Self-consistent T-matrix Approximation Research Articles

Simulating superconducting properties of overdoped cuprates: The role of inhomogeneity

Theoretical studies of disordered $d$-wave superconductors have focused, with a few exceptions, on optimally doped models with strong scatterers. Addressing recent controversies about the nature of the overdoped cuprates, however, requires studies of the weaker scattering associated with dopant atoms. Here we study simple models of such systems in the self-consistent Bogoliubov-de Gennes (BdG) framework, and compare to disorder-averaged results using the self-consistent-T-matrix-approximation (SCTMA). Despite surprisingly linear in energy behavior of the low-energy density of states even for quite disordered systems, the superfluid density in such cases retains a quadratic low-temperature variation of the penetration depth, unlike other BdG results reported recently. We trace the discrepancy to smaller effective system size employed in that work. Overall, the SCTMA performs remarkably well, with the exception of highly disordered systems with strongly suppressed superfluid density. We explore this interesting region where gap inhomogeneity dominates measured superconducting properties, and compare with overdoped cuprates.

Isothermal compressibility and effects of multibody molecular interactions in a strongly interacting ultracold Fermi gas

We theoretically investigate the isothermal compressibility $\kappa_{T}$ in the normal state of an ultracold Fermi gas. Including pairing fluctuations, as well as preformed-pair formations, within the framework of the self-consistent $T$-matrix approximation (SCTMA), we evaluate the temperature dependence of this thermodynamic quantity over the entire BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. While $\kappa_T$ in the weak-coupling BCS regime is dominated by Fermi atoms near the Fermi surface, correlations between tightly bound Cooper-pair molecules are found to play crucial roles in the strong-coupling BEC regime. In the latter region, besides a two-body molecular interaction, a three-body one is shown to sizably affect $\kappa_T$ near the superfluid phase transition temperature. Our results indicate that the strong-coupling BEC regime of an ultracold Fermi gas would provide a unique opportunity to study multi-body correlations between Cooper-pair molecules.

Theory of huge thermoelectric effect based on a magnon drag mechanism: Application to thin-film Heusler alloy

To understand the unexpectedly high thermoelectric performance observed in the thin-film Heusler alloy Fe$_2$V$_{0.8}$W$_{0.2}$Al, we study the magnon drag effect, generated by the tungsten based impurity band, as a possible source of this enhancement, in analogy to the phonon drag observed in FeSb$_2$. Assuming that the thin-film Heusler alloy has a conduction band integrating with the impurity band, originated by the tungsten substitution, we derive the electrical conductivity $L_{11}$ based on the self-consistent t-matrix approximation and the thermoelectric conductivity $L_{12}$ due to magnon drag, based on the linear response theory, and estimate the temperature dependent electrical resistivity, Seebeck coefficient and power factor. Finally, we compare the theoretical results with the experimental results of the thin-film Heusler alloy to show that the origin of the exceptional thermoelectric properties is likely to be due to the magnon drag related with the tungsten-based impurity band.

Doping-controlled surface conduction in topological insulators with warping effects

Based on a self-consistent t-matrix approximation, we explore the influence of magnetic and nonmagnetic doping on the surface electronic states and conductivity of topological insulators. We show that warping parameter has a crucial impact on the density of states and dc conductivity of the doped surfaces. As the warping strength is increased, the surface density of states at high energies is suppressed and the resonant states induced by impurities in the vicinity of the Dirac point gradually disappear. It is found that nonmagnetic impurities break electron-hole symmetry at low warping strength, while the symmetry remains unchanged when the surface is magnetically doped. Our findings reveal that surface conductivity can be controlled by tuning the doping, the direction of external magnetic field and that of impurity magnetic moments. Also, the surface conductivity features in topological insulators with warped energy dispersions are not significantly affected by the presence of impurities compared to that of materials with circular energy contour.

Self-consistent T-matrix approach to gap renormalization in quantum magnets with bond disorder

The analytical theory of density of states (DOS) in three-dimensional quantum magnets with the bond disorder is proposed based on the self-consistent T-matrix approximation (SCTMA). It successfully describes the DOS both for resonant and non-resonant scattering, whose emergence is governed by the ratio of scattering length and the average distance between impurities, which concentration is denoted as c. Corrections to the quasiparticle band gap in these cases are shown to scale as c2/3 and c, respectively. Moreover, the theory yields a semi-circle form of the DOS for the bound states inside the gap, which results in highly nontrivial DOS in the intermediate parameter region between the two limiting cases when the band DOS and the semi-circle overlap. Long-wavelength excitations are discussed. In the resonant regime their damping scales as c2/3, which, according to Ioffe-Regel criterion, corresponds to their localization. Applicability of the theory is illustrated by its quantitative agreement with the recent experimental data on spin-dimer system Ba3−xSrxCr2O8.

