arXiv subjects

A. -M. S. Tremblay

Publications and source records attributed to A. -M. S. Tremblay.

At least 91 records · Page 5Linked to original sources

arXiv2012

Resilience of d-wave superconductivity to nearest-neighbor repulsion

Many theoretical approaches find d-wave superconductivity in the prototypical one-band Hubbard model for high-temperature superconductors. At strong-coupling (U > W, where U is the on-site repulsion and W=8t the bandwidth) pairing is controlled by the exchange energy J=4t^2/U. One may then surmise, ignoring retardation effects, that near-neighbor Coulomb repulsion V will destroy superconductivity when it becomes larger than J, a condition that is easily satisfied in cuprates for example. Using Cellular Dynamical Mean-Field theory with an exact diagonalization solver for the extended Hubbard model, we show that pairing, at strong coupling, is preserved even when V>>J, as long as V<U/2. While at weak coupling V always reduces the spin fluctuations and hence d-wave pairing, at strong coupling, in the underdoped regime, the increase of J=4t^2/(U-V) caused by V increases binding at low frequency while the pair-breaking effect of V is pushed to high frequency. These two effects compensate in the underdoped regime, in the presence of a pseudogap. While the pseudogap competes with superconductivity, the proximity to the Mott transition that leads to the pseudogap, and retardation effects, protect d-wave superconductivity from V.

cond-mat.supr-con↗

arXiv2012

Mott p-n Junctions in layered materials

The p-n junction has provided the basis for the semiconductor-device industry. Investigations of p-n junctions based on Mott insulators is still in its infancy. Layered Mott insulators, such as the cuprates or other transition metal-oxides, present a special challenge since strong in-plane correlations are important. Here we model the planes carefully using plaquette Cellular Dynamical Mean Field Theory with an exact diagonalization solver. The energy associated with inter-plane hopping is neglected compared with the long-range Coulomb interaction that we treat in the Hartree-Fock approximation. Within this new approach, "Dynamical Layer Theory", the charge redistribution is obtained at the final step from minimization of a function of the layer fillings. A simple analytical description of the solution, in the spirit of Thomas-Fermi theory, reproduces quite accurately the numerical results. Various interesting charge reconstructions can be obtained by varying the Fermi energy differences between both sides of the junction. One can even obtain quasi-two dimensional charge carriers at the interface, in the middle of a Mott insulating layer. The density of states as a function of position does not follow the simple band bending picture of semiconductors.

cond-mat.str-el↗

arXiv2012

c-axis resistivity, pseudogap, superconductivity and Widom line in doped Mott insulators

Layered doped Mott insulators, such as the cuprates, show unusual temperature dependence of the resistivity. Intriguingly, the resistivity perpendicular to the CuO$_2$ planes, $ρ_c(T)$, shows both metallic ($dρ_c/dT > 0$) and semi-conducting ($dρ_c/dT<0$) behavior. We shed light on this puzzle by calculating $ρ_c$ for the two-dimensional Hubbard model within plaquette cellular dynamical mean-field theory and strong-coupling continuous-time quantum Monte Carlo as the impurity solver. The temperature, $T$, and doping, $δ$, dependencies of $ρ_c$ are controlled by the first-order transition between pseudogap and correlated metal phases from which superconductivity can emerge. On the large doping side of the transition $ρ_c(T)$ is metallic, while on the low-doping side $ρ_c(T)$ changes from metallic to semi-conducting behavior with decreasing $T$. As a function of doping, the jump in $ρ_c$ across the first-order transition evolves into a sharp crossover at higher temperatures. This crossover coincides with the pseudogap temperature $T^*$ in the single-particle density of states, the spin susceptibility and other observables. Such coincidence in crossovers is expected along the continuation of the first-order transition into the super-critical regime, called the Widom line. This implies that not only the dynamic and the thermodynamic properties but also the DC transport in the normal state are governed by the hidden first-order transition. $ρ_c(T)$ has a high-temperature quasi-linear regime where it can exceed the Mott-Ioffe-Regel limit and when it has a minimum it is nearly parallel to the Widom line.

