arXiv subjects
Publications and source records attributed to R. Combescot.
We investigate, mostly analytically, the nature of the Fulde-Ferrell- Larkin-Ovchinnikov superfluid phases for an isotropic two-dimensional superconductor, which is relevant for the experimental observation of these phases. We show that there is, in the low temperature range, a cascade of transitions toward order parameters with ever increasing complexity.
We consider a dense ultracold Fermi gas in the presence of a Feshbach resonance. We investigate how the treshold for bound state formation, which is just at the Feshbach resonance for a dilute gas, is modified due to the presence of the Fermi sea. We make use of a preceding framework of handling this many-body problem. We restrict ourselves to the simple case where the chemical potential $ μ$ is negative, which allows us to cover in particular the classical limit where the effect is seen to disappear. We show that, within a simple approach where basically only the effect of Pauli exclusion is included, the Fermi sea produces a large shift of the threshold, which is of order of the width of the Feshbach resonance. This is in agreement with very recent experimental findings.
We consider two regimes where a trapped Bose gas behaves as a one-dimensional system. In the first one the Bose gas is microscopically described by 3D mean field theory, but the trap is so elongated that it behaves as a 1D gas with respect to low frequency collective modes. In the second regime we assume that the 1D gas is truly 1D and that it is properly described by the Lieb-Liniger model. In both regimes we find the frequency of the lowest compressional mode by solving the hydrodynamic equations. This is done by making use of a method which allows to find analytical or quasi-analytical solutions of these equations for a large class of models approaching very closely the actual equation of state of the Bose gas. We find an excellent agreement with the recent results of Menotti and Stringari obtained from a sum rule approach.
We propose a coherent framework allowing to deal with many-body effects in dense ultracold Fermi gases in the presence of a Feshbach resonance. We show that the simple effect of Pauli exclusion induces a strong modification of the basic scattering properties, leading in particular to an energy dependence of the effective scattering length on the scale of the chemical potential. This results in a smearing of the Feshbach resonance and provides a natural explanation for recent experimental findings.
We explore analytically the nature of the transition to the Fulde-Ferrel-Larkin-Ovchinnikov superfluid phases in the vicinity of the tricritical point, where these phases begin to appear. We make use of an expansion of the free energy up to an overall sixth order, both in order parameter amplitude and in wavevector. We first explore the minimization of this free energy within a subspace, made of arbitrary superpositions of plane waves with wavevectors of different orientations but same modulus. We show that the standard second order FFLO phase transition is unstable and that a first order transition occurs at higher temperature. Within this subspace we prove that it is favorable to have a real order parameter and that, among these states, those with the smallest number of plane waves are prefered. This leads to an order parameter with a $\cos({\bf q}_{0}. {\bf r})$ dependence, in agreement with preceding work. Finally we show that the order parameter at the transition is only very slightly modified by higher harmonics contributions when the constraint of working within the above subspace is released.
We consider the hydrodynamic modes for dense trapped ultracold gases, where the interparticle distance is comparable to the scattering length. We show that the experimental determination of the hydrodynamic mode frequencies allows to obtain quite directly the equation of state of a dense gas. As an example we investigate the case of two equal fermionic populations in different hyperfine states with attractive interaction and in particular the vicinity of the collapse.
We consider the existence of a BCS superfluid phase in $^{6}$Li due to the pairing of two hyperfine states with unequal number of atoms. We show that the domain of existence for this phase will be increased to a very large extent in the vicinity of the threshold for collapse. This is due to the presence of a new phase with anisotropic order parameter. This phase is induced by the anisotropic part of the scattering, linked to the indirect interaction between atoms through density fluctuation exchange.
