Heron Caldas | UFSJ - Federal University of São João Del-Rei (original) (raw)

Papers by Heron Caldas

The study of multi-band superconductivity is relevant for a variety of systems, from ultra cold a... more The study of multi-band superconductivity is relevant for a variety of systems, from ultra cold atoms with population imbalance to particle physics, and condensed matter. As a consequence, this problem has been widely investigated bringing to light many new and interesting phenomena. In this work we point out and explore a correspondence between a two-band metal with a kkk-dependent hybridization and a uniformly polarized fermionic system in the presence of spin-orbit coupling (SOC). We study the ground state phase diagram of the metal in the presence of an attractive interaction. We find remarkable superconducting properties whenever hybridization mixes orbitals of different parities in neighboring sites. We show that this mechanism enhances superconductivity and drives the crossover from weak to strong coupling in analogy with SOC in cold atoms. We obtain the quantum phase transitions between the normal and superfluid states, as the intensity of different parameters characterizing the metal are varied, including Lifshitz transitions, with no symmetry breaking, associated with the appearance of soft modes in the Fermi surface.

We study the chiral fermion meson model which is the well known linear sigma model of Gell-Mann-a... more We study the chiral fermion meson model which is the well known linear sigma model of Gell-Mann-and-Levy at finite temperature.A modified self-consistent resummation (MSCR) which resums higher order terms in the perturbative expansion is proposed. It is shown that with the MSCR the problem of tachyonic masses is solved, the renormalization of the gap equations is carried out and the Goldstone's theorem is verified. We also apply the method to investigate another known case at high temperature and compare with results found in the literature.

Journal of Statistical Mechanics: Theory and Experiment, 2014

Journal of Physics B: Atomic, Molecular and Optical Physics, 2015

Annals of Physics, 2014

The search for Majorana fermions has been concentrated in topological insulators or superconducto... more The search for Majorana fermions has been concentrated in topological insulators or superconductors. In general, the existence of these modes requires the presence of spin-orbit interactions and of an external magnetic field. The former implies in having systems with broken inversion symmetry, while the latter breaks time reversal invariance. In a recent paper, we have shown that a two-band metal with an attractive inter-band interaction has nontrivial superconducting properties, if the k-dependent hybridization is anti-symmetric in the wave-vector. This is the case, if the crystalline potential mixes states with different parities as for orbitals with angular momentum l and l + 1. In this paper we take into account the effect of an external magnetic field, not considered in the previous investigation, in a two-band metal and show how it modifies the topological properties of its superconducting state. We also discuss the conditions for the appearance of Majorana fermions in this system.

Physical Review B, 2012

In multi-band systems, electrons from different orbitals coexist at the Fermi surface. An attract... more In multi-band systems, electrons from different orbitals coexist at the Fermi surface. An attractive interaction among these quasi-particles gives rise to inter-band or hybrid pairs which eventually condense in a superconducting state. These quasi-particles have a natural mismatch of their Fermi wave-vectors, δkF , which depends on the strength of the hybridization between their orbitals. The existence of this natural scale suggests the possibility of inhomogeneous superconducting ground states in these systems, even in the absence of an applied magnetic field. Furthermore, since hybridization V depends on pressure, this provides an external parameter to control the wave-vectors mismatch at the Fermi surface. In this work, we study the phase diagram of a two-dimensional, twoband metal with inter-band pairing. We show that as the mismatch between the Fermi wave-vectors of the two hybrid bands is reduced, the system presents a normal-to-inhomogeneous superconductor quantum phase transition at a critical value of the hybridization Vc = ∆0. The superconducting ground state for V < Vc is characterized by a wave-vector with magnitude |qc| = qc = 2∆0/v f . Here ∆0 is the superconducting gap in the homogeneous state andv f the average Fermi velocity. We discuss the nature of the quantum critical point (QCP) at Vc and obtain the associated quantum critical exponents.

ABSTRACT The obtaining of bound states of heavy and light quarks interacting via a static quark p... more ABSTRACT The obtaining of bound states of heavy and light quarks interacting via a static quark potential is revisited here. We present an approach that both approximate the relativistic wave equation and allows the obtaining of analytical solutions and binding energies (and consequently, the heavy mesons spectra) of the system.

