C. Bourbonnais

Université de Sherbrooke, Шербрук, Quebec, Canada

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Publications (152)389.37 Total impact

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    Hassan Bakrim, Claude Bourbonnais
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    ABSTRACT: The renormalization group technique is applied to one-dimensional electron-phonon Hubbard models at half-filling and zero temperature. For the Holstein-Hubbard model, the results of one-loop calculations are congruent with the phase diagram obtained by quantum Monte Carlo simulations in the $(U,g_{\rm ph})$ plane for the phonon-mediated interaction $g_{\rm ph}$ and the Coulomb interaction $U$. The incursion of an intermediate phase between a fully gapped charge-density-wave state and a Mott antiferromagnet is supported along with the growth of its size with the molecular phonon frequency $\omega_0$. We find additional phases enfolding the base boundary of the intermediate phase. A Luttinger liquid line is found below some critical $ U^*\approx g^*_{\rm ph}$, followed at larger $U\sim g_{\rm ph}$ by a narrow region of bond-order-wave ordering which is either charge or spin gapped depending on $U$. For the Peierls-Hubbard model, the region of the $(U,g_{\rm ph})$ plane with a fully gapped Peierls-bond-order-wave state shows a growing domination over the Mott gapped antiferromagnet as the Debye frequency $\omega_D$ decreases. A power law dependence $g_{\rm ph} \sim U^{2\eta}$ is found to map out the boundary between the two phases, whose exponent is in good agreement with the existing quantum Monte Carlo simulations performed when a finite nearest-neighbor repulsion term $V$ is added to the Hubbard interaction.
    Physical Review B 02/2015; 91(8). DOI:10.1103/PhysRevB.91.085114
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    Hassan Bakrim, Claude Bourbonnais
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    ABSTRACT: We use the renormalization group method to examine the effect of phonon mediated interaction on d-wave superconductivity, as driven by spin fluctuations in a quasi-one-dimensional electron system. The influence of a tight-binding electron-phonon interaction on the spin-density-wave and d-wave superconducting instability lines is calculated for arbitrary temperature, phonon frequency and antinesting of the Fermi surface.The domain of electron-phonon coupling strength where spin-density-wave order becomes unstable against the formation of a bond-order-wave or Peierls state is determined at weak antinesting. We show the existence of a positive isotope effect for spin-density-wave and d-wave superconducting critical temperatures which scales with the antinesting distance from quantum critical point where the two instabilities merge. We single out a low phonon frequency zone where the bond-oder-wave ordering gives rise to triplet f-wave superconductivity under nesting alteration, with both orderings displaying a negative isotope effect. We also study the electron-phonon strengthening of spin fluctuations at the origin of extended quantum criticality in the metallic phase above superconductivity. The impact of our results on quasi-one-dimensional organic conductors like the Bechgaard salts where a Peierls distortion is absent and superconductivity emerges near a spin-density-wave state under pressure is emphasized.
    Physical Review B 06/2014; 90(12). DOI:10.1103/PhysRevB.90.125119
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    ABSTRACT: We report an investigation of charge, spin and lattice effects in the spin-Peierls state of the organic compound MEM(TCNQ)$_2$. The 16.5 GHz dielectric function along the chain axis shows an enhancement below the spin-Peierls transition temperature near 18 K consistent with the charge coupling to the elastic strain involved in the transition. The velocity of two elastic modes perpendicular to the chain axis presents anomalies at the transition which can be explained with a Landau free energy model including a linear-quadratic coupling energy term between the appropriate elastic strain $e$ and the spin-Peierls magnetic gap $\Delta_q$. The analysis of the dielectric and elastic features aims toward an order parameter with an associated critical exponent $\beta \sim$ 0.36, which is similar to the three-dimensional behavior seen in other spin-Peierls materials. All these effects studied in a magnetic field up to 18 Teslas appear also compatible with a mean-field model of a quasi-one-dimensional spin-Peierls system.
