arXiv subjects

E. C. Marino

Publications and source records attributed to E. C. Marino.

At least 19 recordsLinked to original sources

arXiv2026

Theory of High-Tc Superconductivity in Cuprates

The essential physical processes underlying the phenomenon of High-Tc superconductivity in cuprates occur in the $CuO_2$ planes, found in these materials. The dynamics of the active electrons belonging to such planes is well described by the Three Bands Hubbard Model (3BHM). The complexity of such model, however, led the researchers to look for simpler and yet relevant alternatives. In the attempts to circumvent the complexity of this model,two main simplified versions of the (3BHM) were considered. In the first alternative, one eliminates the doped holes and their respective sub-lattices by tying them to the $Cu^{++}$ electrons, thereby forming the so called Zhang-Rice singlets. The remaining dynamics consists in doping a Mott-Hubbard insulator and is described by the t-J Model. The second alternative maintains that the $Cu^{++}$ electrons form a square lattice of localized spins, while the doped holes move along the oxygen sub-lattices and undergo a Kondo like magnetic interaction with the localized spins, besides the Hubbard-like electric repulsion. This scenario is described by the Spin-Fermion-Hubbard Model. Most of the researchers in the field chose to follow the first road, while, I chose the second one. In this article I review in detail the reasons why that choice has led to a successful theory for High-Tc superconductivity in hole doped cuprates.

cond-mat.supr-con↗

arXiv2025

Critical Behavior and Duality in Dimensionally Reduced Planar Chern-Simons Superconductors

Tha quantum electrodynamics of particles constrained to move on a plane is not a fully dimensionally reduced theory because the gauge fields through which they interact live in higher dimensions. By constraining the gauge field to the surface of the bulk, we obtain a fully reduced planar Abelian Chern-Simons Higgs model that can describe the vortex dynamics and second-order superconducting-normal phase transitions in planar Chern-Simons superconductors. Dual analyses performed before and after dimensional reduction yield the same Lagrangian for describing the vortex dynamics, indicating the self-consistency of our reduced theory. Compared to ordinary (2+1)-dimensional electrodynamics, we obtain anomalous fermion statistical vortices, consistent with results considering boundary effects. An additional electric charge constraint and different Chern-Simons parameter constraints are also found, which may help define a self-dual conformal field theory. Our renormalization group analysis shows that the quantized critical exponent depends on the Chern-Simons parameter. Quench disorder can bring more stable fixed points with different dynamical critical exponents. If we dimensionally reduce to a curved surface, our theory can also be extended to curved spacetimes, where geometric flow will be introduced and compete with vortex flow.

cond-mat.supr-con↗

arXiv2022

Non-Hermitian quantum gases: a platform for imaginary time crystals

One of the most important applications of quantum mechanics is the thermodynamic description of quantum gases. Despite the fundamental importance of this topic, a comprehensive description of the thermodynamic properties of non-Hermitian quantum gases is still lacking. Here, we investigate the properties of bosonic and fermionic non-Hermitian systems at finite temperatures. We show that non-Hermitian systems exihibit oscillations both in temperature and imaginary time. As such, they can be a possible platform to realize an imaginary time crystal (iTC) phase. The Hatano-Nelson model is identified as a simple lattice model to reveal this effect. In addition, we show that the conditions for the iTC to be manifest are the same as the conditions for the presence of disorder points, where the correlation functions show oscillating behavior. This analysis makes clear that our realization of iTC is effectively a way to filter one specific Matsubara mode. In this realization, the Matsubara frequency, that enters as a mathematical tool to compute correlation functions for finite temperatures, can be measured experimentally.

cond-mat.quant-gas↗

arXiv2021

Orbital Order, Superconductivity, Pseudogap and Spectral Weight in High-Tc Cuprates