cond-mat.str-el↗

arXiv2012

Breakdown of Fermi liquid behavior at the (π,π)=2k_F spin-density wave quantum-critical point: the case of electron-doped cuprates

Many correlated materials display a quantum critical point between a paramagnetic and a SDW state. The SDW wave vector connects points (hot spots) on opposite sides of the Fermi surface. The Fermi velocities at these pairs of points are in general not parallel. Here we consider the case where pairs of hot spots coalesce, and the wave vector (π,π) of the SDW connects hot spots with parallel Fermi velocities. Using the specific example of electron-doped cuprates, we first show that Kanamori screening and generic features of the Lindhard function make this case experimentally relevant. The temperature dependence of the correlation length, the spin susceptibility and the self-energy at the hot spots are found using the Two-Particle-Self-Consistent theory and specific numerical examples worked out for parameters characteristic of the electron-doped cuprates. While the curvature of the Fermi surface at the hot spots leads to deviations from perfect nesting, the pseudo-nesting conditions lead to drastic modifications to the temperature dependence of these physical observables: Neglecting logarithmic corrections, the correlation length ξscales like 1/T, i.e. z=1 instead of the naive z=2, the (π,π) static spin susceptibility χlike $1/\sqrt T$, and the imaginary part of the self-energy at the hot spots like $T^{3/2}$. The correction $T_1^{-1}\sim T^{3/2}$ to the Korringa NMR relaxation rate is subdominant. We also consider this problem at zero temperature, or for frequencies larger than temperature, using a field-theoretical model of gapless SDW fluctuations interacting with fermions. The imaginary part of the fermionic self-energy close to the hot spots scales as $-ω^{3/2}\logω$. This is less singular than earlier predictions of the form $-ω\logω$. The difference arises from the effects of umklapp terms that were not included in previous studies.

cond-mat.str-el↗

arXiv2012

Entropy, frustration and large thermopower of doped Mott insulators on the fcc lattice

Electronic frustration and strong correlations may lead to large Seebeck coefficients. To understand this physics on general grounds, we compute the thermopower of the one-band Hubbard model on the 3-dimensional fcc lattice over the whole range of fillings for intermediate and large interaction strength. Dynamical mean-field theory shows that when the density approaches half-filling, the fcc lattice at strong coupling exhibits a large low temperature Seebeck coefficient $S$. The largest effect occurs as one approaches $n=1$ from dopings where electronic frustration is maximized. The high-frequency limit of the thermopower and the Kelvin limit are both used to provide physical insight as well as practical tools to estimate the thermopower. The high-frequency limit gives a reliable estimate of the DC limit at low temperature when the metal becomes coherent. By contrast, the Kelvin approach is useful in the strongly interacting case at high temperature when transport is incoherent. The latter result shows that in doped Mott insulators at high temperature and strong coupling the thermopower can be understood on entropic grounds.

cond-mat.str-el↗

arXiv2012

Optimal doping and entropic origin of giant thermopower in doped Mott insulators

This paper has been withdrawn by the authors because the results were incorrect due to the use of an impurity solver that fails at large interaction strength and above half-filling. This led, first, to the development of a new impurity solver (arXiv:1202.5814 or Phys.Rev. B 86, 085133 (2012)) and, second, to a complete revision of the thermopower results with different conclusions. Therefore a new paper on thermopower was submitted (arXiv:1209.4349) and the present one withdrawn.

cond-mat.str-el↗

arXiv2012

Pseudogap temperature as a Widom line in doped Mott insulators

The pseudogap refers to an enigmatic state of matter with unusual physical properties found below a characteristic temperature $T^*$ in hole-doped high-temperature superconductors. Determining $T^*$ is critical for understanding this state. Here we study the simplest model of correlated electron systems, the Hubbard model, with cluster dynamical mean-field theory to find out whether the pseudogap can occur solely because of strong coupling physics and short nonlocal correlations. We find that the pseudogap characteristic temperature $T^*$ is a sharp crossover between different dynamical regimes along a line of thermodynamic anomalies that appears above a first-order phase transition, the Widom line. The Widom line emanating from the critical endpoint of a first-order transition is thus the organizing principle for the pseudogap phase diagram of the cuprates. No additional broken symmetry is necessary to explain the phenomenon. Broken symmetry states appear in the pseudogap and not the other way around.