Physics Letters A, 2014

We study a two-band model of fermions in a 1d chain with an antisymmetric hybridization that brea... more We study a two-band model of fermions in a 1d chain with an antisymmetric hybridization that breaks inversion symmetry. We find that for certain values of its parameters, the sp-chain maps formally into a p-wave superconducting chain, the archetypical 1d system exhibiting Majorana fermions. The eigenspectra, including the existence of zero energy modes in the topological phase, agree for both models. The end states too share several similarities in both models, such as the behavior of the localization length, the non-trivial topological index and robustness to disorder. However, we show by mapping the s-and p-fermions to two copies of Majoranas, that the excitations in the ends of a finite sp chain are indeed conventional fermions though endowed with protected topological properties. Our results are obtained by a scattering approach in a semi-infinite chain with an edge defect treated within the T -matrix approximation. We augment the analytical results with exact numerical diagonalization that allow us to extend our results to arbitrary parameters and also to disordered systems.

Physics Letters B, 2001

Feynman's functional formulation of statistical mechanics is used to study the renormalizability ... more Feynman's functional formulation of statistical mechanics is used to study the renormalizability of the well known Linear Chiral Sigma Model in the presence of fermionic fields at finite temperature in an alternative way. It is shown that the renormalization conditions coincide with those of the zero temperature model.

Physics Letters A, 2014

We present in this work an exact renormalization group (RG) treatment of a one-dimensional p-wave... more We present in this work an exact renormalization group (RG) treatment of a one-dimensional p-wave superconductor. The model proposed by Kitaev consists of a chain of spinless fermions with a p-wave gap. It is a paradigmatic model of great actual interest since it presents a weak pairing superconducting phase that has Majorana fermions at the ends of the chain. Those are predicted to be useful for quantum computation. The RG allows to obtain the phase diagram of the model and to study the quantum phase transition from the weak to the strong pairing phase. It yields the attractors of these phases and the critical exponents of the weak to strong pairing transition. We show that the weak pairing phase of the model is governed by a chaotic attractor being non-trivial from both its topological and RG properties. In the strong pairing phase the RG flow is towards a conventional strong coupling fixed point. Finally, we propose an alternative way for obtaining p-wave superconductivity in a one-dimensional system without spin-orbit interaction.

Physical Review Letters, 2000

We calculate the effects of induced interactions on the transition temperature to the BCS state i... more We calculate the effects of induced interactions on the transition temperature to the BCS state in dilute Fermi gases. For a pure Fermi system with two species having equal densities, the transition temperature is suppressed by a factor (4e)(1/3) approximately 2.2, and for nu fermion species, the transition temperature is increased by a factor (4e)(nu/3-1) approximately 2.2(nu-3). For mixtures of fermions and bosons the exchange of boson density fluctuations gives rise to an attractive interaction, and we estimate the increase of the transition temperature due to this effect.

Physical Review D, 2002

In this paper we use Modified Self-Consistent Resummation (MSCR) in order to obtain the scalar dr... more In this paper we use Modified Self-Consistent Resummation (MSCR) in order to obtain the scalar dressed mass by evaluating the self-energy up to two loops in the neutral scalar λφ 4 model at finite temperature. With this laboratory model we show that, if a theory is renormalizable at zero temperature, by using MSCR it is always possible to obtain a finite corrected mass at finite temperature. This feature of MSCR is not observed in some other approximation techniques usually found in the literature.

Physical Review D, 2001

We study the chiral fermion meson model which is the well known linear sigma model of Gell-Mann-a... more We study the chiral fermion meson model which is the well known linear sigma model of Gell-Mann-and-Levy at finite temperature. A modified self-consistent resummation (MSCR) which resums higher order terms in the perturbative expansion is proposed. It is shown that with the MSCR the problem of tachyonic masses is solved, the renormalization of the gap equations is carried out and the Goldstone's theorem is verified. We also apply the method to investigate another known case at high temperature and compare with results found in the literature.

Physical Review D, 2003

We investigate the analytic properties of finite-temperature self-energies of bosons interacting ... more We investigate the analytic properties of finite-temperature self-energies of bosons interacting with fermions at one-loop order. A simple boson-fermion model was chosen due to its interesting features of having two distinct couplings of bosons with fermions. This leads to a quite different analytic behavior of the bosons self-energies as the external momentum K µ = (k 0 , k) approaches zero in the two possible limits. It is shown that the plasmon and Debye masses are consistently obtained at the pole of the corrected propagator even when the self-energy is analytic at the origin in the frequency-momentum space.

Physical Review D, 2002

We reinvestigate the interesting phenomenon of symmetry nonrestoration at high temperature in the... more We reinvestigate the interesting phenomenon of symmetry nonrestoration at high temperature in the multifield O(N 1 )XO(N 2 ) model. We apply modified self-consistent resummation (MSCR) in order to obtain the scalar dressed masses and find in what circumstances a resummed multifield theory which has symmetry (non)restoration can be renormalized. It is shown that, aside from the consistency of the MSCR method, the basic ingredient that guarantees the renormalization of a multifield model within a resummation approach is the T 2 mass behavior of field theory at high temperature.

