of the static part of the generalized susceptibility. The advantage of this method is its simplicity, because we only deal with single-particle propagators. We analyze this superconducting susceptibility, which allows us to find a critical hybridization above which there is no superconducting phase, determine the critical and the crossover lines and determine the dynamical critical exponent z for this system. Therefore we can predict the behavior of some quantities measured experimentally at low temperatures close to the superconducting quantum critical point.

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The study of quantum phase transitions provides a new route to ¯nd and understand unconventional phases in Condensed Matter Physics. The past decades have seen a sub- stantial rejuvenation of interest in this area of study, driven by experiments on the cuprate superconductors, heavy fermions' materials, organic conductors and related compounds. Nevertheless, the transitions involving superconducting phases are not as well explored theoretically as transitions involving magnetic phases. Thus, the study of superconduct- ing systems with treatments beyond mean ¯eld theories seems to be necessary to verify the behavior of °uctuations in the normal phase near the transition to the superconductor state. We propose a generalization of the equation of motion method for equilibrium Green's functions to handle systems with time-dependent perturbations. This generalization is based on the properties of Green's functions and in the adiabatic application of the disturbance. We study a two band s-wave superconductor with hybridization, based on an attractive Hubbard model. We consider the system under the action of a fictitious field, time and wave vector dependent, which couples to the superconducting order parameter. We calculate the zero order propagators in the field, using the conventional equation of motion method, and the first order ones, using the generalized equation of motion. The response to the field is given by a generalized susceptibility, which in the one-band case reduces to the one obtained by Thouless. We associate the emergence of superconductivity with the divergence of the static part of the generalized susceptibility. The advantage of this method is its simplicity, because we only deal with single-particle propagators. We analyze this superconducting susceptibility, which allows us to find a critical hybridization above which there is no superconducting phase, determine the critical and the crossover lines and determine the dynamical critical exponent z for this system. Therefore we can predict the behavior of some quantities measured experimentally at low temperatures close to the superconducting quantum critical point.
The past decade has seen a substantial rejuvenation of interest in the study of quantum phase transitions, driven by experiments on cuprate superconductors, heavy fermion materials, organic conductors, and related compounds. Although quantum phase transitions in simple spin systems, like the Ising model in a transverse field, were studied in the early 1970s, much of the subsequent theoretical work examined a particular example: the metal–insulator transition. While this is a subject of considerable experimental importance, the greatest theoretical progress was made for the case of the Anderson transition of non-interacting electrons, which is driven by localization of the electronic states in the presence of a random potential. The critical properties of this transition of noninteracting electrons constituted the primary basis upon which most condensed matter physicists have formed their intuition on the behavior of the systems near a quantum phase transition. However, it is clear that strong electronic interactions play a crucial role in the systems of current interest noted earlier, and simple paradigms for the behavior of such systems near quantum critical points are not widely known. It is the purpose of this book to move interactions to center stage by describing and classifying the physical properties of the simplest interacting systems undergoing a quantum phase transition. The effects of disorder will be neglected for the most part but will be considered in the concluding chapters. Our focus will be on the dynamical properties of such systems at nonzero temperature, and it will become apparent that these differ substantially from the noninteracting case.
In fermionic systems with different types of quasi-particles, attractive interactions can give rise to exotic superconducting states, such as pair density wave (PDW) superconductivity and breached pairing. In recent years the search for these new types of ground states in cold atoms and in metallic systems has been intense. In the case of metals the different quasi-particles may be the up and down spin bands in an external magnetic field or bands arising from distinct atomic orbitals that coexist at a common Fermi surface. These systems present a complex phase diagram as a function of the difference between the Fermi wavevectors of the different bands. This can be controlled by external means, varying the density in the two-component cold atom system or, in a metal, by applying an external magnetic field or pressure. Here we study the zero temperature instability of the normal system as the Fermi wavevector mismatch of the quasi-particles (bands) is reduced and find a second order quantum phase transition to a PDW superconducting state. From the nature of the quantum critical fluctuations close to the superconducting quantum critical point (SQCP), we obtain its dynamic critical exponent. It turns out to be z = 2 and this allows us to fully characterize the SQCP for dimensions d ≥ 2.