After providing a brief genealogy of our recently proposed model for High-Tc cuprates, we investigate the details of the microscopic mechanism that produces an attractive interaction between neighboring holes. We show that a peculiar arrangement of the $p_x$ and $p_y$ oxygen orbitals makes the mutual magnetic interaction of the holes with the localized copper ions to produce a net attractive interaction between themselves, which is responsible for the emergence of a superconducting phase. We also study the connection existing between the proposed pseudogap order parameter and the spectral density. We show that the occurrence of two sharp peaks in the latter, between which the density of states suffers a depletion is a direct consequence of the d-wave character of the pseudogap order parameter dependence on $\mathbf{k}$, which breaks the 90$^\circ$-rotation symmetry of the oxygen lattices. The peak separation in the spectral density works effectively as an overall pseudogap order parameter for the cuprates. We explicitly calculate the spectral density in the strange metal and pseudogap phases of Bi2212, at different temperatures, and show that our results compare very well with the experimental data.

cond-mat.supr-con↗

arXiv2021

Magnetic Field Effects on the Transport Properties of High-Tc Cuprates

Starting from a recently proposed comprehensive theory for the high-Tc superconductivity in cuprates, we derive a general analytic expression for the planar resistivity, in the presence of an applied external magnetic field $\textbf{H}$ and explore its consequences in the different phases of these materials. As an initial probe of our result, we show it compares very well with experimental data for the resistivity of LSCO at different values of the applied field. We also apply our result to Bi2201 and show that the magnetoresistivity in the strange metal phase of this material, exhibits the $H^2$ to $H$ crossover, as we move from the weak to the strong field regime. Yet, despite of that, the magnetoresistivity does not present a quadrature scaling. Remarkably, the resistivity H-field derivative does scale as a function of $\frac{H}{T}$, in complete agreement with recent magneto-transport measurements made in the strange metal phase of cuprates \cite{Hussey2020}. We, finally, address the issue of the $T$-power-law dependence of the resistivity of overdoped cuprates and compare our results with experimental data for Tl2201. We show that this provides a simple method to determine whether the quantum critical point associated to the pseudogap temperature $T^*(x)$ belongs to the SC dome or not.

cond-mat.supr-con↗

arXiv2020

Effects of a Magnetic Field on Superconductivity and Quantum Criticality in Quasi-Two-Dimensional Systems with Dirac Electrons

We study the effects of an external magnetic field on thensuperconducting phase diagram of a quasi-two-dimensional system of Dirac electrons at an arbitrary temperature. At zero temperature, there is a quantum phase transition connecting a normal and a superconducting phase, occurring at a critical line that corresponds to a magnetic field dependent critical coupling parameter, which should be observed in planar materials containing Dirac electrons, such as $Cu_xTiSe_2$. Moreover, the superconducting gap is obtained as a function of temperature, magnetic field and coupling parameter ($λ_{\rm R}$). From this, we extract the critical magnetic field $ B_{ c } $ as a function of the temperature. For small values of $ B_{ c } $, we obtain a linear decay of the critical field, which is similar to the behavior observed experimentally in the copper doped dichalcogenide $Cu_xTiSe_2$ and also in intercalated graphite.

cond-mat.supr-con↗

arXiv2020

Competing effective interactions of Dirac electrons in the Spin-Fermion system

Recently discovered advanced materials, such as heavy fermions, frequently exhibit a rich phase diagram suggesting the presence of different competing interactions. A unified description of the origin of these multiple interactions, albeit very important for the comprehension of such materials is, in general not available. It would be therefore very useful to have a simple model where the common source of different interactions could be possibly traced back. In this work we consider a system consisting in a set of localized spins on a square lattice with antiferromagnetic nearest neighbors interactions and itinerant electrons, which are assumed to be Dirac-like and interact with the localized spins through a Kondo magnetic interaction. This system is conveniently described by the Spin-Fermion model, which we use in order to determine the effective interactions among the itinerant electrons. By integrating out the localized degrees of freedom we obtain a set of different interactions, which includes: a BCS-like superconducting term, a Nambu-Jona-Lasinio-like, excitonic term and a spin-spin magnetic term. The resulting phase diagram is investigated by evaluation of the mean-field free-energy as a function of the relevant order parameters. This shows the competition of the above interactions, depending on the temperature, chemical potential and coupling constants.