cond-mat.str-el↗

arXiv2012

Strong coupling superconductivity, pseudogap and Mott transition

An intricate interplay between superconductivity, pseudogap and Mott transition, either bandwidth driven or doping driven, occurs in materials. Layered organic conductors and cuprates offer two prime examples. We provide a unified perspective of this interplay in the two-dimensional Hubbard model within cellular dynamical mean-field theory on a $2\times 2$ plaquette and using the continuous-time quantum Monte Carlo method as impurity solver. Both at half filling and at finite doping, the metallic normal state close to the Mott insulator is unstable to d-wave superconductivity. Superconductivity can destroy the first-order transition that separates the pseudogap phase from the overdoped metal, yet that normal state transition leaves its marks on the dynamic properties of the superconducting phase. For example, as a function of doping one finds a rapid change in the particle-hole asymmetry of the superconducting density of states. In the doped Mott insulator, the dynamical mean-field superconducting transition temperature $T_c^d$ does not scale with the order parameter when there is a normal-state pseudogap. $T_c^d$ corresponds to the local pair formation temperature observed in tunneling experiments and is distinct from the pseudogap temperature.

cond-mat.str-el↗

arXiv2012

Benchmark of a modified Iterated Perturbation Theory approach on the 3d FCC lattice at strong coupling

The Dynamical Mean-Field theory (DMFT) approach to the Hubbard model requires a method to solve the problem of a quantum impurity in a bath of non-interacting electrons. Iterated Perturbation Theory (IPT) has proven its effectiveness as a solver in many cases of interest. Based on general principles and on comparisons with an essentially exact Continuous-Time Quantum Monte Carlo (CTQMC) solver, here we show that the standard implementation of IPT fails away from half-filling when the interaction strength is much larger than the bandwidth. We propose a slight modification to the IPT algorithm that replaces one of the equations by the requirement that double occupancy calculated with IPT gives the correct value. We call this method IPT-$D$. We recover the Fermi liquid ground state away from half-filling. The Fermi liquid parameters, density of states, chemical potential, energy and specific heat on the FCC lattice are calculated with both IPT-$D$ and CTQMC as benchmark examples. We also calculated the resistivity and the optical conductivity within IPT-$D$. Particle-hole asymmetry persists even at coupling twice the bandwidth. Several algorithms that speed up the calculations are described in appendices.

cond-mat.str-el↗

arXiv2011

Importance of subleading corrections for the Mott critical point

The interaction-induced metal-insulator transition should be in the Ising universality class. Experiments on layered organic superconductors suggest that the observed critical endpoint of the first-order Mott transition belongs instead to a different universality class. To address this question, we use dynamical mean-field theory and a cluster generalization that is necessary to account for short-range spatial correlations in two dimensions. Such calculations can give information on crossover effects, in particular quantum ones, that are not included in the simplest mean-field. In the cluster calculation, a canonical transformation that minimizes the sign problem in continuous-time quantum Monte Carlo calculations allows us to obtain very accurate results for double occupancy. These results show that there are important subleading corrections that can lead to apparent exponents that are different from mean-field. Experiments on optical lattices could verify our predictions.

cond-mat.str-el↗

arXiv2011

Two-Particle-Self-Consistent Approach for the Hubbard Model

Even at weak to intermediate coupling, the Hubbard model poses a formidable challenge. In two dimensions in particular, standard methods such as the Random Phase Approximation are no longer valid since they predict a finite temperature antiferromagnetic phase transition prohibited by the Mermin-Wagner theorem. The Two-Particle-Self-Consistent (TPSC) approach satisfies that theorem as well as particle conservation, the Pauli principle, the local moment and local charge sum rules. The self-energy formula does not assume a Migdal theorem. There is consistency between one- and two-particle quantities. Internal accuracy checks allow one to test the limits of validity of TPSC. Here I present a pedagogical review of TPSC along with a short summary of existing results and two case studies: a) the opening of a pseudogap in two dimensions when the correlation length is larger than the thermal de Broglie wavelength, and b) the conditions for the appearance of d-wave superconductivity in the two-dimensional Hubbard model.

