Conventional Mean-field Theory Research Articles

Ion filling of a one-dimensional nanofluidic channel in the interaction confinement regime.

Ion transport measurements are widely used as an indirect probe for various properties of confined electrolytes. It is generally assumed that the ion concentration in a nanoscale channel is equal to the ion concentration in the macroscopic reservoirs it connects to, with deviations arising only in the presence of surface charges on the channel walls. Here, we show that this assumption may break down even in a neutral channel due to electrostatic correlations between the ions arising in the regime of interaction confinement, where Coulomb interactions are reinforced due to the presence of the channel walls. We focus on a one-dimensional channel geometry, where an exact evaluation of the electrolyte's partition function is possible with a transfer operator approach. Our exact solution reveals that in nanometer-scale channels, the ion concentration is generally lower than in reservoirs and depends continuously on the bulk salt concentration, in contrast to the conventional mean-field theory that predicts an abrupt filling transition. We develop a modified mean-field theory taking into account the presence of ion pairs that agrees quantitatively with the exact solution and provides predictions for experimentally relevant observables, such as the ionic conductivity. Our results will guide the interpretation of nanoscale ion transport measurements.

Puddle formation and persistent gaps across the non-mean-field breakdown of superconductivity in overdoped (Pb,Bi)2Sr2CuO6+δ

The cuprate high-temperature superconductors exhibit many unexplained electronic phases, but the superconductivity at high doping is often believed to be governed by conventional mean-field Bardeen–Cooper–Schrieffer theory1. However, it was shown that the superfluid density vanishes when the transition temperature goes to zero2,3, in contradiction to expectations from Bardeen–Cooper–Schrieffer theory. Our scanning tunnelling spectroscopy measurements in the overdoped regime of the (Pb,Bi)2Sr2CuO6+δ high-temperature superconductor show that this is due to the emergence of nanoscale superconducting puddles in a metallic matrix4,5. Our measurements further reveal that this puddling is driven by gap filling instead of gap closing. The important implication is that it is not a diminishing pairing interaction that causes the breakdown of superconductivity. Unexpectedly, the measured gap-to-filling correlation also reveals that pair breaking by disorder does not play a dominant role and that the mechanism of superconductivity in overdoped cuprate superconductors is qualitatively different from conventional mean-field theory.

Singularities in the Loschmidt echo of quenched topological superconductors

We study the Loschmidt echo in the quenched two-dimensional $p$-wave topological superconductor. We find that if this superconductor is quenched out of the critical point separating its topological and nontopological phases into either of the two gapful phases, its Loschmidt echo features singularities occurring periodically in time where the second derivative of the Loschmidt echo over time diverges logarithmically. Conversely, we give arguments towards $s$-wave superconductors not having singularities in their Loschmidt echo regardless of the quench. We also demonstrate that the conventional mean-field theory calculates classical echo instead of its quantum counterpart, and show how it should be modified to capture the full quantum Loschmidt echo.

Electronic Structure and Transport Properties of Superlattices: La(1-X)SrxTiO3 (X =0, 0.20, 0.80, 1)

The conventional density functional theory (DFT) and dynamical mean field theory (DMFT) is used to study the structural, electronic and the Mott-Hubbard metal-insulator phase transition of the pristine and superstructures, La(1-x)SrxTiO3 (x = 0, 0.20, 0.80, 1). The electrical and thermal conductivities, Seebeck coefficient, Figure of merit are calculated using the BoltzTraP codes. The present study reveals that the direct band gap of 2.20 eV and indirect band gap ~2.0 eV at the Γ point in the Brillouin zone of SrTiO3 is upgraded to 3.423eV by using modified Beck-Johnson (mBJ) interaction potential. The metal-insulator transition (MIT) of LaTiO3 and the superlattice La(1-x)SrxTiO3 have been investigated by using conventional density functional theory (DFT) and dynamical mean field theory (DMFT). The Mott-Hubbard metal-insulator transitions for pristine LaTiO3 for a Coulombian parameter, U = 2.5 eV and the thermodynamic parameter β = 6 (eV)-1 are consistent with the experimental results. A typical set of these correlation parameters for MIT La0.20Sr0.80TiO3 and La0.80Sr0.20TiO3 systems are found to be U = 3.5 eV and β = 10(eV)-1 and U = 3.2 eV and β = 10 (eV)-1 respectively. The characteristic sharp quasi-particle peak for a sample of La0.80Sr0.20TiO3 superlattice systems is obtained correlation parameter U = 3.0 eV and β = 6(eV)-1. A thermoelectric phase transition is observed for Seebeck Coefficient at temperature 300 K at near chemical potential, μ = 1eV of SrTiO3. The corresponding figure of merit (ZT) with chemical potential (μ) appears to be unity at near μ = 1eV.