Numerical study of disorder on the orbital magnetization in two dimensions

The modern theory of orbital magnetization (OM) was developed by using Wannier function method, which has a formalism similar with the Berry phase. In this manuscript, we perform a numerical study on the fate of the OM under disorder, by using this method on the Haldane model in two dimensions, which can be tuned between a normal insulator or a Chern insulator at half filling. The effects of increasing disorder on OM for both cases are simulated. Energy renormalization shifts are observed in the weak disorder regime and topologically trivial case, which was predicted by a self-consistent T-matrix approximation. Besides this, two other phenomena can be seen. One is the localization trend of the band orbital magnetization. The other is the remarkable contribution from topological chiral states arising from nonzero Chern number or large value of integrated Berry curvature. If the fermi energy is fixed at the gap center of the clean system, there is an enhancement of |M| at the intermediate disorder, for both cases of normal and Chern insulators, which can be attributed to the disorder induced topological metal state before localization.

Isothermal Compressibility of an Ultracold Fermi Gas in the BCS–BEC Crossover

We theoretically investigate the isothermal compressibility $$\kappa _{\mathrm{T}}$$ in the normal state of an ultracold Fermi gas with a tunable attractive interaction. We calculate this thermodynamic quantity by considering fluctuations in the Cooper channel, within the framework of the self-consistent T-matrix approximation (SCTMA). For comparison, we also evaluate this quantity in a “non”-self-consistent T-matrix approximation (TMA). We show that the calculated $$\kappa _{\mathrm{T}}$$ diverges at $$T_{\mathrm{c}}$$ in the BCS–BEC crossover region. On the other hand, such a singular behavior is absent when we deal with this quantity in SCTMA. We point out that the origin of this difference is the neglect of an effective inter-pair interaction in the former approximation. We also explicitly show how such an interaction is involved in the theory when one deals with pairing fluctuations in SCTMA. Our results indicate that the isothermal compressibility is a useful quantity in considering how preformed Cooper pairs interact with one another in the BCS–BEC crossover regime of an ultracold Fermi gas.

Erratum: Disorder and superfluid density in overdoped cuprate superconductors [Phys. Rev. B 96, 024501 (2017)

We calculate superfluid density for a dirty d-wave superconductor. The effects of impurity scattering are treated within the self-consistent t-matrix approximation, in weak-coupling BCS theory. Working from a realistic tight-binding parameterization of the Fermi surface, we find a superfluid density that is both correlated with T_c and linear in temperature, in good correspondence with recent experiments on overdoped La2-xSrxCuO4.

Pairing fluctuations in a strongly interacting two-dimensional Fermi gas

We theoretically investigate strong-coupling properties of a two-dimensional Fermi gas in the normal phase. Including pairing fluctuations within the framework of a self-consistent T-matrix approximation, we calculate the single-particle density of states (DOS) near the observed Berezinskii-Kosterlitz-Thouless phase transition temperature TBKT. We show that the pseudogap phenomenon associated with strong pairing fluctuations appears as an almost fully gapped single-particle density of states in the strong-coupling regime, indicating that amplitude fluctuations of the order parameter are almost absent and the system is dominated by phase fluctuations of the order parameter, as expected in a two-dimensional system near TBKT. On the other hand, although pairing fluctuations are enhanced by the low-dimensionality of the system, they are found to be still not strong enough to open such a full gap in the intermediate coupling (crossover) regime. In this regime, a dip structure is only seen in DOS around ω = 0, indicating that amplitude of the superfluid order parameter is also fluctuating, in addition to phase fluctuations. In theoretically determining TBKT in a two-dimensional Fermi gas, it is frequently assumed that, while phase fluctuations exist, the amplitude of the superfluid order parameter is fixed. However, our results indicate the necessity of including both amplitude and phase fluctuations of the order parameter in evaluating TBKT in the crossover region. Since the BKT phase transition has recently been reported in a two-dimensional 6Li Fermi gas, our results would be useful for the theoretical study of this observed novel Fermi superfluid and effects of strong low-dimensional pairing fluctuations.

Possible High Thermoelectric Power in Semiconducting Carbon Nanotubes ∼A Case Study of Doped One-Dimensional Semiconductors∼

We have theoretically investigated the thermoelectric properties of impurity-doped one-dimensional semiconductors, focusing on nitrogen-substituted (N-substituted) carbon nanotubes (CNTs), using the Kubo formula combined with a self-consistent t-matrix approximation. N-substituted CNTs exhibit extremely high thermoelectric power factor (PF) values originating from a characteristic of one-dimensional materials where decrease in the carrier density increase both the electrical conductivity and the Seebeck coefficient in the low-N regime. The chemical potential dependence of the PF values of semiconducting CNTs has also been studied as a field-effect transistor and it turns out that the PF values show a noticeable maximum in the vicinity of the band edges. This result demonstrates that “band-edge engineering” will be crucial for solid development of high-performance thermoelectric materials.