cond-mat.str-el↗

arXiv2011

Optical and DC conductivity of the two-dimensional Hubbard model in the pseudogap regime and across the antiferromagnetic quantum critical point, including vertex corrections

The conductivity of the two-dimensional Hubbard model is particularly relevant for high-temperature superconductors. Vertex corrections are expected to be important because of strongly momentum dependent self-energies. We use the Two-Particle Self-Consistent approach that satisfies crucial constraints such as the Mermin-Wagner theorem, the Pauli principle and sum rules in order to reach non-perturbative regimes. This approach is reliable from weak to intermediate coupling. A functional derivative approach ensures that vertex corrections are included in a way that satisfies the f sum-rule. The two types of vertex corrections that we find are the antiferromagnetic analogs of the Maki-Thompson and Aslamasov-Larkin contributions of superconducting fluctuations to the conductivity but, contrary to the latter, they include non-perturbative effects. The resulting analytical expressions must be evaluated numerically. The calculations are impossible unless a number of advanced numerical algorithms are used. A maximum entropy approach is specially developed for analytical continuation of our results. The numerical results are for nearest neighbor hoppings. In the pseudogap regime induced by two-dimensional antiferromagnetic fluctuations, the effect of vertex corrections is dramatic. Without vertex corrections the resistivity increases as we enter the pseudogap regime. Adding vertex corrections leads to a drop in resistivity, as observed in some high temperature superconductors. At high temperature, the resistivity saturates at the Ioffe-Regel limit. At the quantum critical point and beyond, the resistivity displays both linear and quadratic temperature dependence and there is a correlation between the linear term and the superconducting transition temperature. A hump is observed in the mid-infrared range of the optical conductivity in the presence of antiferromagnetic fluctuations.

cond-mat.str-el↗

arXiv2011

Mott physics and first-order transition between two metals in the normal state phase diagram of the two-dimensional Hubbard model

For doped two-dimensional Mott insulators in their normal state, the challenge is to understand the evolution from a conventional metal at high doping to a strongly correlated metal near the Mott insulator at zero doping. To this end, we solve the cellular dynamical mean-field equations for the two-dimensional Hubbard model using a plaquette as the reference quantum impurity model and continuous-time quantum Monte Carlo method as impurity solver. The normal-state phase diagram as a function of interaction strength $U$, temperature $T$, and filling $n$ shows that, upon increasing $n$ towards the Mott insulator, there is a surface of first-order transition between two metals at nonzero doping. That surface ends at a finite temperature critical line originating at the half-filled Mott critical point. Associated with this transition, there is a maximum in scattering rate as well as thermodynamic signatures. These findings suggest a new scenario for the normal-state phase diagram of the high temperature superconductors. The criticality surmised in these systems can originate not from a T=0 quantum critical point, nor from the proximity of a long-range ordered phase, but from a low temperature transition between two types of metals at finite doping. The influence of Mott physics therefore extends well beyond half-filling.

cond-mat.str-el↗

arXiv2011

d-Wave superconductivity on the checkerboard Hubbard model at weak and strong coupling

It has been argued that inhomogeneity generally can enhance superconductivity in the cuprate high-Tc materials. To check the validity of this claim, we study d-wave superconductivity on the checkerboard Hubbard model on a square lattice using the Cellular Dynamical Mean Field theory method with an exact diagonalization solver at zero temperature. The d-wave order parameter is computed for various inhomogeneity levels over the entire doping range of interest in both strong and weak coupling regimes. At a given doping, the size of the d-wave order parameter manifests itself directly in the height of the coherence peaks and hence is an appropriate measure of the strength of superconductivity. The weak coupling results reveal a suppression of the order parameter in the presence of inhomogeneity for small to intermediate hole dopings, while it is enhanced for large dopings. In contrast, for strong coupling there is a monotonic decrease in the maximum amplitude of the superconducting order parameter with inhomogeneity over the entire doping range of interest. Furthermore, at moderately high inhomogeneity, the system undergoes a first-order transition from the superconducting to the normal state in the underdoped regime. In the overdoped regime, the change in the value of the superconducting order parameter correlates with the height of the lowest energy peak in the spectral weight of antiferromagnetic spin fluctuations, confirming the connection between antiferromagnetic fluctuations and d-wave superconductivity found in earlier studies on the homogeneous case. Our results are benchmarked by comparisons with numerically exact results on the checkerboard Hubbard ladder.