Physical Review A, 2012

We investigate the superfluid transition temperature of quasi-two-dimensional imbalanced Fermi ga... more We investigate the superfluid transition temperature of quasi-two-dimensional imbalanced Fermi gases beyond the mean-field approximation, through the second-order (or induced) interaction effects. For a balanced Fermi system the transition temperature is suppressed by a factor ≈2.72. For imbalanced Fermi systems, the polarization and transition temperature of the tricritical point are significantly reduced as the two-body binding energy | B | increases.

Nuclear Physics B, 2002

We reinvestigate the interaction of massless fermions with massless bosons at finite temperature.... more We reinvestigate the interaction of massless fermions with massless bosons at finite temperature. Specifically, we calculate the self-energy of massless fermions due the interaction with massless bosons at high temperature, which is the region where thermal effects are maximal. The calculations are concentrated in the limit of vanishing fermion three momentum and after considering the effective fermion and boson dressed masses, we obtain the damping rate of the fermion up to order g 3 . It is shown that in the limit k 0 T the fermion acquire a thermal mass of order gT and the leading term of the fermion damping rate is of order g 2 T + g 3 T . 

Nuclear Physics A, 1997

Sophisticated calculations of the dynamics of relativistic heavy-ion collisions often need as inp... more Sophisticated calculations of the dynamics of relativistic heavy-ion collisions often need as input properties of light mesons in medium. In this context simple analytical expressions for these quantities which respect chiral symmetry and low-energy current algebra results are most desirable. In the present work we provide such simple expressions based on a bosonized version of the microscopic NJL model. We also study the pion lifetime in hot and dense matter showing ~-(,rr -~tz-+~ ) that the ratio ~(___,~_+~) changes by a factor about three and thus carries a clear signature of the chiral phase transition. @ 1997 Elsevier Science B.V.

Modern Physics Letters A, 1997

We re-investigate the problem of the renormalizability of the chiral fermion meson model on the l... more We re-investigate the problem of the renormalizability of the chiral fermion meson model on the light of the regularization-independent algebraic method. The present letter is intended as a useful application of a modern technique in theory of current interest for the description of low energy hadron phenomenology. We show that the model is stable under radiative corrections and anomaly free

The study of multi-band superconductivity is relevant for a variety of systems, from ultra cold a... more The study of multi-band superconductivity is relevant for a variety of systems, from ultra cold atoms with population imbalance to particle physics, and condensed matter. As a consequence, this problem has been widely investigated bringing to light many new and interesting phenomena. In this work we point out and explore a correspondence between a two-band metal with a kkk-dependent hybridization and a uniformly polarized fermionic system in the presence of spin-orbit coupling (SOC). We study the ground state phase diagram of the metal in the presence of an attractive interaction. We find remarkable superconducting properties whenever hybridization mixes orbitals of different parities in neighboring sites. We show that this mechanism enhances superconductivity and drives the crossover from weak to strong coupling in analogy with SOC in cold atoms. We obtain the quantum phase transitions between the normal and superfluid states, as the intensity of different parameters characterizing the metal are varied, including Lifshitz transitions, with no symmetry breaking, associated with the appearance of soft modes in the Fermi surface.

We study the chiral fermion meson model which is the well known linear sigma model of Gell-Mann-a... more We study the chiral fermion meson model which is the well known linear sigma model of Gell-Mann-and-Levy at finite temperature.A modified self-consistent resummation (MSCR) which resums higher order terms in the perturbative expansion is proposed. It is shown that with the MSCR the problem of tachyonic masses is solved, the renormalization of the gap equations is carried out and the Goldstone's theorem is verified. We also apply the method to investigate another known case at high temperature and compare with results found in the literature.

Journal of Statistical Mechanics: Theory and Experiment, 2014

Journal of Physics B: Atomic, Molecular and Optical Physics, 2015

Annals of Physics, 2014

The search for Majorana fermions has been concentrated in topological insulators or superconducto... more The search for Majorana fermions has been concentrated in topological insulators or superconductors. In general, the existence of these modes requires the presence of spin-orbit interactions and of an external magnetic field. The former implies in having systems with broken inversion symmetry, while the latter breaks time reversal invariance. In a recent paper, we have shown that a two-band metal with an attractive inter-band interaction has nontrivial superconducting properties, if the k-dependent hybridization is anti-symmetric in the wave-vector. This is the case, if the crystalline potential mixes states with different parities as for orbitals with angular momentum l and l + 1. In this paper we take into account the effect of an external magnetic field, not considered in the previous investigation, in a two-band metal and show how it modifies the topological properties of its superconducting state. We also discuss the conditions for the appearance of Majorana fermions in this system.

