Weak-coupling Theory Research Articles

Numerical Study of a Superconductor-Insulator Transition in a Half-Filled Hubbard Chain with Distant Transfers

The ground state of a one-dimensional Hubbard model having the next-nearest neighbor hopping (t') as well as the nearest-neighbor one (t) is numerically investigated at half-filling. A quantum Monte Carlo result shows a slowly decaying pairing correlation for a sizeable interaction strength $(U \leq 2t)$, while the system is shown to become insulating for yet larger $U>U_C\sim 3t$ from a direct evaluation of the charge gap with the density-matrix renormalization group method. The results are consistent with Fabrizio's recent weak-coupling theory which suggests a transition from a superconductor into an insulator at a finite U.

Stopping of ions and local electron densities at strong coupling

We employ molecular dynamics (MD) computer simulations to investigate ions in electron plasmas at strong coupling. We observed in this regime a stopping power of highly charged ions at low velocities which scales with the charge like Z1.5. This clearly deviates from the Z2 ln(const./Z) scaling of the conventional weak coupling theories and is connected with a strongly enhanced local density of electrons around the ions which is caused by the trapping of electrons in high Rydberg states due to multi-particle collisions occurring at strong coupling. For the parameters corresponding to the less strongly coupled situation in an electron cooler we find a moderate enhancement of the local electron density created under the influence of the external magnetic field.

Higher-order results for the relation between channel conductance and the Coulomb blockade for two tunnel-coupled quantum dots.

We extend earlier results on the relation between the dimensionless tunneling channel conductance g and the fractional Coulomb-blockade peak splitting f for two electrostatically equivalent dots connected by an arbitrary number ${\mathit{N}}_{\mathrm{ch}}$ of tunneling channels with bandwidths W much larger than the two-dot differential charging energy ${\mathit{U}}_{2}$. By calculating f through the second order in g in the limit of weak coupling (g\ensuremath{\rightarrow}0), we illuminate the difference in behavior of the large-${\mathit{N}}_{\mathrm{ch}}$ and small-${\mathit{N}}_{\mathrm{ch}}$ regimes and make more plausible extrapolation to the strong-coupling (g\ensuremath{\rightarrow}1) limit. For the special case of ${\mathit{N}}_{\mathrm{ch}}$=2 and strong coupling, we eliminate an apparent ultraviolet divergence and obtain the next leading term of an expansion in (1-g). We show that the results we calculate are independent of such band structure details as the fraction of occupied fermionic single-particle states in the weak-coupling theory and the nature of the cutoff in the bosonized strong-coupling theory. The results agree with calculations for metallic junctions in the ${\mathit{N}}_{\mathrm{ch}}$\ensuremath{\rightarrow}\ensuremath{\infty} limit and improve the previous good agreement with recent two-channel experiments. \textcopyright{} 1996 The American Physical Society.

The Quantum Hall Effect of Field Induced Spin Density Wave Phases: the Physics of the Ultra Quantum Crystal

The Quantum Hall Effect of Field Induced Spin Density Wave Phases is accounted for within a weak coupling theory which assumes that in the relevant low temperature part of the phase diagram the quasi one dimensional conductor is well described by Fermi liquid theory. Recent experimental results show that sign inversion of the Hall Plateaux takes place all the way down from the instability line of the normal state. The Quantum Nesting model, when it takes into account small perturbations away from perfect nesting, describes well not only the usual sequence of Hall plateaux, but also the anomalies connected with sign inversion of the Hall Effect. Experimental observation of de-doubling of sub-phase to sub-phase transition lines suggests that superposition of SDW order parameters occurs in some parts of the phase diagram. The collective excitations of the Ultra Quantum Crystal have a specific magneto-roton structure. The SDW case exhibits,apart from the usual spin waves, topological excitations which are either skyrmions or half skyrmions. It is suggested that magneto-rotons may have been observed some years ago in specific heat experiments.

Quantum Monte Carlo study of the pairing correlation in the Hubbard ladder.

