Numerical results for electron localization with site-diagonal and off-diagonal disorder

Numerical calculations of eigenfunctions and the participation ratio P are carried out for a two-dimensional square lattice where the site diagonal and/or off-diagonal matrix elements of a one-electron Hamiltonian are disordered. We show that, for purely off-diagonal disorder, states near the centre of the band will never be localized but states in the wings of the band are localized. We also see that the combined effects of diagonal and off-diagonal disorder yield several interesting results. Moreover, we confirm that, as suggested by Economou and Antoniou, the mobility-edge surface takes a bottle-neck shape in the three-dimensional space defined by energy E, the degree of diagonal randomness Γ and the degree of off-diagonal randomness V₁.     

A field-theoretical approach to the extended Hubbard model

We transform the quartic Hubbard terms in the extended Hubbard model to a quadratic form by making the Hubbard–Stratonovich transformation for the electron operators. This transformation allows us to derive exact results for mass operator and charge–charge and spin–spin correlation functions for s-wave superconductivity. We discuss the application of the method to the d-wave superconductivity.     

Supersolidity for hard-core-bosons coupled to optical phonons

The coexistence of diagonal long-range order (DLRO) and off-diagonal long-range order (ODLRO), manifested in some systems, is still a theoretical enigma. Here, we present a novel microscopic mechanism for supersolidity or the homogeneous coexistence of charge-density-wave state (an example of DLRO) and superfluidity/superconductivity (a realization of ODLRO). We derive an effective d-dimensional Hamiltonian for a system of hard-core-bosons coupled to optical phonons in a lattice. At non-half-fillings, a superfluid/superconductor to a supersolid transition occurs at intermediate boson–phonon couplings, while at strong-couplings the system phase separates. We demonstrate explicitly that the presence of next-nearest-neighbor hopping and nearest-neighbor repulsion leads to supersolidity.     

A theorem for the existence of Majorana fermion modes in spin-orbit-coupled semiconductors

We prove an index theorem for the existence of Majorana zero modes in a semiconducting thin film with a sizable spin-orbit coupling when it is adjacent to an s-wave superconductor. The theorem, which is analogous to the Jackiw-Rebbi index theorem for the zero modes in mass domain walls in one-dimensional Dirac theory, applies to vortices with odd flux-quantum in a semiconducting film in which s-wave superconductivity and a Zeeman splitting are induced by proximity effect. The momentum space construction of the zero-mode solution presented here is complementary to the approximate real space solution of the Bogoliubov-de Gennes equations at a vortex core (Sau et al., arXiv:0907.2239 [17]), proving the existence of non-degenerate zero-energy Majorana excitations and the resultant non-Abelian topological order in the semiconductor heterostructure. With increasing magnitude of the proximity-induced pairing potential, the non-Abelian superconducting state makes a topological quantum phase transition to an ordinary s-wave superconducting state which no topological order.     

Double fluctuations on the attractive Hubbard model: ladder approximation

We explore, for the first time, the effect of double fluctuations on both the diagonal and off-diagonal selfenergy. We use the T-Matrix equations below T _c , developed recently by the Zürich group (M.H. Pedersen et al) for the local pair attraction Hamiltonian. Here, we include as well the effect of fluctuations on the order parameter (beyond the BCS solution) up to second order in U/t. This is equivalent to approximating the effective interaction by U in the off-diagonal self-energy. For U/t = ?6.0, T/t = 0.05, μ/t = ?5.5 and Δ/t = 1.5, we find four peaks both for the diagonal, A(n(π/16, π/16), ω), the far left peak has a vanishing small weight; (b) in B(n(π/16, π/16), ω) the far left and far right peaks have very small weights. The physical picture is, then, that the pair physics in the normal phase (T > T _c is still valid below T _c . However, the condensation of the e-h pairs produces an additional gap around the chemical potential as in BCS, in other words, superconductivity opens a gap in the lower branch of a Hubbard-type-I solution.     

Anomalous Josephson vortex solutions in Josephson junctions with multiple tunneling channels

We construct a theory for Josephson junction with multiple tunneling channels. We focus on two situations, i.e., a heterotic junction composed of two-gap-superconductor, insulator, and one-gap-superconductor, and a grain-boundary junction formed by two identical multi-gap superconductors. Then, we show that the magnetic field distribution of the Josephson vortex for ±s-wave superconductivity is much more enlarged than that for s-wave without sign change between the order parameters. We display such anomalous vortices and suggest how to evaluate the enlargement.     