Physical Review B, 2012

In multi-band systems, electrons from different orbitals coexist at the Fermi surface. An attract... more In multi-band systems, electrons from different orbitals coexist at the Fermi surface. An attractive interaction among these quasi-particles gives rise to inter-band or hybrid pairs which eventually condense in a superconducting state. These quasi-particles have a natural mismatch of their Fermi wave-vectors, δkF , which depends on the strength of the hybridization between their orbitals. The existence of this natural scale suggests the possibility of inhomogeneous superconducting ground states in these systems, even in the absence of an applied magnetic field. Furthermore, since hybridization V depends on pressure, this provides an external parameter to control the wave-vectors mismatch at the Fermi surface. In this work, we study the phase diagram of a two-dimensional, twoband metal with inter-band pairing. We show that as the mismatch between the Fermi wave-vectors of the two hybrid bands is reduced, the system presents a normal-to-inhomogeneous superconductor quantum phase transition at a critical value of the hybridization Vc = ∆0. The superconducting ground state for V < Vc is characterized by a wave-vector with magnitude |qc| = qc = 2∆0/v f . Here ∆0 is the superconducting gap in the homogeneous state andv f the average Fermi velocity. We discuss the nature of the quantum critical point (QCP) at Vc and obtain the associated quantum critical exponents.

ABSTRACT The obtaining of bound states of heavy and light quarks interacting via a static quark p... more ABSTRACT The obtaining of bound states of heavy and light quarks interacting via a static quark potential is revisited here. We present an approach that both approximate the relativistic wave equation and allows the obtaining of analytical solutions and binding energies (and consequently, the heavy mesons spectra) of the system.

Physics Letters A, 2014

We study a two-band model of fermions in a 1d chain with an antisymmetric hybridization that brea... more We study a two-band model of fermions in a 1d chain with an antisymmetric hybridization that breaks inversion symmetry. We find that for certain values of its parameters, the sp-chain maps formally into a p-wave superconducting chain, the archetypical 1d system exhibiting Majorana fermions. The eigenspectra, including the existence of zero energy modes in the topological phase, agree for both models. The end states too share several similarities in both models, such as the behavior of the localization length, the non-trivial topological index and robustness to disorder. However, we show by mapping the s-and p-fermions to two copies of Majoranas, that the excitations in the ends of a finite sp chain are indeed conventional fermions though endowed with protected topological properties. Our results are obtained by a scattering approach in a semi-infinite chain with an edge defect treated within the T -matrix approximation. We augment the analytical results with exact numerical diagonalization that allow us to extend our results to arbitrary parameters and also to disordered systems.

Physics Letters B, 2001

Feynman's functional formulation of statistical mechanics is used to study the renormalizability ... more Feynman's functional formulation of statistical mechanics is used to study the renormalizability of the well known Linear Chiral Sigma Model in the presence of fermionic fields at finite temperature in an alternative way. It is shown that the renormalization conditions coincide with those of the zero temperature model.

Physics Letters A, 2014

We present in this work an exact renormalization group (RG) treatment of a one-dimensional p-wave... more We present in this work an exact renormalization group (RG) treatment of a one-dimensional p-wave superconductor. The model proposed by Kitaev consists of a chain of spinless fermions with a p-wave gap. It is a paradigmatic model of great actual interest since it presents a weak pairing superconducting phase that has Majorana fermions at the ends of the chain. Those are predicted to be useful for quantum computation. The RG allows to obtain the phase diagram of the model and to study the quantum phase transition from the weak to the strong pairing phase. It yields the attractors of these phases and the critical exponents of the weak to strong pairing transition. We show that the weak pairing phase of the model is governed by a chaotic attractor being non-trivial from both its topological and RG properties. In the strong pairing phase the RG flow is towards a conventional strong coupling fixed point. Finally, we propose an alternative way for obtaining p-wave superconductivity in a one-dimensional system without spin-orbit interaction.

Physical Review Letters, 2000

We calculate the effects of induced interactions on the transition temperature to the BCS state i... more We calculate the effects of induced interactions on the transition temperature to the BCS state in dilute Fermi gases. For a pure Fermi system with two species having equal densities, the transition temperature is suppressed by a factor (4e)(1/3) approximately 2.2, and for nu fermion species, the transition temperature is increased by a factor (4e)(nu/3-1) approximately 2.2(nu-3). For mixtures of fermions and bosons the exchange of boson density fluctuations gives rise to an attractive interaction, and we estimate the increase of the transition temperature due to this effect.