Slave rotor approach to exciton condensation in a two-band system

We have studied exciton formation and condensation in an extended Falicov–Kimball model, going beyond the weak coupling approach, employing a semi-analytical technique: the slave-rotor mean-field theory (SRMF). In this essentially strong coupling theory, charge and spin (or orbital/pseudospin) degrees are treated as independent degrees of freedom, coupled by a local constraint. Using a two-site-extension of SRMF, we capture the effective many body scale beyond conventional mean-field theory. While the formation of excitons is favoured by the interband hybridization , it is strongly influenced by the on-site Coulomb interaction . Beyond a critical hybridization, there is condensation of excitons, leading to a transition from a metal to an excitonic insulator phase. Moreover, the behaviour of excitonic averages differs from the usual Hartree–Fock mean-field theory. Low- results show that excitonic order parameter (Δ) is continuous across the transition both for single as well as two-site approximation, changing to weakly first order one at intermediate for the later. The large- limit shows a continuous transition for two-site analysis but remains first order in the single-site approximation. The slave rotor theory gives a mixed state of excitons and metal in both the analyses. We have also checked the effect of intersite correlation and localized band hopping on the exciton condensation.

Topological pair-density-wave superconducting states.

We show that the pair-density-wave (PDW) superconducting state emergent in extended Heisenberg-Hubbard models in two-leg ladders is topological in the presence of an Ising spin symmetry and supports a Majorana zero mode (MZM) at an open boundary and at a junction with a uniform d-wave one-dimensional superconductor. Similarly to a conventional finite-momentum paired state, the order parameter of the PDW state is a charge-2e field with finite momentum. However, the order parameter here is a quartic electron operator and conventional mean-field theory cannot be applied to study this state. We use bosonization to show that the 1D PDW state has a MZM at a boundary. This superconducting state is an exotic topological phase supporting Majorana fermions with finite-momentum pairing fields and charge-4e superconductivity.

Study of Si-based three-dimensional photonic crystals infiltrated with liquid crystal within a one-dimensional effective model

In this work, we study Si-based three-dimensional photonic crystals infiltrated with liquid crystal (LC), within a one-dimensional effective medium model. Two specific systems of diamond crystal structure compatible with the mature Si technology are considered, namely, (i) diamond-1 which is composed of LC spheres embedded in the Si background, and (ii) diamond-2 which is the inverse of the foregoing structure, with Si spheres immersed in the LC background. For each system, the study is carried out with the LC being in the isotropic/nematic phase. The one-dimensional effective medium model employed in the study is an improved version of the conventional mean field theory (MFT). While retaining partially the typical advantage of MFT, e.g., physical transparency, analytical capability, and computational efficiency, it goes beyond the conventional MFT by taking into account the modulation of dielectric constant in the direction of wave propagation. As such, it improves greatly the poor numerical accuracy inherent in the MFT. We find a partial gap between the 2nd and 3rd bands, with the gap-to-midgap ratio being a few percents. Moreover, the edge of partial gap may be shifted by about 1% (in relative unit) when optical, thermal, or electrical means are applied to alter the phase of LC or rotate the axis of nematic molecules.