cond-mat.str-el↗

arXiv2020

A quantum critical superconducting phase transition in quasi-two-dimensional systems with Dirac electrons

We present a theory describing the superconducting (SC) interaction of Dirac electrons in a quasi-two-dimensional system consisting of a stack of N planes. The occurrence of a SC phase is investigated both at T = 0 and T 5 0. At T = 0, we find a quantum phase transition connecting the normal and SC phases. Our theory qualitatively reproduces the SC phase transition occurring in the underdoped regime of the high-Tc cuprates. This fact points to the possible relevance of Dirac electrons in the mechanism of high-Tc superconductivity.

cond-mat.str-el↗

arXiv2020

Antiferromagnetic phase diagram of the cuprate superconductors

Taking the spin-fermion model as the starting point for describing the cuprate superconductors, we obtain an effective nonlinear sigma-field hamiltonian, which takes into account the effect of doping in the system. We obtain an expression for the spin-wave velocity as a function of the chemical potential. For appropriate values of the parameters we determine the antiferromagnetic phase diagram for the YBa$_2$Cu$_3$O$_{6+x}$ compound as a function of the dopant concentration in good agreement with the experimental data. Furthermore, our approach provides a unified description for the phase diagrams of the hole-doped and the electron doped compounds, which is consistent with the remarkable similarity between the phase diagrams of these compounds, since we have obtained the suppression of the antiferromagnetic phase as the modulus of the chemical potential increases. The aforementioned result then follows by considering positive values of the chemical potential related to the addition of holes to the system, while negative values correspond to the addition of electrons.

cond-mat.supr-con↗

arXiv2020

Temperature vs. doping phase diagram of cuprate superconductors

Starting from a spin-fermion model for the cuprate superconductors, we obtain an effective interaction for the charge carriers by integrating out the spin degrees of freedom. Our model predicts a quantum critical point for the superconducting interaction coupling, which sets up a threshold for the onset of superconductivity in the system. We show that the physical value of this coupling is below this threshold, thus explaining why there is no superconducting phase for the undoped system. Then, by including doping, we find a dome-shaped dependence of the critical temperature as charge carriers are added to the system, in agreement with the experimental phase diagram. The superconducting critical temperature is calculated without adjusting any free parameter and yields, at optimal doping $ T_c \sim $ 45 K, which is comparable to the experimental data.

cond-mat.supr-con↗

arXiv2020

The Resistivity of High-Tc Cuprates

We show that the resistivity in each phase of the High-Tc cuprates is a special case of a general expression derived from the Kubo formula. We obtain, in particular, the T-linear behavior in the strange metal (SM) and upper pseudogap (PG) phases, the pure $T^2$, Fermi liquid (FL) behavior observed in the strongly overdoped regime as well as the $T^{1+δ}$ behavior that interpolates both in the crossover. We calculate the coefficients: a) of $T$ in the linear regime and show that it is proportional to the PG temperature $T^*(x)$; b) of the $T^2$-term in the FL regime, without adjusting any parameter; and c) of the $T^{1.6}$ term in the crossover regime, all in excellent agreement with the experimental data. From our model, we are able to infer that the resistivity in cuprates is caused by the scattering of holes by excitons, which naturally form as holes are doped into the electron background.

cond-mat.supr-con↗

arXiv2020

Projected Proca Field Theory: a One-Loop Study

The recent discovery of two-dimensional Dirac materials, such as graphene and transition-metaldichalcogenides, has raised questions about the treatment of hybrid systems, in which electrons moving in a two-dimensional plane interact via virtual photons from the three-dimensional space. In this case, a projected non-local theory, known as Pseudo-QED, or reduced QED, has shown to provide a correct framework for describing the interactions displayed by these systems. In a related situation, in planar materials exhibiting a superconducting phase, the electromagnetic field has a typical exponential decay that is interpreted as the photons having an effective mass, as a consequence of the Anderson-Higgs mechanism. Here, we use an analogous projection to that used to obtain the pseudo-QED to derive a Pseudo-Proca equivalent model. In terms of this model, we unveil the main effects of attributing a mass to the photons and to the quasi-relativistic electrons. The one-loop radiative corrections to the electron mass, to the photon and to the electron-photon vertex are computed. We calculate the quantum corrections to the electron g-factor and show that it smoothly goes to zero in the limit when the photon mass is much larger than the electron mass. In addition, we correct the results obtained for graphene within Pseudo-QED in the limit when the photon mass vanishes.