Physical Review D, 2002

In this paper we use Modified Self-Consistent Resummation (MSCR) in order to obtain the scalar dr... more In this paper we use Modified Self-Consistent Resummation (MSCR) in order to obtain the scalar dressed mass by evaluating the self-energy up to two loops in the neutral scalar λφ 4 model at finite temperature. With this laboratory model we show that, if a theory is renormalizable at zero temperature, by using MSCR it is always possible to obtain a finite corrected mass at finite temperature. This feature of MSCR is not observed in some other approximation techniques usually found in the literature.

Physical Review D, 2001

We study the chiral fermion meson model which is the well known linear sigma model of Gell-Mann-a... more We study the chiral fermion meson model which is the well known linear sigma model of Gell-Mann-and-Levy at finite temperature. A modified self-consistent resummation (MSCR) which resums higher order terms in the perturbative expansion is proposed. It is shown that with the MSCR the problem of tachyonic masses is solved, the renormalization of the gap equations is carried out and the Goldstone's theorem is verified. We also apply the method to investigate another known case at high temperature and compare with results found in the literature.

Physical Review D, 2003

We investigate the analytic properties of finite-temperature self-energies of bosons interacting ... more We investigate the analytic properties of finite-temperature self-energies of bosons interacting with fermions at one-loop order. A simple boson-fermion model was chosen due to its interesting features of having two distinct couplings of bosons with fermions. This leads to a quite different analytic behavior of the bosons self-energies as the external momentum K µ = (k 0 , k) approaches zero in the two possible limits. It is shown that the plasmon and Debye masses are consistently obtained at the pole of the corrected propagator even when the self-energy is analytic at the origin in the frequency-momentum space.

Physical Review D, 2002

We reinvestigate the interesting phenomenon of symmetry nonrestoration at high temperature in the... more We reinvestigate the interesting phenomenon of symmetry nonrestoration at high temperature in the multifield O(N 1 )XO(N 2 ) model. We apply modified self-consistent resummation (MSCR) in order to obtain the scalar dressed masses and find in what circumstances a resummed multifield theory which has symmetry (non)restoration can be renormalized. It is shown that, aside from the consistency of the MSCR method, the basic ingredient that guarantees the renormalization of a multifield model within a resummation approach is the T 2 mass behavior of field theory at high temperature.

Physical Review A, 2012

We investigate the superfluid transition temperature of quasi-two-dimensional imbalanced Fermi ga... more We investigate the superfluid transition temperature of quasi-two-dimensional imbalanced Fermi gases beyond the mean-field approximation, through the second-order (or induced) interaction effects. For a balanced Fermi system the transition temperature is suppressed by a factor ≈2.72. For imbalanced Fermi systems, the polarization and transition temperature of the tricritical point are significantly reduced as the two-body binding energy | B | increases.

Nuclear Physics B, 2002

We reinvestigate the interaction of massless fermions with massless bosons at finite temperature.... more We reinvestigate the interaction of massless fermions with massless bosons at finite temperature. Specifically, we calculate the self-energy of massless fermions due the interaction with massless bosons at high temperature, which is the region where thermal effects are maximal. The calculations are concentrated in the limit of vanishing fermion three momentum and after considering the effective fermion and boson dressed masses, we obtain the damping rate of the fermion up to order g 3 . It is shown that in the limit k 0 T the fermion acquire a thermal mass of order gT and the leading term of the fermion damping rate is of order g 2 T + g 3 T . 

Nuclear Physics A, 1997

Sophisticated calculations of the dynamics of relativistic heavy-ion collisions often need as inp... more Sophisticated calculations of the dynamics of relativistic heavy-ion collisions often need as input properties of light mesons in medium. In this context simple analytical expressions for these quantities which respect chiral symmetry and low-energy current algebra results are most desirable. In the present work we provide such simple expressions based on a bosonized version of the microscopic NJL model. We also study the pion lifetime in hot and dense matter showing ~-(,rr -~tz-+~ ) that the ratio ~(___,~_+~) changes by a factor about three and thus carries a clear signature of the chiral phase transition. @ 1997 Elsevier Science B.V.

Modern Physics Letters A, 1997

We re-investigate the problem of the renormalizability of the chiral fermion meson model on the l... more We re-investigate the problem of the renormalizability of the chiral fermion meson model on the light of the regularization-independent algebraic method. The present letter is intended as a useful application of a modern technique in theory of current interest for the description of low energy hadron phenomenology. We show that the model is stable under radiative corrections and anomaly free