The discovery of high-temperature superconductors has raises questions that extend beyond the scope of quasiparticles, a foundational concept in condensed matter theory. This dissertation explores new theoretical approaches to quantum matter without quasiparticle excitations, with a particular focus on quantum criticality and the associated superconductivity in correlated electron compounds. The soluble Sachdev-Ye-Kitaev (SYK) model has recently emerged as a fascinating platform to address the unusual metallic states with T-linear resistivity. We first consider differ- ent variants of random Hubbard models, which share many similarities to key aspects of the original SYK model. Using a large M analysis and a renormalization group method, we propose the existence of quantum critical points with fractionalized excitations separating two distinct phases, which provides insights into the quantum phase transitions and non-Fermi liquid behaviors observed in cuprate superconductors. In the second part of this dissertation, we examine the interplay between non-Fermi liquids and superconductivity with two different pairing mechanisms. Under the framework of random Hubbard model, we demonstrate that superconductivity emerging from non-Fermi liquids strongly deviates from the BCS theory by tuning the relative strength of hopping and exchange interactions. Furthermore, we investigate a two-dimensional Yukawa-SYK model with spatially randomn interactions coupling a Fermi surface to a scalar field associated with a quantum phase transition. Our theory agrees well with transport properties analysed in cuprates, such as a T-linear resistivity and Planckian dissipation.
Introduction The quantum phase transitions considered so far in this book are mostly continuous, second order. They are associated with the divergence of a correlation length and of a characteristic time that renders the quantum critical point scale invariant. However, there are many important phase transitions at which the order parameter goes abruptly to zero and, more important, at which the characteristics of length and critical time do not diverge. In general there is also a latent heat , or work required, to transform one phase into another. In this and the next chapter we study these discontinuous quantum phase transitions. We proceed by considering initially some important cases of what is known as fluctuation induced quantum phase transitions to next treat a more general case of a first-order quantum phase transition. We will show through the study of these problems that the concepts of critical exponents and scaling remain useful, even though these systems do not exhibit scale invariance at their critical point. In Chapter 15 we present the scaling theory of first-order quantum phase transitions and use its results to treat some general problems. One of the most interesting cases of fluctuation-induced transitions occurs in superconductors due to the coupling of the charged carriers to the electromagnetic field. We consider initially a wider class of systems with macroscopic wave functions, the superfluids, of which superconductors are the charged version. We adopt a macroscopic approach to this problem and describe the superfluid by a complex order parameter φ , such that | φ | 2 is proportional to the density of condensed particles. The zero temperature phase diagram is expressed in terms of a control parameter, m 2 , such that, at m 2 = 0, the system presents a quantum phase transition from a superfluid state, for m 2 < 0, φ ≠ 0, to a normal state for m 2 > 0 where φ = 0. In the case of the superconductor with particles of charge q = 2 e , we will include the coupling of these particles to the electromagnetic field and study its effect in the phase diagram of these systems. We show that in the neutral superfluid, the zero temperature transition to the normal state is continuous and occurs at a quantum critical point.
In this thesis a systematic, functional matrix field theory is developed to describe both clean and disordered s-wave and d-wave superconductors and the quantum phase transitions associated with them. The thesis can be divided into three parts. The first part includes chapters 1 to 3. In chapter one a general physical introduction is given. In chapters two and three the theory is developed and used to compute the equation of state as well as the number-density susceptibility, spin-density susceptibility, the sound attenuation coefficient, and the electrical conductivity in both clean and disordered s-wave superconductors. The second part includes chapter four. In this chapter we use the theory to describe the disorder-induced metal - superconductor quantum phase transition. The key physical idea here is that in addition to the superconducting order-parameter fluctuations, there are also additional soft fermionic fluctuations that are important at the transition. We develop a local field theory for the coupled fields describing superconducting and soft fermionic fluctuations. Using simple renormalization group and scaling ideas, we exactly determine the critical behavior at this quantum phase transition. Our theory justifies previous approaches. The third part includes chapter five. In this chapter we study the analogous quantum phase transition in disordered d-wave superconductors. This theory should be related to high TcT_cTc​ superconductors. Surprisingly, we show that in both the underdoped and overdoped regions, the coupling of superconducting fluctuations to the soft disordered fermionic fluctuations is much weaker than that in the s-wave case. The net result is that the disordered quantum phase transition in this case is a strong coupling, or described by an infinite disordered fixed point, transition and cannot be described by the perturbative RG description that works so well in the s-wave case. The transition appears to be related to the one that occurs in disordered quantum antiferromagnets.
The study of superconductivity in correlated systems is an exciting area of condensed matter physics. In this paper we consider superconducting ground states in systems described by two-band models with different effective masses. These two bands are coupled through an effective hybridization that can be directly tuned by pressure. We consider the cases of s-wave superconductivity associated with the electrons in a narrow band and also with inter-band pairing. To study the system in the strong coupling regime we introduce the s-wave scattering length a(s), and obtain the superconducting order parameters and the chemical potential as functions of the interaction strength 1/k(F)a(s) along the BCS-BEC crossover at T = 0. Finally, we discuss the phase diagram of this model as a function of external pressure and how our results can be applied for two-band systems as Fe pnictides or heavy fermions. The main result of this study is the occurrence of a superconducting quantum critical point (SQCP) in this two-band model.