An extensive Quantum Monte Carlo calculation is performed for the two-leg Hubbard ladder model to clarify whether the singlet pairing correlation decays slowly, which is predicted from the weak-coupling theory but controversial from numerical studies. Our result suggests that the discreteness of energy levels in finite systems affects the correlation enormously, where the enhanced pairing correlation is indeed detected if we make the energy levels of the bonding and anti-bonding bands lie close to each other at the Fermi level to mimic the thermodynamic limit.

Lattice formulation of chiral gauge theories.

We present a method for formulating gauge theories of chiral fermions in lattice field theory. The method makes use of a Wilson mass to remove doublers. Gauge invariance is then restored by modifying the theory in two ways: The magnitude of the fermion determinant is replaced with the square root of the determinant for a fermion with vectorlike couplings to the gauge field; a double limit is taken, in which the lattice spacing associated with the fermion field is sent to zero before the lattice spacing associated with the gauge field. The method applies only to theories whose fermions are in an anomaly-free representation of the gauge group. We also present a related technique for computing matrix elements of operators involving fermion fields. Although the analyses of these methods are couched in weak-coupling perturbation theory, it is argued that the computational prescriptions are gauge invariant in the presence of a nonperturbative gauge-field configuration.

Multiple-Scale Analysis of the Quantum Anharmonic Oscillator.

Conventional weak-coupling perturbation theory suffers from problems that arise from resonant coupling of successive orders in the perturbation series. Multiple-scale perturbation theory avoids such problems by implicitly performing an infinite reordering and resummation of the conventional perturbation series. Multiple-scale analysis provides a good description of the classical anharmonic oscillator. Here, it is extended to study the Heisenberg operator equations of motion for the quantum anharmonic oscillator. The analysis yields a system of nonlinear operator differential equations, which is solved exactly. The solution provides an operator mass renormalization of the theory.

Energy loss of heavy ions in strongly coupled plasmas

We investigate the energy loss of heavy ions in strongly coupled plasmas, by performing molecular dynamics (MD) computer simulations. These studies are of interest in heavy-ion-driven inertial confinement fusion, as well as for electron cooling. We consider the non-linear behavior for strong target-ion coupling parameters, i.e. ZΓ 3 2 ,≳ 1 , in non-ideal plasmas with Γ ≳ 0.1 ( Z is the charge number of the ion and Γ is the plasma parameter of the target). The new features that we found from our simulation results can be summarized as follows. (1) For strong ion-target coupling, the energy loss of the ions at low velocities scales with Z as Z 1.5, in agreement with recent experimental and other theoretical results. This clearly deviates from the Z 2 ln( const. Z ) scaling of the conventional weak coupling theories. (2) The change in the Z scaling has its origin in a non-linear screening that occurs for strong coupling and is associated with an increase in the (static) screening length above the Debye-Hückel result of the linear theory. (3) The non-linear screening is accompanied by electrons trapped by the ion into high Rydberg states, through multi-particle collisions. Compared with the case of linear coupling, this trapping causes an enhanced electron density around the ion. (4) The transient time dependence of the stopping power after switching on the ion-target interaction has characteristic time-scales that are a fraction of the plasma period.

Propagation of zero sound in superfluid3He-B under magnetic field

We present a theory of zero sound propagation in super fluid3He-B with an order parameter strongly distorted by magnetic field. A general formula of the dispersion relation for arbitrary magnetic field in the collisionless regime is derived within the weak coupling theory and under the assumption of particle-hole symmetry. The Landau parameters are taken into account up toF 2 andF 0 . Numerical results for the sound velocity and absorption spectrum are presented. We show that the collective modeJ = 1,J z = 0 yields a sizable peak in the sound absorption spectrum under weak but finite magnetic field. The quasi-particle excitations under magnetic field also exhibit cusp-like fine structures in the absorption spectrum. We show that the anomalies discovered by Ling et al. and Sounders et al. near the pair breaking edge in theq ⊥H geometry consist of theJ = 1,J z = 0 collective mode and the pair breaking cusps in theJ z = 0, ±2 channels.

Pressure dependence of the electronic density of states and Tc in superconducting Rb3C60.