Theory of the spin-triplet superconductivity in Sr2RuO4 based on perturbation approach to three-band Hubbard model

We investigate a mechanism of the spin-triplet superconductivity in Sr₂RuO₄ by solving Eliashberg equation for three-band Hubbard model, where the effective pairing interaction is expanded perturbatively up to the third order with respect to the Coulomb integrals and the transition temperature is estimated numerically. The most significant momentum dependence of the effective interaction for the spin-triplet p-wave superconductivity does not originate from that of the spin susceptibility, but is brought by the third order vertex corrections. The results show that the p-wave pairing state is stabilized for not so strong inter-orbit couplings.     

What is the highest T c for phonon-mediated superconductivity?

We suggest that the high-temperature superconductivity can be attributed to the director-roles of the van Hove singularity between an electron-electron interaction and an electron-phonon interaction. The difference between the critical temperature and the pairing temperature is presented, and the Fermi arc, the d-wave symmetry and the poor conductivity, etc., are discussed. In particular, the non-s-wave symmetry is predicted to have the highest T _c for superconductors.     

Competing effects of Hund’s splitting and symmetry-breaking perturbations on electronic order in Pb<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Sn<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Te

We study the effect of a uniform external magnetization on p-wave superconductivity on the (001) surface of the crystalline topological insulator (TCI) Pb_1?xSn_xTe. It was shown by us in an earlier work that a chiral p-wave finite-momentum pairing (FFLO) state can be stabilized in this system in the presence of weak repulsive interparticle interactions. In particular, the superconducting instability is very sensitive to the Hund’s interaction in the multiorbital TCI, and no instabilities are found to be possible for the “wrong” sign of the Hund’s splitting. Here we show that for a finite Hund’s splitting of interactions, a significant value of the external magnetization is needed to degrade the surface superconductivity, while in the absence of the Hund’s interaction, an arbitrarily small external magnetization can destroy the superconductivity. This implies that multiorbital effects in this system play an important role in stabilizing electronic order on the surface.     

A comment on Anderson's transition in systems with purely off-diagonal disorder

We make a comment on a recent paper by Antoniou and Economou concerning the electron localization in systems with off-diagonal randomness. Particularly, we discuss the validity of the ordinary cluster coherent potential approximation and of the L(E) method, both of which were used as grounds to draw their conclusion.     

The competition and coexistence of antiferromagnetism and <Emphasis Type="Italic">d</Emphasis>-wave superconductivity: probing coupled thermal fluctuations in a two dimensional minimal model

We consider the coexistence of antiferromagnetism and d-wave superconductivity, motivated by what one observes in the quasi-two dimensional organic salts. We study an electronic model that approximates some features of the Hubbard model, e.g., a repulsion that promotes local moments and Neel order, and an attractive intersite density–density coupling that promotes d-wave superconductivity. Staying at half-filling and a fixed attractive interaction we probe the effect of varying repulsion, using mean field theory for the ground state but retaining the full O(3) × U(1) spectrum of classical fluctuations at finite temperature. The ground state is superconducting at weak repulsion, a Neel ordered insulator at large repulsion, and a coexistence of the two orders in the intermediate regime. We observe four distinct kinds of thermal behaviour depending on the strength of repulsion. Starting with weak repulsion these are, first, a d-wave superconductor renormalised by magnetic fluctuations, second, a d-wave state transiting to an antiferromagnetic insulator and then to the normal state, third, a coexistent state transiting to the antiferromagnetic insulator and then the normal state, and, fourth, a Neel ordered insulator with weak pairing fluctuations. The low temperature state is either “nodal” or gapped, due to long range order, and the low energy spectral weight generally increases monotonically with temperature. At intermediate repulsion, however, the transition from the d-wave state to Neel antiferromagnet causes a loss of low energy weight which is gradually regained only at high temperature.     

Numerical results for Anderson localisation in the presence of off-diagonal disorder

Numerical calculations of the inverse participation ratio have been performed for the diamond cubic lattice with nearest neighbour interactions, and both diagonal and off-diagonal disorder. We confirm the prediction of Economou and Antoniou that off-diagonal disorder cannot, per se, produce an Anderson transition, although it reduces the amount of diagonal disorder necessary for the transition. In the presence of off-diagonal disorder alone we do not detect any substantial localisation even in the wings of the band.     