Pseudogap Phenomena Near the BKT Transition of a Two-Dimensional Ultracold Fermi Gas in the Crossover Region

We investigate strong-coupling properties of a two-dimensional ultracold Fermi gas in the normal phase. In the three-dimensional case, it has been shown that the so-called pseudogap phenomena can be well described by a (non-self-consistent) $T$-matrix approximation (TMA). In the two-dimensional case, while this strong coupling theory can explain the pseudogap phenomenon in the strong-coupling regime, it unphysically gives large pseudogap size in the crossover region, as well as in the weak-coupling regime. We show that this difficulty can be overcome when one improve TMA to include higher order pairing fluctuations within the framework of a self-consistent $T$-matrix approximation (SCTMA). The essence of this improvement is also explained. Since the observation of the BKT transition has recently been reported in a two-dimensional $^6$Li Fermi gas, our results would be useful for the study of strong-coupling physics associated with this quasi-long-range order.

Self-consistent T-matrix approach to Bose-glass in one dimension

Based on the self-consistent T-matrix approximation (SCTMA), the Mott insulator – Bose-glass phase transition of one-dimensional noninteracting bosons subject to binary disorder is considered. The results obtained differ essentially from the conventional case of box distribution of the disorder. The Mott insulator – Bose-glass transition is found to exist at arbitrary strength of the impurities. The single particle density of states is calculated within the frame of SCTMA, numerically, and (for infinite disorder strength) analytically. A good agreement is reported among all three methods. We speculate that certain types of the interaction may lead to the Bose-glass – superfluid transition absent in our theory.

Hetero-pairing and pseudogap phenomena in an ultracold Fermi gas with mass imbalance

We investigate strong-coupling properties of a unitary Fermi gas consisting of two different species with different masses. Including pairing fluctuations within the self-consistent T-matrix approximation, we calculate the single-particle density of states in the normal state. We show that the pseudogap phenomenon, which is characterized by a dip structure in the density of states around ω = 0, appears more remarkably in the light mass component than in the heavy mass component. As a result, the pseudogap temperature, which is determined as the temperature at which the pseudogap disappears in the density of states, is higher in the former than in the latter. We also find that this different pseudogap temperatures lead to the existence of two kinds of pseudogap regions. That is, one is the ordinary pseudogap regime where the pseudogap appears in both the component, and the other case is that the light mass component only exhibits the pseudogap phenomenon. As the origin of these component- dependent pseudogap phenomena, we point out the importance of different Fermi temperatures between the two components. Since the formation of hetero-Cooper pairs and their condensation are expected in various systems, such as a 6Li-40K Fermi gas mixture, an exciton (polariton) gas, as well as color superconductivity, our results would be useful for the understanding of strong-coupling properties of these novel Fermi condensates.

Density of states in graphene with vacancies: midgap power law and frozen multifractality.

The density of states ϱ(E) of graphene is investigated numerically and within the self-consistent T-matrix approximation in the presence of vacancies within the tight binding model. The focus is on compensated disorder, where the concentration of vacancies n(A) and n(B) in both sublattices is the same. Formally, this model belongs to the chiral symmetry class BDI. The onlinear sigma model predicts for BDI a Gade-type singularity ϱ(E)∼|E|(-1)exp[-|log(E)|(-1/x)]. Our numerical data are comparable to this result in a preasymptotic regime that gives way, however, at even lower energies to ϱ(E)∼E(-1)|log(E)|(-x̃), 1≤x̃<2. We take this finding as evidence that, similar to the case of dirty d-wave superconductors, generic bipartite random hopping models may also exhibit unconventional (strong-coupling) fixed points for certain kinds of randomly placed scatterers if these are strong enough. Our research suggests that graphene with (effective) vacancy disorder is a physical representative of such systems.