    Physical Review B 11/2013; 88(24). DOI:10.1103/PhysRevB.88.245134
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    ABSTRACT: An inductive method is used to follow the magnetic-field–dependent susceptibility of the coupled charge density wave (CDW) and spin-Peierls (SP) ordered state behavior in the dual-chain organic conductor perylene2[Pt(mnt)2]. In addition to the coexisting SP-CDW state phase below 8 K and 20 T, the measurements show that a second spin-gapped phase appears above 20 T that coincides with a field-induced insulating phase. The results support a strong coupling of the CDW and SP order parameters even in high magnetic fields, and provide new insight into the nature of the magnetic susceptibility of dual-chain spin and charge systems.
    EPL (Europhysics Letters) 08/2013; 103(3):37008. DOI:10.1209/0295-5075/103/37008
  • Alain Moÿse Dikandé, Claude Bourbonnais
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    ABSTRACT: The Peierls instability in one-dimensional electron--phonon systems is known to be qualitatively well described by the mean-field theory, however the related self-consistent problem so far has only been able to predict a partial suppression of the transition even with proper account of classical lattice fluctuations. Here the Hartree--Fock approximation scheme is extended to the full quantum regime, by mapping the momentum--frequency spectrum of order-parameter fluctuations onto a continuous two-parameter space. For the one-dimensional half-filled Su--Schrieffer--Heeger model the ratio d=Ω/2π Tc0, where Ω is the characteristic phonon frequency and 2π Tc0 the lowest finite phonon Matsubara frequency at the mean-field critical point Tc0, provides a natural measure of the adiabaticity of lattice fluctuations. By integrating out finite-frequency phonons, it is found that a variation of d from the classical regime d=0 continuously connects Tc0 to a zero-temperature charge-density-wave transition setting up at a finite crossover d=dc. This finite crossover decreases within the range 0≤ d≈ 1 as the electron--phonon coupling strength increases but remaining small enough for weak-coupling considerations to still hold. Implications of Tc suppression on the Ginzburg criterion is discussed, and evidence is given of a possible coherent description of the charge-density-wave problem within the framework of a renormalized mean-field theory encompassing several aspects of the transition including its thermodynamics close to the quantum critical point.
    Journal of the Physical Society of Japan 02/2013; 82(2):4003-. DOI:10.7566/JPSJ.82.024003
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    Yuki Fuseya, Claude Bourbonnais, Kazumasa Miyake
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    ABSTRACT: Upper critical field, H_c2, in quasi-1D superconductors is investigated by the weak coupling renormalization group technique. It is shown that H_c2 greatly exceeds not only the Pauli limit, but also the conventional paramagnetic limit of the Flude-Ferrell-Larkin-Ovchinnikov (FFLO) state. This increase is mainly due to quasi-1D fluctuations effect as triggered by interference between unconventional superconductivity and density-wave instabilities. Our results give a novel viewpoint on the large H_c2 observed in TMTSF-salts in terms of a d-wave FFLO state that is predicted to be verified by the H_c2 measurements under pressure.
    EPL (Europhysics Letters) 09/2012; 100(5). DOI:10.1209/0295-5075/100/57008
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    ABSTRACT: We report an ultrasonic study of the magneto-elastic coupling of the hydrogenated and deuterated (TMTTF)2PF6 organic salts. For both salts the temperature dependence of the longitudinal velocity along the c* axis displays a monotonic stiffening of the C33 compressibility modulus upon cooling. Below the characteristic temperature scale 40 K the modulus stiffening becomes markedly enhanced, in concomitance with the reduction of spin degrees of freedom previously seen in magnetic measurements as low-dimensional precursors of the spin-Peierls transition. The magneto-elastic coupling appears to be much weaker in the hydrogenated salt due to the highly inhomogeneous elastic behavior induced by the proximity of the charge ordering transition to the spin-Peierls phase. For the deuterated salt, an important anomaly in the ultrasound velocity is observed below the spin-Peierls transition temperature TSP in agreement with scaling of the elastic deformation with the spin-Peierls order parameter. In spite of the weakly inhomogeneous character of the spin-Peierls phase transition, the magnetic field dependence of TSP is well captured with the mean-field prediction for the lattice distorted Heisenberg spin chain.