The functional dependence of the superconducting transition temperature {ital T}{sub {ital c}} on the electronic density of states {ital N}({ital E}{sub {ital f}}) was determined for Rb{sub 3}C{sub 60} by measuring the magnetic susceptibility under hydrostatic pressure to {approximately} 1 GPa in a commercial SQUID magnetometer. Both {ital T}{sub {ital c}} and {ital N}({ital E}{sub {ital f}}) decrease under pressure at the rates {minus}31{percent}/GPa and {minus}14.5{percent}/GPa, respectively, but lie above the corresponding values for K{sub 3}C{sub 60} at the same lattice parameter. The present results are consistent with weak-coupling BCS theory with characteristic energy {ital E}{sub char}/{ital k}{sub {ital B}}{approx_equal} 320{endash}810 K. {copyright} {ital 1996 The American Physical Society.}

Single-polaron band structure of the Holstein model.

The single-polaron band structure of the Holstein model in one and two dimensions is studied using resummed strong-coupling perturbation theory. Well-converged results are obtained for phonon frequencies of the order of the hopping integral and strong-to-intermediate electron-phonon coupling. The polaron band structure at intermediate coupling is shown to deviate markedly from that of a nearest-neighbor tight-binding model and is in fact similar in shape to the prediction of weak-coupling self-consistent perturbation theory. \textcopyright{} 1996 The American Physical Society.

Theory of rough surface effects on the anisotropic BCS states

We present a Green's function theory of the rough surface effects on the anisotropic BCS states using the formulation developed in the randomly rippled wall model. It is shown that the randomly rippled wall formulation is general enough to treat rough surface effects from the specular limit to the diffusive limit. We propose a statistical wall configuration such that gives the diffusive limit in the normal state. Within the weak coupling theory, we give a formal solution of the quasi-classical Green's function in a slab geometry and in a semi-infinite geometry with arbitrarily rough surfaces. The formal solution already satisfies the boundary condition. In the diffusive limit, the present theory correctly recovers the linearized gap equation obtained by Kjaldman et al. for the p-wave state in a slab geometry.

An upper bound for the gap ratio of superconductors within the BCS theory for weak coupling

We find an upper bound for the ratio R= 2Δ 0 k BT c ≤4 within the weak coupling theory of superconductivity. This is strongly proved for a purely attracting electron-electron interaction (which is taken in the BCS model). The density of states is arbitrary, it may have all types of physically meaningful singularities. On the other hand, the inclusion of Coulomb repulsion may cause gap ratios R>4. Some consequences for the van Hove scenario of HTSC are discussed.

Superconducting parameters of YBCO and BSCCO from ‘tunneling’ spectroscopy

The differential conductivities of Bi 2Sr 2CaCu 2O 8+ x /Au and YBa 2Cu 3O 7− δ /Au point contacts were measured. The superconducting order parameter Δ and the Fermi velocity v F of both superconductors were determined making use of the modified Blonder—Tinkham—Klapwijk theory. The coherence length and penetration depth of Bi 2Sr 2CaCu 2O 8+ x and YBa 2Cu 3O 7− δ were calculated from Δ and v F, by applying a weak-coupling theory of superconductors with anisotropic single-particle dispersion and order parameter. Our results are compared to other experimental data.

D-wave superconductivity in a strongly correlated electron-phonon system.

The problem of phonon-mediated and phonon-free contributions to d-wave superconductivity in the two-dimensional Hubbard model has been addressed. Strong local correlations (U\ensuremath{\rightarrow}\ensuremath{\infty} limit) have been incorporated in the slave boson formulation. In order to consider electron-boson and electron-phonon coupling on equal footing, fluctuations of the auxiliary boson fields over their mean-field value have been introduced. The magnitude of effective pairing interactions derived with the help of a canonical transformation indicates that within the weak-coupling theory, phonon-mediated pairing plays a marginal role and can be dominated by a phonon-free pairing mechanism. On the other hand, in the strong-coupling limit (Eliashberg formulation), electron-phonon and electron-phonon-boson interactions can significantly enhance the superconducting transition temperature. It is also shown that Coulomb correlations together with the electron-phonon interaction can effectively stabilize a d-wave superconducting state. \textcopyright{} 1996 The American Physical Society.

Specific heat of an anisotropic superconductor: Nb3X4 with X=S, Se, and Te.

