arXiv subjects

Alain Mauger

Publications and source records attributed to Alain Mauger.

At least 19 recordsLinked to original sources

arXiv2026

Condensation mechanism of high-$T_c$ cuprates: the key role of pairon excitations

In this article we show that the condensation mechanism in cuprates involves the strong coupling of the condensate to pairon excited states. We present an accessible formalism that significantly extends our previous work, providing a theoretical basis for the energy-dependent gap function $\Delta(E)$. The latter is proportional to the effective spin exchange energy, $J_{eff}$, with no retardation effects, such as the case of spin-fluctuation or phonon mediated couplings. The fundamental parameters of the superconducting (SC) state are the condensation energy per pair, $\beta_c$, and the antinodal energy gap, $\Delta_p$, which are quantitatively extracted by fitting the cuprate quasiparticle spectrum from tunneling experiments. An explicit formula for the critical temperature is also derived in the model. Valid for any doping, we find $T_c$ to be proportional to $\beta_c$, and not the gap $\Delta_p$, in sharp contrast to conventional SC. The numerical factor $\beta_c/k_BT_c\simeq 2.24$ originates from pair excitations of the condensate, following Bose statistics, with a mini-gap $\delta_M \simeq 1\,$meV in the excitation spectrum. These results strongly suggest that the same `all-electron' mechanism is at work all along the $T_c$-dome.

cond-mat.supr-con↗

arXiv2025

Magnetic phase diagram of cuprates and universal scaling laws

In this article we consider the magnetic field phase diagram of hole-doped high-$T_c$ cuprates, which has been given much less attention than the temperature diagram. In the framework of the {\it pairon model}, we show that the two characteristic energies, the pair binding energy (the gap $\Delta_p$) and the condensation energy ($\beta_c$) resulting from pair correlations, give rise to two major magnetic fields, the upper critical field $B_{c2}$ and a second field, $B_{pg}$, associated with the pseudogap (PG). The latter implies a second length scale in addition to the coherence length, characteristic of incoherent pairs. Universal scaling laws for both $B_{c2}$ and $B_{pg}$ are derived: $B_{c2}$ scales with the critical temperature, $B_{c2}/T_c\simeq 1.65$ T/K, in agreement with many experiments, and $B_{pg}$ has a similar scaling with respect to $T^*$. Finally, Fermi arcs centered on the nodal directions are predicted to appear as a function of magnetic field, an effect testable experimentally.

cond-mat.supr-con↗

arXiv2024

Unraveling pairon excitations and the antiferromagnetic contributions in the cuprate specific heat

Thermal measurements, such as the entropy and the specific heat, reveal key elementary excitations for understanding the cuprates. In this paper, we study the specific heat measurements on three different compounds La$_{2-x}$Sr$_x$CuO$_4$, Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ and YBa$_2$Cu$_3$O$_{7-\delta}$ and show that the data are compatible with `pairons' and their excitations. However, the precise fits require the contribution of the antiferromagnetic entropy deduced from the magnetic susceptibility $\chi(T)$. Two temperature scales are involved in the excitations above the critical temperature $T_c$: the pseudogap $T^*$, related to pairon excitations, and the magnetic correlation temperature, $T_{max}$, having very different dependencies on the carrier density ($p$). In agreement with our previous analysis of $\chi(T)$, the $T_{max}(p)$ line is not the signature of a gap in the electronic density of states, but is rather the temperature scale of strong local antiferromagnetic correlations which dominate for low carrier concentration. These progressively evolve into paramagnetic fluctuations in the overdoped limit. Our results are in striking contradiction with the model of J. L. Tallon and J. G. Storey [Phys. Rev. B {\bf 107}, 054507 (2023)], who reaffirm the idea of a $T$-independent gap $E_g$, whose temperature scale $T_g=E_g/k_B$ decreases linearly with $p$ and vanishes at a critical value $p_c \sim 0.19$. Finally, we discuss the unconventional fluctuation regime above $T_c$, which is associated with a mini-gap $\delta\sim$ 2\,meV in the pairon excitation spectrum. This energy scale is fundamental to the condensation mechanism.