Possible universal cause of high-<Emphasis Type="Italic">T</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript> superconductivity in different metals

Using the theory of high-temperature superconductivity based on the idea of the fermion-condensation quantum phase transition (FCQPT), we show that neither the d-wave pairing symmetry, the pseudogap phenomenon, nor the presence of the Cu-O₂ planes is of decisive importance for the existence of high-T _c superconductivity. We analyze recent experimental data on this type of superconductivity in different materials and show that these facts can be understood within the theory of superconductivity based on the FCQPT. The latter can be considered as a universal cause of high-T _c superconductivity. The main features of a room-temperature superconductor are discussed.     

The dependence of the photodisintegration cross section on the off-shell T-matrix

Nucleon-nucleon scattering phase shifts determine the diagonal element of the transition matrix. The off-diagonal elements are not completely arbitrary but have conditions imposed on them by the range and the tail of the potential. Electromagnetic interaction can also be used to place restrictions on the off-diagonal elements. We find that the cross section of the deuteron photodisintegration is sensitive to the off-shell transition matrix. The integrated cross section can be varied by as much as 30 % or more, and the matrix element for the El transition by a factor of 2. While the matrix element for the photodisintegration depends on the off-shell elements of the T-matrix, it cannot be used to discriminate between alternative off-shell T-matrices. We have constructed classes of different off-shell T-matrices, which produce identical photo-disintegration cross sections and other two-body scattering and bound-state properties.     

Corrections to the single-particle M1 and Gamow-Teller matrix elements

Consideration of second-order core-polarisation, isobar-current and meson-exchange-current processes gives a satisfactory understanding of the ground-state magnetic moments and mirror β-decay transition probabilities in closed-shell-plus- (or minus) one nuclei, A = 3, 15, 17, 39 and 41. Perturbation contributions from high-lying excited states (tensor correlations) from one-body and two-body meson-exchange operators cancel strongly in diagonal matrix elements, but in off-diagonal matrix elements between spin-orbit partners the cancellation is less. Similarly, with isobar currents, there is a strong cancellation between direct and exchange contributions in diagonal matrix elements, while the exchange term is suppressed in off-diagonal cases. Of the two contributions, tensor correlations are found to be as important as, if not more important than, isobar currents. The calculated lowest-order meson-exchange-current contributions to magnetic moments are close to the soft-pion limit predictions.     

Phase separation and d-wave superconductivity induced by extended electron–exciton interaction

Using an auxiliary-field quantum Monte Carlo (AFQMC) method, we have studied a two-dimensional tight-binding model in which the conduction electrons can polarize an adjacent layer of molecules through electron–electron repulsion. Calculated average conduction electron density as a function of chemical potential exhibits a clear break characteristic of phase separation. Compared to the noninteracting system, the d-wave pair-field correlation function shows significant enhancement. The simultaneous presence of phase separation and d-wave superconductivity suggests that an effective extended pairing force is induced by the electron–exciton coupling.     

Could Pd in confined geometries be a “p-wave” superconductor or an intenerant ferromagnet?

It is proposed that reduced dimensionalities (films or powders) could favorize the observation of p-wave superconductivity in Pd. Susceptibility measurements are suggested as a first test to know whether the reduced dimensionality plays a role and in which direction.     

Renormalization group approach to a p-wave superconducting model

We present in this work an exact renormalization group (RG) treatment of a one-dimensional p-wave superconductor. The model proposed by Kitaev consists of a chain of spinless fermions with a p-wave gap. It is a paradigmatic model of great actual interest since it presents a weak pairing superconducting phase that has Majorana fermions at the ends of the chain. Those are predicted to be useful for quantum computation. The RG allows to obtain the phase diagram of the model and to study the quantum phase transition from the weak to the strong pairing phase. It yields the attractors of these phases and the critical exponents of the weak to strong pairing transition. We show that the weak pairing phase of the model is governed by a chaotic attractor being non-trivial from both its topological and RG properties. In the strong pairing phase the RG flow is towards a conventional strong coupling fixed point. Finally, we propose an alternative way for obtaining p-wave superconductivity in a one-dimensional system without spin–orbit interaction.