cond-mat.supr-con↗

arXiv2010

Dynamical electronic nematicity from Mott physics

Very large anisotropies in transport quantities have been observed in the presence of very small in-plane structural anisotropy in many strongly correlated electron materials. By studying the two-dimensional Hubbard model with dynamical-mean-field theory for clusters, we show that such large anisotropies can be induced without static stripe order if the interaction is large enough to yield a Mott transition. Anisotropy decreases at large frequency. The maximum effect on conductivity anisotropy occurs in the underdoped regime, as observed in high temperature superconductors.

cond-mat.str-el↗

arXiv2010

Generalized DC and AC Josephson effects in antiferromagnets and in antiferromagnetic d-wave superconductors

The Josephson effect is generally described as Cooper pair tunneling, but it can also be understood in a more general context. The DC Josephson effect is the pseudo-Goldstone boson of two coupled systems with a broken continuous abelian U(1) symmetry. Hence, an analog should exist for systems with broken continuous non-Abelian symmetries. To exhibit the generality of the phenomenon and make predictions from a realistic model, we study tunneling between antiferromagnets and also between antiferromagnetic d-wave superconductors. Performing a calculation analogous to that of Ambegaokar and Baratoff for the Josephson junction, we find an equilibrium current of the staggered magnetization through the junction that, in antiferromagnets, is proportional to s_L X s_R where s_L and s_R are the Neel vectors on either sides of the junction. Microscopically, this effect exists because of the coherent tunneling of spin-one particle-hole pairs. In the presence of a magnetic field which is different on either sides of the junction, we find an analog of the AC Josephson effect where the angle between Neel vectors depends on time. In the case of antiferromagnetic d-wave superconductors we predict that there is a contribution to the critical current that depends on the antiferromagnetic order and a contribution to the spin-critical current that depends on superconducting order. The latter contributions come from tunneling of the triplet Cooper pair that is necessarily present in the ground state of an antiferromagnetic d-wave superconductor. All these effects appear to leading order in the square of the tunneling matrix elements.

cond-mat.mes-hall↗

arXiv2010

Finite doping signatures of the Mott transition in the two-dimensional Hubbard model

Experiments on layered materials call for a study of the influence of short-range spin correlations on the Mott transition. To this end, we solve the cluster dynamical mean-field equations for the Hubbard model on a plaquette with continuous-time quantum Monte Carlo. The normal state phase diagram as a function of temperature $T$, interaction strength $U$ and filling $n$ reveals that upon increasing $n$ towards the insulator, there is a surface of first-order transition between two metals at non-zero doping. For $T$ above the critical end line there is a maximum in scattering rate.

cond-mat.str-el↗

arXiv2009

Mixed pairing symmetry in κ-(BEDT-TTF)_2 X organic superconductors from ultrasonic velocity measurements

Discontinuities in elastic constants are detected at the superconducting transition of layered organic conductors κ-(BEDT-TTF)_{2}X by longitudinal and transverse ultrasonic velocity measurements. Symmetry arguments show that discontinuities in shear elastic constants can be explained in the orthorhombic compound only if the superconducting order parameter has a mixed character that can be of two types, either A_{1g}+B_{1g} or B_{2g}+B_{3g} in the classification of irreducible representations of the orthorhombic point group D_{2h}. Consistency with other measurements suggests that the A_{1g}+B_{1g} (d_{xy}+d_{z(x+y)}) possibility is realized. Such clear symmetry-imposed signatures of mixed order parameters have not been observed in other superconducting compounds.

cond-mat.supr-con↗