cond-mat.supr-con↗

arXiv2023

Statistics of the cuprate pairon states on a square lattice

In this paper the fundamental parameters of high-$T_c$ superconductivity are shown to be connected to the statistics of pairons (hole pairs in their antiferromagnetic environment) on a square lattice. In particular, we study the density fluctuations and the distribution of the area surrounding each pairon on the scale of the antiferromagnetic correlation length $\xi_{AF}$, for the complete range of hole concentration. We show that the key parameters of the phase diagram, the $T_c$ dome, and the pseudogap temperature $T^*$, emerge from the statistical properties of the pairon disordered state. In this approach, the superconducting and the pseudogap states appear as inseparable phenomena. The condensation energy, which fixes the critical temperature, is directly proportional to the {\it correlation energy} between pairons and {\it not} to the energy gap, contrary to conventional superconductors. When the correlation energy between pairons is suppressed by fluctuations, either thermally, by disorder, or in the vortex core, the pseudogap state of disordered pairons is obtained. We attribute the unique features of cuprate superconductivity to this order-disorder transition in real space, which clearly differs from the BCS mechanism. Our predictions are in quantitative agreement with low-temperature tunneling and photoemission spectroscopy experiments.

cond-mat.supr-con↗

arXiv2022

Superconductivity in cuprates governed by topological constraints

The remarkable universality of the cuprate $T_c$ dome suggests a very fundamental unifying principle. Moreover, the superconducting gap is known to persist above $T_c$ in the pseudogap phase of all cuprates. So, contrary to BCS, the gap cannot be the order parameter of the transition. In this work, we show that both the $T_c$-dome and the pseudogap line $T^*(p)$ arise from a unique and identifiable principle: the interaction of localized `pairons' on an antiferromagnetic square lattice. The topological constraints on such preformed pairons give rise to both the $T_c$ dome and the pairing energy {\it simultaneously}. It also provides a natural explanation for the critical doping points of the phase diagram. The model matches perfectly both the $T^*$ and $T_c$ experimental lines, with only one adjustable parameter.

cond-mat.supr-con↗

arXiv2022

Cuprates phase diagram deduced from magnetic susceptibility: what is the `true' pseudogap line?

Two contradictory phase diagrams have dominated the literature of high-$T_c$ cuprate superconductors. Does the pseudogap line cross the superconducting $T_c$-dome or not? To answer, we have revisited the experimental magnetic susceptibility and knight shift of four different compounds, La$_{1-x}$Sr$_x$CuO$_4$, Bi$_2$Sr$_2$Ca$_{1-x}$Y$_x$Cu$_2$O$_8$, Bi$_2$Sr$_2$CaCu$_2$O$_{8+y}$, and YBa$_2$Cu$_3$O$_{6+y}$, as a function of temperature and doping. The susceptibility can be described by the same function for all materials, having a magnetic and an electronic contributions. The former is the 2D antiferromagnetic (AF) square lattice response, with a characteristic temperature of magnetic correlations $T_{max}$. The latter is the `Pauli' term, revealing the gap opening in the electronic density of states at the pseudogap temperature $T^*$. From precise fits of the data, we find that $T_{max}(p)$ decreases linearly as a function of doping ($p$) over a wide range, but saturates abruptly in the overdoped regime. Concomitantly, $T^*(p)$ is {\it linear and tangent} to the dome, either crossing or approaching $T_{max}(p)$ at the top of the dome, indicating a qualitative change of behavior from underdoped to overdoped regimes. Contrary to the idea that the pseudogap terminates just above optimal doping, our analysis suggests that the gap exists throughout the phase diagram. It is consistent with a pseudogap due to hole pairs, or `pairons', above $T_c$. We conclude that $T_{max}$, reflecting the AF magnetic correlations, has often been misinterpreted as the pseudogap temperature $T^*$.

cond-mat.supr-con↗

arXiv2020

How 'pairons' are revealed in the electronic specific heat of cuprates

Understanding the thermodynamic properties of high-$T_c$ cuprate superconductors is a key step to establish a satisfactory theory of these materials. The electronic specific heat is highly unconventional, distinctly non-BCS, with remarkable doping-dependent features extending well beyond $T_c$. The pairon concept, bound holes in their local antiferromagnetic environment, has successfully described the tunneling and photoemission spectra. In this article, we show that the model explains the distinctive features of the entropy and specific heat throughout the temperature-doping phase diagram. Their interpretation connects unambiguously the pseudogap, existing up to $T^*$, to the superconducting state below $T_c$. In the underdoped case, the specific heat is dominated by pairon excitations, following Bose statistics, while with increasing doping, both bosonic excitations and fermionic quasiparticles coexist.

cond-mat.supr-con↗

arXiv2018

Origin of the Fermi arcs in cuprates: a dual role of quasiparticle and pair excitations

ARPES mesurements in cuprates have given key information on the temperature and angle dependence of the gap ($d$-wave order parameter, Fermi arcs and pseudogap). We show that these features can be understood in terms of a Bose condensation of interacting {\it pairons} (preformed hole pairs which form in their local antiferromagnetic environment). Starting from the basic properties of the pairon wavefunction, we derive the corresponding k-space spectral function. The latter explains the variation of the ARPES spectra as a function of temperature and angle up to T*, the onset temperature of pairon formation. While Bose excitations dominate at the antinode, the fermion excitations dominate around the nodal direction, giving rise to the Fermi arcs at finite temperature. This dual role is the key feature distinguishing cuprate from conventional superconductivity.