Heteropairing and component-dependent pseudogap phenomena in an ultracold Fermi gas with different species with different masses

We investigate the superfluid phase transition and single-particle excitations in the BCS (Bareen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas with mass imbalance. In our recent paper [R. Hanai, et. al., Phys. Rev. A 88, 053621 (2013)], we showed that an extended $T$-matrix approximation (ETMA) can overcome the serious problem known in the ordinary (non-self-consistent) $T$-matrix approximation that it unphysically gives double-valued superfluid phase transition temperature $T_{\rm c}$ in the presence of mass imbalance. However, at the same time, the ETMA was also found to give the vanishing $T_{\rm c}$ in the weak-coupling and highly mass-imbalanced case. In this paper, we inspect the correctness of this ETMA result, using the self-consistent $T$-matrix approximation (SCTMA). We show that the vanishing $T_{\rm c}$ is an artifact of the ETMA, coming from an internal inconsistency of this theory. The superfluid phase transition actually always occurs, irrespective of the ratio of mass imbalance. We also apply the SCTMA to the pseudogap problem in a mass-imbalanced Fermi gas. We show that pairing fluctuations induce different pseudogap phenomena between the the light component and heavy component. We also point out that a $^6$Li-$^{40}$K mixture is a useful system for the realization of a hetero pairing state, as well as for the study of component-dependent pseudogap phenomena.

Impurity effects in quasiparticle spectrum of high-Tc superconductors (Review Article)

The revision is made of Green function methods that describe the dynamics of electronic quasiparticles in disordered superconducting systems with d-wave symmetry of order parameter. Various types of impurity perturbations are analyzed within the simplest T-matrix approximation. The extension of the common self-consistent T-matrix approximation (SCTMA) to the so-called group expansions in clusters of interacting impurity centers is discussed and hence the validity criteria for SCTMA are established. A special attention is paid to the formation of impurity resonance states and localized states near the characteristic points of energy spectrum, corresponding to nodal points on the Fermi surface.

Statistics of the subgap states ofs±superconductors

There is strong support in favor of an unusual $s_{\pm}$ superconducting state in the new iron-based superconductors, in which the gap parameter has opposite signs in different bands. In this case scattering between different bands by impurities has a pair-breaking effect and introduces states inside the gap. We studied the statistics of disorder-induced subgap states in $s_{\pm}$ superconductors due to collective effects of impurities. Numerically solving the two-band Bogolyubov equations, we explored the behavior of the density of states and localization length. We located the mobility edge separating the localized and delocalized states for the 3D case and the crossover between the weak and strong localization regimes for the 2D case. We found that the widely used self-consistent T-matrix approximation is not very accurate in describing subgap states.

Disorder Effects on the Intrinsic Nonlinear Current Density in ${\rm YBa}_{2}{\rm Cu}_{3}{\rm O}_{7-\delta}$

We present harmonic generation measurements of the intrinsic nonlinear current density j <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> of YBa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7-delta</sub> (YBCO) films at temperatures close the T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> . Experiments on a range of different quality samples allow us to extract the dependence of j <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> on the penetration depth of the superconductor. In order to model these results, we calculate the intrinsic nonlinear current response of d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-y</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> -wave superconductors in the Meissner regime in the presence of nonmagnetic impurities within the self-consistent T-matrix approximation.

Entropy of a correlated system of nucleons

Realistic nucleon-nucleon interactions induce correlations to the nuclear many-body system, which lead to a fragmentation of the single-particle strength over a wide range of energies and momenta. We address the question of how this fragmentation affects the thermodynamical properties of nuclear matter. In particular, we show that the entropy can be computed with the help of a spectral function, which can be evaluated in terms of the self-energy obtained in the self-consistent Green's function approach. Results for the density and temperature dependences of the entropy per particle for symmetric nuclear matter are presented and compared to the results of lowest order finite-temperature Brueckner-Hartree-Fock calculations. The effects of correlations on the calculated entropy are small, if the appropriate quasiparticle approximation is used. The results demonstrate the thermodynamical consistency of the self-consistent T-matrix approximation for the evaluation of the Green's functions.

Theory of Transport Properties in the p-Wave Superconducting State of Sr2RuO4 –A Microscopic Determination of the Gap Structure–

We provide a detailed quantitative analysis of transport properties in the p-wave superconducting state of Sr2RuO4. Specifically, we calculate ultrasound attenuation rate and electronic thermal conductivity within the mean field approximation. The impurity scattering of the quasi-particles are treated within the self-consistent T-matrix approximation, and assumed to be in the unitarity limit. The momentum dependence of the gap function is determined by solving the Eliashberg equation for a three-band Hubbard model with the realistic electronic structure of Sr2RuO4. On the basis of the microscopic theory, we can naturally expect nodal structures along the c-axis on the cylindrical Fermi surfaces, even if we assume the chiral pairing state (i.e., \Delta(k) \sim k_x \pm {\rm i} k_y). Consequently, we obtain the temperature dependence of the transport coefficients in agreement with the experimental results. We can clarify that actually the thermal excitations on the passively superconducting bands contribute significantly to the thermal conductivity in a wide temperature range, in contrast to the case of other physical quantities.