    Physical review. B, Condensed matter 07/2012; 86(8). DOI:10.1103/PhysRevB.86.085111
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    ABSTRACT: Comparing resistivity data of the quasi-one-dimensional superconductors (TMTSF)(2)PF(6) and (TMTSF)(2)ClO(4) along the least conducting c(⋆)-axis and along the high conductivity a-axis as a function of temperature and pressure, a low temperature regime is observed in which a unique scattering time governs the transport along both directions of these anisotropic conductors. However, the pressure dependence of the anisotropy implies a large pressure dependence of the interlayer coupling. This is in agreement with the results of first-principles density functional theory calculations implying methyl group hyperconjugation in the TMTSF molecule. In this low temperature regime, both materials exhibit for ρ(c) a temperature dependence aT + bT(2). Taking into account the strong pressure dependence of the anisotropy, the T-linear ρ(c) is found to correlate with the suppression of the superconducting T(c), in close analogy with ρ(a) data. This work reveals the domain of existence of the three-dimensional coherent regime in the generic (TMTSF)(2)X phase diagram and provides further support for the correlation between T-linear resistivity and superconductivity in non-conventional superconductors.
    Journal of Physics Condensed Matter 08/2011; 23(34):345702. DOI:10.1088/0953-8984/23/34/345702
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    Claude Bourbonnais, Abdeliouahab Sedeki
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    ABSTRACT: Superconductivity in the Bechgaard salts series of quasi-one-dimensional organic conductors occurs on the verge of spin-density-wave ordering when hydrostatic pressure is applied. The sequence of instabilities is intimately connected to normal state anomalies in various quantities like the temperature dependence of electrical transport and nuclear spin-lattice relaxation rate. We discuss how such a connection takes its origin in the interference between the different pairing mechanisms responsible for antiferromagnetism and superconductivity, a duo that can be comprehended in terms of a weak coupling renormalization group theory. The recent developments along this line of though are presented in relation to experiments.
    Comptes Rendus Physique 08/2011; 12(5). DOI:10.1016/j.crhy.2011.04.005
  • Claude Bourbonnais, Hassan Bakrim
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    ABSTRACT: The stabilization of unconventional superconductivity (SCd) close to a spin-density-wave state (SDW) under pressure in organic conductors like the Bechgaard salts points out the primary importance of the repulsive Coulomb term in the origin of these phases. However, the electron-(acoustic) phonon interaction is known to be finite in practice, as borne out for example by diffuse X-ray scattering experiments. The question then arises about the role of this coupling, if any, in the mechanism of interaction between SDW and SCd orders in such materials. In this work, we address this issue using the renormalization group method. This is done in the framework of the quasi-1D electron gas model with repulsive direct Coulomb terms and weak retarded electron-phonon interaction, which are treated on equal footing. The impact of electron-phonon interaction on the SDW and SCd instability lines of the phase diagram and on the strength of spin correlations in the normal phase are analyzed at arbitrary phonon frequency, and discussed in connection with experiments in organic superconductors like the Bechgaard salts.
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    C. Bourbonnais, L. G. Caron
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    ABSTRACT: In this paper we discuss the limitations of classical field treatments of one-dimensional systems in the static approximation. Two exactly solvable Hamiltonians, the ferromagnetic Ising model, and its extension to a zero-width half-filled band, are studied after their transformation to a classical field form via the Hubbard–Stratonovich identity. The more usual two-field transformation consists of using one field to describe the divergent order parameter and another to represent the nondivergent modes. The fluctuations in this latter one are usually neglected and this is shown to lead to incorrect thermodynamic behavior throughout the critical region, which is unusually large in one-dimensional systems, and even beyond to the high temperature limit. Any limited expansion of the free energy is further seen to lead to incorrect treatment of the amplitude fluctuations. A rigorous treatment of both fields is required. Alternately, a one-field transformation can assure a simpler approach although all terms in the free energy expansion must be retained. The findings are extrapolated to other known Hamiltonians: Hubbard, Peierls and spin-Peierls, and Bardeen–Cooper–Schrieffer (BCS) superconductivity. The Peierls case is examined in some detail because the usual one-field free energy functional is not obtained by a straightforward use of the Hubbard–Stratonovich transformations. As for the BCS Hamiltonian, it is seen to be in a special class because both symmetry fields are equally divergent and are automatically treated on an equal footing.