cond-mat.supr-con↗

arXiv2017

Cooper pairs without 'glue' in high-$T_c$ superconductors

We address the origin of the Cooper pairs in high-$T_c$ cuprates and the unique nature of the superconducting (SC) condensate. Itinerant holes in an antiferromagnetic background form pairs spontaneously, without any `glue', defining a new quantum object the `pairon'. In the incoherent pseudogap phase, above $T_c$ or within the vortex core, the pairon binding energies are distributed statistically, forming a `Cooper-pair glass'. Contrary to conventional SC, it is the mutual pair-pair interaction that is responsable for the condensation. We give a natural explanation for the {\it ergodic rigidity} of the excitation gap, being uniquely determined by the carrier concentration $p$ and $J$. The phase diagram can be understood, without spin fluctuations, in terms of a single energy scale $\sim J$, the exchange energy at the metal-insulator transition.

cond-mat.supr-con↗

arXiv2016

From Cooper-pair glass to unconventional superconductivity: a unified approach to cuprates and pnictides

We report a microscopic model wherein the unconventional superconductivity emerges from an incoherent `Cooper-pair glass' state. Driven by the pair-pair interaction, a new type of quasi-Bose phase transition is at work. The interaction leads to the unconventional coupling of the quasiparticles to excited pair states, or `super-quasiparticles', with a non-retarded energy-dependent gap. The model describes quantitatively the quasiparticle excitation spectra of both cuprates and pnictides, including the universal `peak-dip-hump' signatures, and for the pseudogap phase above $T_c$. The results show that instantaneous pair-pair interactions account for the SC condensation without a collective mode.

cond-mat.supr-con↗

arXiv2016

Unconventional temperature dependence of the cuprate excitation spectrum

Key properties of the cuprates, such as the pseudogap observed above the critical temperature $T_c$, remain highly debated. Given their importance, we recently proposed a novel mechanism based on the Bose-like condensation of mutually interacting Cooper pairs [W. Sacks, A. Mauger, Y. Noat, Superconduct. Sci. Technol. 28 105014, (2015)]. In this work, we calculate the temperature dependent DOS using this model for different doping levels from underdoped to overdoped. In all situations, due to the presence of excited pairs, a pseudogap is found above $T_c$ while the normal DOS is recovered at $T^*$, the pair formation temperature. A similar behavior is found as a function of magnetic field, crossing a vortex, where a pseudogap exists in the vortex core. We show that the precise DOS shape depends on combined pair (boson) and quasiparticle (fermion) excitations, allowing for a deeper understanding of the SC to the PG transition.

cond-mat.supr-con↗

arXiv2015

Pair-pair interactions as a mechanism for high-T$_c$ superconductivity

The mutual interaction between Cooper pairs is proposed as a mechanism for the superconducting state. Above $T_c$, pre-existing but fluctuating Cooper pairs give rise to the unconventional {\it pseudogap} (PG) state, well-characterized by experiment. At the critical temperature, the pair-pair interaction induces a Bose-like condensation of these preformed pairs leading to the superconducting (SC) state. Below $T_c$, both the condensation energy and the pair-pair interaction $β$ are proportional to the condensate density $N_{oc}(T)$, whereas the usual Fermi-level spectral gap $Δ_p$ is independent of temperature. The new order parameter $β(T)$, can be followed as a function of temperature, carrier concentration and disorder - i.e. the phase diagrams. The complexity of the cuprates, revealed by the large number of parameters, is a consequence of the {\it coupling of quasiparticles to Cooper-pair excitations}. The latter interpretation is strongly supported by the observed quasiparticle spectral function.

cond-mat.supr-con↗

arXiv2003

Anomalous diffusion of a particle in an aging medium

We report new results about the anomalous diffusion of a particle in an aging medium. For each given age, the quasi-stationary particle velocity is governed by a generalized Langevin equation with a frequency-dependent friction coefficient proportional to $|ω|^{δ-1}$ at small frequencies, with $0<δ<2$. The aging properties of the medium are encoded in a frequency dependent effective temperature $T_{\rm eff.}(ω)$. The latter is modelized by a function proportional to $|ω|^α$ at small frequencies, with $α<0$, thus allowing for the medium to have a density of slow modes proportionally larger than in a thermal bath. Using asymptotic Fourier analysis, we obtain the behaviour at large times of the velocity correlation function and of the mean square displacement. As a result, the anomalous diffusion exponent in the aging medium appears to be linked, not only to $δ$ as it would be the case in a thermal bath, but also to the exponent $α$ characterizing the density of slow modes.