Many-Body Theory of Synchronization by Long-Range Interactions

Synchronization of coupled oscillators on a d-dimensional lattice with the power-law coupling G(r) = g0/rα and randomly distributed intrinsic frequency is analyzed. A systematic perturbation theory is developed to calculate the order parameter profile and correlation functions in powers of ϵ = α/d-1. For α ≤ d, the system exhibits a sharp synchronization transition as described by the conventional mean-field theory. For α > d, the transition is smeared by the quenched disorder, and the macroscopic order parameter ψ decays slowly with g0 as |ψ| ∝ g(0)(2).

Thermal Quenches in Spin Ice

We study the diffusion-annihilation process which occurs when spin ice is quenched from a high temperature paramagnetic phase deep into the spin-ice regime, where the excitations--magnetic monopoles--are sparse. We find that due to the Coulomb interaction between the monopoles, a dynamical arrest occurs, in which nonuniversal lattice-scale constraints impede the complete decay of charge fluctuations. This phenomenon is outside the reach of conventional mean-field theory for a two-component Coulomb liquid. We identify the relevant time scales for the dynamical arrest and propose an experiment for detecting monopoles and their dynamics in spin ice based on this nonequilibrium phenomenon.

Covariant density functional theory: The role of the pion

We investigate the role of the pion in covariant density functional theory. Starting from conventional relativistic mean field (RMF) theory with a nonlinear coupling of the $\ensuremath{\sigma}$ meson and without exchange terms we add pions with a pseudovector coupling to the nucleons in relativistic Hartree-Fock approximation. In order to take into account the change of the pion field in the nuclear medium the effective coupling constant of the pion is treated as a free parameter. It is found that the inclusion of the pion to this sort of density functionals does not destroy the overall description of the bulk properties by RMF. On the other hand, the noncentral contribution of the pion (tensor coupling) does have effects on single particle energies and on binding energies of certain nuclei.

Generalized dynamical mean-field theory for Bose-Fermi mixtures in optical lattices

We give a detailed discussion of the recently developed generalized dynamical mean-field theory (GDMFT) for a mixture of bosonic and fermionic particles. We show that this method is nonperturbative and exact in infinite dimensions, and reliably describes the full range from weak to strong coupling. Like in conventional dynamical mean-field theory, the small parameter is $1/z$, where $z$ is the lattice coordination number. We apply the GDMFT scheme to a mixture of spinless fermions and bosons in an optical lattice. We investigate the possibility of a supersolid phase, focusing on the case of 1/2 filling for the fermions and 3/2 filling for the bosons.

Improved chain mean-field theory for quasi-one-dimensional quantum magnets

A mean-field approximation for quasi-one-dimensional (Q1D) quantum magnets is formulated. Our mean-field approach is based on the Bethe-type effective-field theory, where thermal and quantum fluctuations between the nearest-neighbor chains as well as those in each chain are taken into account exactly. The self-consistent equation for the critical temperature contains the boundary-field magnetic susceptibilities of a multichain cluster, which can be evaluated accurately by some analytic or numerical methods, such as the powerful quantum Monte Carlo method. We show that the accuracy of the critical temperature of Q1D magnets as a function of the strength of interchain coupling is significantly improved compared with the conventional chain mean-field theory. It is also demonstrated that our approximation can predict nontrivial dependence of critical temperature on the sign (i.e., ferromagnetic or antiferromagnetic) of interchain coupling as well as on the impurity concentration in randomly diluted Q1D Heisenberg antiferromagnets.