hep-th↗

arXiv2020

Renormalization of the band gap in 2D materials through the competition between electromagnetic and four-fermion interactions

Recently the renormalization of the band gap $m$, in both WSe$_2$ and MoS$_2$, has been experimentally measured as a function of the carrier concentration $n$. The main result establishes a decreasing of hundreds of meV, in comparison with the bare band gap, as the carrier concentration increases. These materials are known as transition metal dichalcogenides and their low-energy excitations are, approximately, described by the massive Dirac equation. Using Pseudo Quantum Electrodynamics (PQED) to describe the electromagnetic interaction between these quasiparticles and from renormalization group analysis, we obtain that the renormalized mass describes the band gap renormalization with a function given by $m(n)/m_0=(n/n_0)^{C_λ/2}$, where $m_0=m(n_0)$ and $C_λ$ is a function of the coupling constant $λ$. We compare our theoretical results with the experimental findings for WSe$_2$ and MoS$_2$, and we conclude that our approach is in agreement with these experimental results for reasonable values of $λ$. In addition we introduced a Gross-Neveu (GN) interaction which could simulate an disorder/impurity-like microscopic interaction. In this case, we show that there exists a critical coupling constant, namely, $λ_c \approx 0,66$ in which the beta function of the mass vanishes, providing a stable fixed point in the ultraviolet limit. For $λ>λ_c$, the renormalized mass decreases while for $λ<λ_c$ it increases with the carrier concentration.

hep-th↗

arXiv2020

Superconducting and Pseudogap Transition Temperatures in High-Tc Cuprates and the $T_{c}$ Dependence on Pressure

We derive analytic expressions for the critical temperatures of the superconducting (SC) and pseudogap (PG) transitions of the high-Tc cuprates as a function of doping. These are in excellent agreement with the experimental data both for single-layered materials such as LSCO, Bi2201 and Hg1201 and multi-layered ones, such as Bi2212, Bi2223, Hg1212 and Hg1223. Optimal doping occurs when the chemical potential vanishes, thus leading to an universal expression for the optimal SC transition temperatures. This allows for the obtainment of a quantitative description of the growth of such temperatures with the number of layers, N, which accurately applies to the $Bi$, $Hg$ and $Tl$ families of cuprates. We study the pressure dependence of the SC transition temperatures, obtaining excellent agreement with the experimental data for different materials and dopings. These results are obtained from an effective Hamiltonian for the itinerant oxygen holes, which includes both the electric repulsion between them and their magnetic interactions with the localized copper ions. We show that the former interaction is responsible for the SC and the latter, for the PG phases, the phase diagram of cuprates resulting from the competition of both. The Hamiltonian is defined on a bipartite oxygen lattice, which results from the fact that only the $p_x$ and $p_y$ oxygen orbitals alternatively hybridize with the $3d$ copper orbitals. From this, we can provide an unified explanation for the $d_{x^2-y^2}$ symmetry of both the SC and PG order parameters and obtain the Fermi pockets observed in ARPES experiments.

cond-mat.supr-con↗

arXiv2019

Bosonic interactions in a nonlocal theory in (2+1) dimensions

Pseudo-Quantum Electrodynamics (PQED) provides an excellent description of the interaction between charged particles confined to a plane. When we couple pseudo-gauge field with a bosonic matter field, we obtain the so-called Scalar Pseudo-Quantum Electrodynamics (SPQED). In this work, we make a perturbative analysis of SPQED via Feynman diagrams. We compute the one loop Green functions: bosonic field self-energy, electromagnetic field self-energy, and vertex corrections. Finally, we consider the non-relativistic interaction potential between two bosonic particles. We compute the radiative corrections to the usual Coulomb potential and comment on the analogies and the differences with the fermionic case.