We investigate a simple explanation for the high maximum gap to $T_{c}$ ratio found experimentally in high $T_{c}$ compounds. We ascribe this observation to the lowering of $T_{c}$ by boson scattering of electrons between parts of the Fermi surface with opposite sign for the order parameter. We study the simplest possible model within this picture. Our quantitative results show that we can account for experiment for a rather small value of the coupling constant, all the other ingredients of our model being already known to exist in these compounds. A striking implication of this theory is the fairly high value of the critical temperature in the absence of boson scattering.
We consider the effect of the indirect interaction due to the exchange of density fluctuations on the critical temperature of superfluid $^{6}$Li . We obtain the strong coupling equation giving this critical temperature. This equation is solved approximately by retaining the same set of diagrams as in the paramagnon model. We show that, near the instability threshold, the attractive interaction due to density fluctuations gives rise to a strong increase in the critical temperature, providing a clear signature of the existence of fluctuation induced interactions.
Electronic Raman scattering measurements have been performed on $HgBa_{2}Ca_{2}Cu_{3}O_{8+δ} $ single crystals in the superconducting state. Pure electronic Raman spectra with no phonon structures hindering the analysis of the electronic continuum have been obtained. As a consequence, the spectra in the pure $B_{1g} $ and $B_{2g} $ symmetries are directly and reliably analyzed and the pure $A_{1g} $ contribution can be easily identified. Below the critical temperature $T_{c}, $ two electronic structures at $2Δ\sim 6.4 k_{B}T_{c} $ and $2Δ\sim 9.4 $ $k_{B}T_{c} $ are clearly seen. Both are observed simultaneously in pure $A_{1g} $ symmetry, the highest energy one being located at the energy of the $B_{1g} $ maximum. These two maxima disappear at $T_{c} $ and do not soften significantly as the temperature is raised up to $T_{c}. $ The low energy frequency dependence of the $B_{1g} $ electronic response is strongly linear, for various excitation lines in the 476.5 to 647.1 nm range. Such experimental data cannot be reconciled with a pure $d_{x^{2}-y^{2}} $ symmetry. Instead, they strongly advocate in favor of an anisotropic superconducting gap with two distinct gap maxima and of nodes existing outside the [110] and [1,$\bar{1}$,0] directions in {\bf k}-space. We discuss in detail the simplest order parameter compatible with our experimental findings.
For a completely general anisotropic order parameter (including changes of sign), we show that weak coupling theory is incompatible with high values of the maximum Δ_{M} of the zero temperature gap as compared to the critical temperature T_{c}, such as those found experimentally in Bi_{2}Sr_{2}CaCu_{2}O_{8+δ} where 2 Δ_{M} / T_{c} \approx 7.5 . This gives evidence for strong coupling effects. In particular this comes as a major support for a spin fluctuation mechanism with strong coupling, if one assumes that only a repulsive pairing interaction is at work in high T_{c} superconductors.
We propose an extension to other high T_{c } compounds of a model introduced earlier for YBCO. In the ''self-doped'' compounds we assume that the doping part (namely the BiO, HgO, TlO planes in BSCCO, HBCCO, TBCCO respectively) is metallic, which leads to a multiband model. This assumption is supported by band structure calculations. Taking a repulsive pairing interaction between these doping bands and the CuO_{2} bands leads to opposite signs for the order parameter on these bands and to nodes whenever the Fermi surfaces of these bands cross. We show that in BSCCO the low temperature dependence of the penetration depth is reasonably accounted for. In this case the nodes are not located near the 45^{o} direction, which makes the experimental determination of the node locations an important test for our model. The situation in HBCCO and TBCCO is rather analogous to BSCCO. We consider the indications given by NMR and find that they rather favor a metallic character for the doping bands. Finally we discuss the cases of NCCO and LSCO which are not ''self-doped'' and where our model does not give nodes.