The specific heats of ${\mathrm{Nb}}_{3}$${\mathrm{S}}_{4}$, ${\mathrm{Nb}}_{3}$${\mathrm{Se}}_{4}$, and ${\mathrm{Nb}}_{3}$${\mathrm{Te}}_{4}$ were measured in the temperature range from 0.5 to 30 K. The magnitude of the jump at the superconducting transition temperature ${\mathit{T}}_{\mathit{c}}$ was 1.11\ifmmode\pm\else\textpm\fi{}0.02\ensuremath{\gamma}${\mathit{T}}_{\mathit{c}}$ for ${\mathrm{Nb}}_{3}$${\mathrm{S}}_{4}$ and 0.66\ifmmode\pm\else\textpm\fi{}0.01\ensuremath{\gamma}${\mathit{T}}_{\mathit{c}}$ for ${\mathrm{Nb}}_{3}$${\mathrm{Se}}_{4}$. The superconducting property for both compounds is discussed on the basis of the weak-coupling BCS theory as extended by Clem to include the effects of energy-gap anisotropy. We estimated the mean-squared anisotropy 〈${\mathit{a}}^{2}$〉=0.07\ifmmode\pm\else\textpm\fi{}0.02 and the reduced-energy gap 2${\mathrm{\ensuremath{\varepsilon}}}_{0}$/(${\mathit{k}}_{\mathit{BT}}$)=3.1\ifmmode\pm\else\textpm\fi{}0.1 for ${\mathrm{Nb}}_{3}$${\mathrm{S}}_{4}$, and 〈${\mathit{a}}^{2}$〉=0.14\ifmmode\pm\else\textpm\fi{}0.03 and 2${\mathrm{\ensuremath{\varepsilon}}}_{0}$/(${\mathit{k}}_{\mathit{BT}}$)=2.8\ifmmode\pm\else\textpm\fi{}0.1 for ${\mathrm{Nb}}_{3}$${\mathrm{Se}}_{4}$. For ${\mathrm{Nb}}_{3}$${\mathrm{Te}}_{4}$, although it becomes superconducting at about 2 K in the electrical-resistivity measurement, an excess of specific heat due to the superconducting transition was not found down to about 0.5 K. We also discuss the superconducting property of ${\mathrm{Nb}}_{3}$${\mathrm{Te}}_{4}$. \textcopyright{} 1996 The American Physical Society.

Extended Van-Hove Singularity and Related Non-Fermi Liquids

A weak coupling theory of extended Van Hove Singularity (VHS) is developed. Effects of interaction are so strong that the VHS cannot be reached from the Fermi liquid side and a whole area in energy-momentum space around it is occupied by a non-Fermi liquid. Phenomenology of the non-Fermi liquid is discussed including the possibility that the non-Fermi liquid is a separate thermodynamic phase.

Convergent strong-coupling expansions from divergent weak-coupling perturbation theory.

As an application of a recently developed variational perturbation theory we find the first 22 terms of the convergent strong-coupling series expansion for the ground state energy of the quartic anharmonic oscillator.

PAIRING SYMMETRY AND ISOTOPE EFFECT IN HIGH-TEMPERATURE SUPERCONDUCTOR

It is demonstrated that various forms of the 2D pairing parameter lead to an unusual type of the isotope effect quite distinct from the ordinary BCS behavior. The special form of the local pairing in the real space is considered in order to better use the density of states singularities and explain critical lattice distortion for high-temperature superconductors. The isotope effect is also studied for the recently suggested weak coupling theory with the order parameter antisymmetric in energy with respect to Fermi level.

Surface and size effect of a dxy-state superconductor.

We study a ${\mathit{d}}_{\mathit{x}\mathit{y}}$-state superconducting film with specularly reflecting surfaces parallel to the y-z plane. The self-consistent pair potential and the surface density of states are calculated in the clean limit by use of the quasiclassical Green's-function method within weak-coupling theory. The surface states have midgap states with energies around \ensuremath{\omega}=0 as was pointed out by Hu [Phys. Rev. Lett. 72, 1526 (1994)]. We discuss the size dependence of the transition temperature.