Comparative study of electron- and hole-doped high-T c compounds in pseudogap regime: LDA+DMFT+Σ k approach

Pseudogap regime for the prototype high-T c compounds hole-doped Bi 2Sr 2CaCu 2O 8− x (Bi2212) and electron-doped Nd 2− x Ce x CuO 4 (NCCO) is described by means of novel generalized LDA+DMFT+Σ k approach. Here, conventional dynamical mean-field theory (DMFT) equations are supplied with additional (momentum dependent) self-energy Σ k . In the present case, Σ k describes nonlocal dynamical correlations induced by short-ranged collective Heisenberg-like antiferromagnetic spin fluctuations. Material-specific model parameters of two neighboring CuO 2 layers of Bi2212 and single CuO 2 layer of NCCO were obtained within local density approximation (LDA) and constrained LDA method. We show that Fermi surface in presence of the pseudogap fluctuations have perfectly visible “hot-spots” for NCCO, while in Bi2212 there is just a rather broad region with strong antiferromagnetic scattering. Results obtained are in good agreement with recent ARPES and optical experiments.

Mean-field theory of nucleation and growth on strained surfaces

Mean-field nucleation and growth modeling is important for understanding various adsorbate-substrate systems, particularly in the context of epitaxial growth. Conventional mean-field theory does not take into account nonlocal interactions, but adparticles may interact with strained islands via long range elastic interactions mediated by the substrate. We show that recent extensions of mean-field theory to deal with nonlocal interactions do not describe such processes faithfully. Here, we derive a generally applicable mean-field theory of adparticle dynamics on strained surfaces, when interdiffusion is neglected. This approach enables us to determine the transport coefficients from the microscopic physics; in particular, we find explicit expressions for the diffusion coefficient and drift velocity at all positions relative to an arbitrarily strained island. We demonstrate the role of strain on island growth, using island strain fields that are dynamically updated, for $\mathrm{Ge}∕\mathrm{Si}(001)$ parameters. This approach has important applications in the modeling of nucleation and growth of many nanostructures, such as metal nanoclusters, semiconductor hut clusters, and silicide nanowires.

The Transport Properties of the Cell Membrane Ion Channels in Electric Fields: Bethe Lattice Treatment

The interactive two-state model of cell membrane ion channels in an electric field is formulated on the Bethe lattice by means of the exact recursion relations. The probability of channel opening or maximum fractions of open potassium and sodium channels are obtained by solving a non-linear algebraic equation. Using known parameters for the conventional mean-field theory the model gives a good agreement with the experiment both at low and high trans-membrane potential values. For intermediate voltages, the numerical results imply that collective effects are introduced by trans-membrane voltage.

Pseudogap in normal underdoped phase of Bi2212: LDA + DMFT + Σk

Pseudogap phenomena are observed for normal underdoped phase of different high- T c cuprates. Among others Bi 2Sr 2CaCu 2O 8− δ (Bi2212) compound is one of the most studied experimentally [A. Damascelli, Z. Hussain, Z.-X. Shen, Rev. Mod. Phys. 75 (2003) 473; J.C. Campuzano, M.R. Norman, M. Randeria, in: K.H. Bennemann, J.B. Ketterson (Eds.), Physics of Superconductors, vol. 2, Springer, Berlin, 2004, p. 167; J. Fink et al., cond-mat/0512307; X.J. Zhou et al., cond-mat/0604284]. To describe pseudogap regime in Bi2212, we employ novel generalized DMFT + Σ k approach [E.Z. Kuchinskii, I.A. Nekrasov, M.V. Sadovskii, JETP Lett. 82 (2005) 198; M.V. Sadovskii et al., Phys. Rev. B 72 (2005) 155105, and these proceedings, doi:10.1016/j.physc.2007.03.367]. This approach gives possibility to preserve conventional dynamical mean-field theory (DMFT) equations [A. Georges et al., Rev. Mod. Phys. 68 (1996) 13] and include an additional (momentum dependent) self-energy Σ k . In the present case, Σ k describes non-local dynamical correlations induced by short-ranged collective Heisenberg-like antiferromagnetic spin fluctuations [M.V. Sadovskii, Physics-Uspekhi 44 (2001) 515, cond-mat/0408489]. The effective single impurity problem in the DMFT + Σ k is solved by numerical renormalization group (NRG) [R. Bulla, A.C. Hewson, Th. Pruschke, J. Phys. Cond. Mat. 10 (1998) 8365; R. Bulla, Phys. Rev. Lett. 83 (1999) 136]. To take into account material specific properties of two neighboring CuO 2 layers of Bi2212 we employ local density approximation (LDA) to calculate necessary model parameters, e.g. the values of intra- and interlayer hopping integrals between Cu-sites. Onsite Coulomb interaction U for x 2– y 2 orbital was calculated in constrained LDA method [O. Gunnarsson et al., Phys. Rev. B 39 (1989) 1708]. The value of pseudogap potential Δ was obtained within DMFT(NRG) [E.Z. Kuchinskii, I.A. Nekrasov, M.V. Sadovskii, JETP Lett. 82 (2005) 198; M.V. Sadovskii et al., Phys. Rev. B 72 (2005) 155105, and these proceedings, doi:10.1016/j.physc.2007.03.367]. Here, we report theoretical LDA + DMFT + Σ k quasiparticle bands dispersion, Fermi surface (FS) and angular resolved photoemission (ARPES) spectra accounting for pseudogap and bilayer splitting effects for normal underdoped Bi2212 ( δ = 0.15). We show that LDA-calculated value of bilayer splitting (BS) is too small to describe experimentally observed peak-dip-hump structure. Fermi surface in presence of the pseudogap fluctuations is almost insensitive to the BS value. Results obtained are in good agreement with recent ARPES experiments.