cond-mat.stat-mech↗

arXiv2003

On reducing Terrorism Power: A Hint from Physics

The September 11 attack on the US has revealed an unprecedented terrorism worldwide range of destruction. Recently, it has been related to the percolation of worldwide spread passive supporters. This scheme puts the suppression of the percolation effect as the major strategic issue in the fight against terrorism. Accordingly the world density of passive supporters should be reduced below the percolation threshold. In terms of solid policy, it means to neutralize millions of random passive supporters, which is contrary to ethics and out of any sound practical scheme. Given this impossibility we suggest instead a new strategic scheme to act directly on the value of the terrorism percolation threshold itself without harming the passive supporters. Accordingly we identify the space hosting the percolation phenomenon to be a multi-dimensional virtual social space which extends the ground earth surface to include the various independent terrorist-fighting goals. The associated percolating cluster is then found to create long-range ground connections to terrorism activity. We are thus able to modify the percolation threshold pc in the virtual space to reach p<pc by decreasing the social space dimension, leaving the density p unchanged. At once that would break down the associated world terrorism network to a family of unconnected finite size clusters. The current world terrorism threat would thus shrink immediately and spontaneously to a local geographic problem. There, military action would become limited and efficient.

cond-mat.dis-nn↗

arXiv2001

Aging effects in the quantum dynamics of a dissipative free particle: non-ohmic case

We report new results related to the two-time dynamics of the coordinate of a quantum free particle, damped through its interaction with a fractal thermal bath (non-ohmic coupling $\simω^δ$ with $0<δ<1$ or $1<δ<2)$. When the particle is localized, its position does not age. When it undergoes anomalous diffusion, only its displacement may be defined. It is shown to be an aging variable. The finite temperature aging regime is self-similar. It is described by a scaling function of the ratio ${t_w/τ}$ of the waiting time to the observation time, as characterized by an exponent directly linked to $δ$.

cond-mat.stat-mech↗

arXiv2000

Quantum fluctuation-dissipation theorem: a time domain formulation

A time-domain formulation of the equilibrium quantum fluctuation-dissipation theorem (FDT) in the whole range of temperatures is presented. In the classical limit, the FDT establishes a proportionality relation between the dissipative part of the linear response function and the derivative of the corresponding equilibrium correlation function. At zero temperature, the FDT takes the form of Hilbert transform relations between the dissipative part of the response function and the corresponding symmetrized equilibrium correlation function, which allows to establish a connection with analytic signal theory. The time-domain formulation of the FDT is especially valuable when out-of-equilibrium dynamics is concerned, as it is for instance the case in the discussion of aging phenomena.

cond-mat.stat-mech↗

arXiv1999

Aging effects in free quantum Brownian motion

The two-time correlation function of the displacement of a free quantum Brownian particle with respect to its position at a given time is calculated analytically in the framework of the Caldeira and Leggett ohmic dissipation model (linear coupling of the particle with a thermal bath with a continuum of modes, proportional to the frequency at low frequency). As a result, at any temperature, the displacement correlation function exhibits aging, i.e. it depends explicitly on both times involved and not only on their difference, even in the limit of large age (or waiting time), in contrast with a dynamic variable in equilibrium such as the particle velocity. The equilibrium quantum fluctuation-dissipation theorem (QFDT) has to be modified in order to relate the displacement response and correlation functions, since this latter quantity takes into account even those fluctuations of the displacement which take place during the waiting time. We describe the deviation from the equilibrium QFDT in terms of an effective temperature which depends both on the time difference and of the waiting time. The definition of this quantity heavily relies on the time-dependent diffusion coefficient. The behavior of the effective temperature as a function of the time difference for given values of the bath temperature and of the waiting time is analyzed.

cond-mat.stat-mech↗

arXiv1998

Topology invariance in Percolation Thresholds

An universal invariant for site and bond percolation thresholds (p_{cs} and p_{cb} respectively) is proposed. The invariant writes {p_{cs}}^{1/a_s}{p_{cb}}^{-1/a_b}=δ/d where a_s, a_b and δare positive constants,and d the space dimension. It is independent of the coordination number, thus exhibiting a topology invariance at any d.The formula is checked against a large class of percolation problems, including percolation in non-Bravais lattices and in aperiodic lattices as well as rigid percolation. The invariant is satisfied within a relative error of \pm 5% for all the twenty lattices of our sample at d=2, d=3, plus all hypercubes up to d=6.

cond-mat.dis-nn↗