We have studied the penetration depth for a model of $YBa_{2}Cu_{3}O_{7}$ involving pairing both in the $CuO_{2}$ planes and in the CuO chains. In this model pairing in the planes is due to an attractive interaction, while Coulomb repulsion induces in the chains an order parameter with opposite sign. Due to the anticrossing produced by hybridization between planes and chains, one obtains a d-wave like order parameter which changes sign on a single sheet of the Fermi surface and has nodes in the gap. We find that our model accounts quite well for the anisotropy of the penetration depth and for the absolute values. We reproduce fairly well the whole temperature dependence for both the a and the b directions, including the linear dependence at low temperature. We use a set of parameters which are all quite reasonable physically. Our results for the c direction are also satisfactory, although the situation is less clear both experimentally and theoretically.
Pure electronic Raman spectra with no phonon structures superimposed to the electronic continuum, are reported for the first time, in optimally doped $HgBa_{2}CaCu_{2}O_{6+δ} $ single crystals $(T_{c }=126 $ K). Our low temperature spectra (15 K) for the $A_{1g}$, $B_{1g} $ and $B_{2g} $ symmetries exhibit striking differences with previous data in $Bi_{2}Sr_{2}CaCu_{2}O_{8+δ}. $ The shape of the spectra for the various symmetries cannot be fitted by Devereaux's $d_{x^{2}-y^{2}} $ calculations, but strongly suggests a $d_{x y } $ gap, with its minima in the [100] and [010] directions.
We have studied the effect of impurities on $T_{c}$ for a model of YBCO involving pairing both in the CuO$_{2}$ planes and in the CuO chains. In this model pairing in the planes is due to phonons, while Coulomb repulsion induces in the chains an order parameter with opposite sign. Due to the anticrossing produced by hybridization between planes and chains, the order parameter changes sign on a single sheet of the Fermi surface resulting in nodes in the gap. We find that $T_{c}$ is much less sensitive to impurities than in standard d-wave models. One reason is that impurities produce essentially plane-plane and chain-chain scattering, which does not affect the critical temperature. $T_{c } $ is reduced by plane-chain scattering, which is smaller by a factor of order hybridization coupling over Fermi energy. In the specific case which we have studied in details and which reduces to the two-band model, we have found a further reduction of the sensitivity of $T_{c}$ to impurities with a behaviour which can vary continuously from s-wave like to d-wave like depending on the parameters. We expect a similar reduction to occur in the general case.
We proceed to a systematic exploration of the low temperature dependence of the London penetration depth of isotropic superconductors within strong coupling theory in the clean limit. For a sizeable range of parameters, we find that strong coupling effects can reasonably simulate a power law dependence, sometimes with an excellent precision. In such cases it would be quite difficult to distinguish experimentally between a pure power law and the strong coupling result. Physically we have been able to ascribe this temperature dependence to low frequency phonons which produce a quasi elastic scattering for electrons. The presence of these low frequency phonons requires rather wide phonon spectra and their effectiveness in scattering implies fairly strong coupling.
We calculate the optical conductivity of superconductors in the strong-coupling limit. In this anomalous limit the typical energy scale is set by the coupling energy, and other energy scales such as the energy of the bosons mediating the attraction are negligibly small. We find a universal frequency dependence of the optical absorption which is dominated by bound states and differs significantly from the weak coupling results. A comparison with absorption spectra of superconductors with enhanced electron-phonon coupling shows that typical features of the strong-coupling limit are already present at intermediate coupling.
We have measured the penetration depth $λ(T)$ on $\rm YBa_{2}Cu_{3}O_{7}$ thin films from transmission at 120, 330 and 510~GHz, between 5 and 50~K. Our data yield simultaneously the absolute value and the temperature dependence of $λ(T)$. In high quality films $λ(T)$ exhibits the same linear temperature dependence as single crystals, showing its intrinsic nature, and $λ(0)=1750\,{\rm Å}$. In a lower quality one, the more usual $T^2$ dependence is found, and $λ(0)=3600\,{\rm Å}$. This suggests that the $T^2$ variation is of extrinsic origin. Our results put the $d$-wave like interpretation in a much better position.