hep-th↗

arXiv2019

Bounded particle interactions driven by a nonlocal dual Chern-Simons model

Quantum electrodynamics (QED) of electrons confined in a plane and that yet can undergo interactions mediated by an unconstrained photon has been described by the so-called {\it pseudo-QED} (PQED), the (2+1)-dimensional version of the equivalent dimensionally reduced original QED. In this work, we show that PQED with a nonlocal Chern-Simons term is dual to the Chern-Simons Higgs model at the quantum level. We apply the path-integral formalism in the dualization of the Chern-Simons Higgs model to first describe the interaction between quantum vortex particle excitations in the dual model. This interaction is explicitly shown to be in the form of a Bessel-like type of potential in the static limit. This result {\it per se} opens exciting possibilities for investigating topological states of matter generated by interactions, since the main difference between our new model and the PQED is the presence of a nonlocal Chern-Simons action. Indeed, the dual transformation yields an unexpected square root of the d'Alembertian operator, namely, $(\sqrt{-\Box})^{-1}$ multiplied by the well-known Chern-Simons action. Despite the nonlocality, the resulting model is still gauge invariant and preserves the unitarity, as we explicitly prove. {}Finally, when coupling the resulting model to Dirac fermions, we then show that pairs of bounded electrons are expected to appear, with a typical distance between the particles being inversely proportional to the topologically generated mass for the gauge field in the dual model.

hep-th↗

arXiv2019

The Superconducting and Pseudogap Phase Diagram of High-Tc Cuprates

We derive analytic expressions for the critical temperatures of the superconducting (SC) and pseudogap (PG) phases of the high-Tc cuprates, which are in excellent agreement with the experimental data for single-layered materials such as LSCO, Bi2201 and Hg1201. Our effective Hamiltonian, defined in the oxygen square sub-lattices formed by the alternate hybridization of $p_x$ and $p_y$ orbitals with the $3d$ copper orbitals, provides an unified explanation for the $d_{x^2-y^2}$ symmetry of both the SC and PG order parameters. Attractive and repulsive interactions involve holes of the two different sublattices and can be derived from the spin-fermion model. Optimal doping occurs when the chemical potential vanishes. For $N$-layered cuprates, the growth of the optimal temperature with $N$, as well as the trend of the SC and AF domes to superimpose, can be simply understood. Our results for the optimal SC transition temperature are in excellent agreement with the experiments for $N=2$ materials of the $Bi$ and $Hg$ families. For $N=3$ the agreement is still satisfactory, while for $N>3$, it becomes poor. The explanation for these facts allows us to suggest a method for increasing the critical SC temperature in cuprates.

cond-mat.supr-con↗

arXiv2018

Quantum-electrodynamical approach to the exciton spectrum in Transition-Metal Dichalcogenides

Manipulation of intrinsic electron degrees of freedom, such as charge and spin, gives rise to electronics and spintronics, respectively. Electrons in monolayer materials with a honeycomb lattice structure, such as the Transition-Metal Dichalcogenides (TMD's), can be distinguished according to the region (valley) of the Brillouin zone to which they belong. Valleytronics, the manipulation of this electron's property, is expected to set up a new era in the realm of electronic devices. In this work, we accurately determine the energy spectrum and lifetimes of exciton (electron-hole) bound-states for different TMD materials, namely WSe$_2$, WS$_2$ and MoS$_2$. For all of them, we obtain a splitting of the order of 170 meV between the exciton energies from different valleys, corresponding to an effective Zeeman magnetic field of 1400 T. Our approach, which employs quantum-field theory (QFT) techniques based on the Bethe-Salpeter equation and the Schwinger-Dyson formalism, takes into account the full electromagnetic interaction among the electrons. The valley selection mechanism operates through the dynamical breakdown of the time-reversal (TR) symmetry, which originally interconnects the two valleys. This symmetry is spontaneously broken whenever the full electromagnetic interaction vertex is used to probe the response of the system to an external field.

cond-mat.str-el↗