    Canadian Journal of Physics 02/2011; 61(4):550-563. DOI:10.1139/p83-070
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    ABSTRACT: An exhaustive investigation of metallic electronic transport and superconductivity of organic superconductors (TMTSF)2ClO4 and (TMTSF)2PF6 in the pressure-temperature phase diagram between T = 0 and 20 K and a theoretical description based on the weak coupling renormalization group method are reported. The analysis of the data reveals a high temperature domain (T ≈ 20 K) in which a regular T 2 electron-electron Umklapp scattering obeys a Kadowaki-Woods law and a low temperature regime (T < 8 K) where the resistivity is dominated by a linear-in temperature component. In both compounds a correlated behavior exists between the linear transport and the extra nuclear spin-lattice relaxation due to antiferromagnetic fluctuations. In addition, a tight connection is clearly established between linear transport and T c . We propose a theoretical description of the anomalous resistivity based on a weak coupling renormalization group determination of electron-electron scattering rate. A linear resistivity is found and its origin lies in antiferromagnetic correlations sustained by Cooper pairing via constructive interference. The decay of the linear resistivity term under pressure is correlated with the strength of antiferromagnetic spin correlations and T c , along with an unusual build-up of the Fermi liquid scattering. The results capture the key features of the low temperature electrical transport in the Bechgaard salts.
    Physics of Condensed Matter 11/2010; 78(1):23-36. DOI:10.1140/epjb/e2010-10571-4
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    M. Ménard, C. Bourbonnais
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    ABSTRACT: The phase diagram of the one-dimensional extended Hubbard model at half-filling is investigated by a weak coupling renormalization group method applicable beyond the usual continuum limit for the electron spectrum and coupling constants. We analyze the influence of irrelevant momentum dependent interactions on asymptotic properties of the correlation functions and the nature of dominant phases for the lattice model under study.
    Physical review. B, Condensed matter 09/2010; 83(7). DOI:10.1103/PhysRevB.83.075111
  • A. Sedeki, D. Bergeron, C. Bourbonnais
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    ABSTRACT: In this short note we summarize recent results obtained by the renormalization group approach to quasi-one-dimensional electron gas model The approach is applied to the Bechgaard salts series (TMTSF)(2)X and the results are shown to give a satisfactory account of the Interdependence between antiferromagnetism and superconductivity featured by their phase diagram the anomalous enhancement of the nuclear relaxation and the electron-electron scattering rate under pressure (C) 2009 Elsevier B V All rights reserved
    Physica B Condensed Matter 06/2010; 405(11). DOI:10.1016/j.physb.2009.11.056
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    H. Bakrim, C. Bourbonnais
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    ABSTRACT: We use the weak coupling renormalization group method to examine the interplay between charge-density-wave and s-wave superconducting orders in a quasi-one-dimensional model of electrons interacting with acoustic phonons. The relative stability of both types of order is mapped out at arbitrary nesting deviations and Debye phonon frequency $\omega_D$. We singled out a power law increase of the superconducting $T_c\sim \omega_D^{0.7}$ from a quantum critical point of charge-density-wave order triggered by nesting alterations. The results capture the key features shown by the proximity between the two types of ordering in the phase diagram of the recently discovered Perylene based organic superconductor under pressure. The impact of Coulomb interaction on the relative stability of the competing phases is examined and discussed in connection with the occurrence of s-wave superconductivity in low dimensional charge-density-wave materials. Comment: 6 pages, 5 figures
    EPL (Europhysics Letters) 01/2010; DOI:10.1209/0295-5075/90/27001
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    ABSTRACT: The quasi-one-dimensional organic Bechgaard salt (TMTSF)2PF6 displays spin-density-wave (SDW) order and superconductivity in close proximity in the temperature-pressure phase diagram. We have measured its normal-state electrical resistivity ρa(T) as a function of temperature and pressure, in the T→0 limit. At the critical pressure where SDW order disappears, ρa(T)∝T down to the lowest measured temperature (0.1 K). With increasing pressure, ρa(T) acquires a curvature that is well described by ρa(T)=ρ0+AT+BT2, where the strength of the linear term, measured by the A coefficient, is found to scale with the superconducting transition temperature Tc. This correlation between A and Tc strongly suggests that scattering and pairing in (TMTSF)2PF6 have a common origin, most likely rooted in the antiferromagnetic spin fluctuations associated with SDW order. Analysis of published resistivity data on the iron-pnictide superconductor Ba(Fe1−xCox)2As2 reveals a detailed similarity with (TMTSF)2PF6, suggesting that antiferromagnetic fluctuations play a similar role in the pnictides.