Structural properties ofErFeO3in the spin-reorientation region

In spin-reorientation transition in orthoferrites the temperature dependence of the magnetization differs from that predicted by conventional mean-field theory. One of the explanations of this discrepancy is based on the assumption that structural changes accompany magnetic transitions. Recently we proposed an explanation of this phenomena based on purely magnetic grounds. In this x-ray study a possible structural change in an $\mathrm{Er}\mathrm{Fe}{\mathrm{O}}_{3}$ single crystal is probed. Our measurements find no lattice distortions in the spin-reorientation region, thus supporting the purely magnetic nature of spin rotation.

Master-equation for cascade damage modeling

This paper is a continuation of our effort to understand and model irradiation effects under cascade damage. The conventional master equation for the evolution of a void ensemble is reformulated to include the stochastic effects due to the random cascade initiation. Numerical solution of the modified master equations to model the evolution of an ensemble of voids explicitly shows that stochastic fluctuations due to random cascade initiation produce important effects that cannot be accounted for by the conventional mean-field rate theory approach. The results are in good agreement with those derived previously using the Fokker–Planck equation.

Interaction between irreversibly adsorbed polymer layers: Is the mean field picture really inadequate?

We found out that the mean-field theory (MFT), if done consistently, is in good agreement with experimental observations for the force between irreversibly adsorbed polymer layers. This result is fairly unexpected in light of the conventional Cahn-de Gennes mean-field (CdGMF) theory that claims this force is zero. We reexamine the CdGMF equations and show that the consistency of the CdGMF approach is broken. This motivated us to derive an equation for the polymer density on the adsorbing surface that describes a minimum of the surface free energy. This equation replaces the conventional boundary condition used in CdGMF. The disjoining pressure is calculated by making use of the developed theory. An excellent agreement with the experimental results is indicated. We believe that our findings rehabilitate the mean-field theory as one of the most powerful tools for investigating the polymer-mediated interaction between colloids. Our result show that the unphysical predictions of CdGMF are due to its inconsistency rather than because this approach is "completely inadequate to discuss the plate-plate interactions in good solvent" [Macromolecules 15, 492 (1982)]].

Electronic structure and magnetic properties of GdM 2 compounds

Electronic structure calculations are carried out for the ferromagnetic GdM 2 compounds (M=Mg, Al, Fe, Co, Ni, Rh, Ir, Pt). By using the calculated susceptibilities, densities of electronic states, and exchange parameters, the Curie temperatures were evaluated for these compounds in the framework of a modified molecular-field approach. The calculated magnetic ordering temperatures appeared to be in improved agreement with experimental data, in contrast to the results obtained within a conventional mean-field theory.