    Physical review. B, Condensed matter 12/2009; 80(21). DOI:10.1103/PhysRevB.80.214531
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    ABSTRACT: We report a study of the 16.5 GHz dielectric function of hydrogenated and deuterated organic salts (TMTTF)2PF6. The temperature behavior of the dielectric function is consistent with short-range polar order whose relaxation time decreases rapidly below the charge-ordering temperature. If this transition has more a relaxor character in the hydrogenated salt, charge ordering is strengthened in the deuterated one where the transition temperature has increased by more than thirty percent. We give the first account of anomalies in the dielectric function related to the spin-Peierls ground state revealing some interaction between both phases in their domain of coexistence in temperature. The variation of the spin-Peierls ordering temperature obtained under magnetic field completes the structure of the phase diagram at low field and are analyzed in the framework of the mean-field prediction.
    Physical review. B, Condensed matter 07/2009; 81(12). DOI:10.1103/PhysRevB.81.125101
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    ABSTRACT: Superconductivity of quasi-one-dimensional organic conductors with a quarter-filled band is investigated using the two-loop renormalization group approach to the extended Hubbard model for which both the single electron hopping t_{\perp} and the repulsive interaction V_{\perp} perpendicular to the chains are included. For a four-patches Fermi surface with deviations to perfect nesting, we calculate the response functions for the dominant fluctuations and possible superconducting states. By increasing V_{\perp}, it is shown that a d-wave (singlet) to f-wave (triplet) superconducting state crossover occurs, and is followed by a vanishing spin gap. Furthermore, we study the influence of a magnetic field through the Zeeman coupling, from which a triplet superconducting state is found to emerge. Comment: 11 pages, 15 figures, published version
    Journal of the Physical Society of Japan 06/2009; DOI:10.1143/JPSJ.78.104702
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    ABSTRACT: A linear temperature dependence of the electrical resistivity as T -> 0 is the hallmark of quantum criticality in heavy-fermion metals and the archetypal normal-state property of high-Tc superconductors, yet in both cases it remains unexplained. We report a linear resistivity on the border of spin-density-wave order in the organic superconductor (TMTSF)2X (X = PF6, ClO4), whose strength scales with the superconducting temperature Tc. This scaling, also present in the pnictide superconductors, reveals an intimate connection between linear-T scattering and pairing, shown by renormalization group theory to arise from antiferromagnetic fluctuations, enhanced by the interference of superconducting correlations. Our results suggest that linear resistivity in general may be a consequence of such interference and pairing in overdoped high-Tc cuprates is driven by antiferromagnetic fluctuations, as in organic and pnictide superconductors.
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    C. Bourbonnais, D. Jerome
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    ABSTRACT: This review covers the study of some basic properties of the phase diagram of quasi-one-dimensional organic superconductors from both experimental and theoretical viewpoints.

Publication Stats

2k Citations
389.37 Total Impact Points

Institutions

  • 1987–2015
    • Université de Sherbrooke
      • Department of Physics
      Шербрук, Quebec, Canada
  • 1983–2007
    • Université Paris-Sud 11
      • Laboratoire de Physique des Solides
      Paris, Ile-de-France, France
  • 1998
    • University of Cologne
      Köln, North Rhine-Westphalia, Germany