One-band Case Research Articles

Comparing the effective enhancement of local and nonlocal spin-orbit couplings on honeycomb lattices due to strong electronic correlations

We investigate the interplay of electronic correlations and spin-orbit coupling (SOC) for a one-band and a two-band honeycomb lattice model. The main difference between the two models concerning SOC is that in the one-band case the SOC is a purely non-local term in the basis of the $p_z$ orbitals, whereas in the two-band case with $p_x$ and $p_y$ as basis functions it is purely local. In order to grasp the correlation effects on non-local spin-orbit coupling, we apply the TRILEX approach that allows to calculate non-local contributions to the self-energy approximatively. For the two-band case we apply dynamical mean-field theory. In agreement with previous studies, we find that for all parameter values in our study, the effect of correlations on the spin-orbit coupling strength is that the bare effective SOC parameter is increased. However, this increase is much weaker in the non-local than in the local SOC case. Concerning the TRILEX method, we introduce the necessary formulas for calculations with broken SU(2) symmetry.

Theoretical Possibilities for Flat Band Superconductivity

One novel arena for designing superconductors with high $T_C$ is the flat-band systems. A basic idea is that flat bands, arising from quantum mechanical interference, give unique opportunities for enhancing $T_C$ with (i) many pair-scattering channels between the dispersive and flat bands, and (ii) an even more interesting situation when the flat band is topological and highly entangled. Here we compare two routes, which comprise a multi-band system with a flat band coexisting with dispersive ones, and a one-band case with a portion of the band being flat. Superconductivity can be induced in both cases when the flat band or portion is "incipient" (close to, but away from, the Fermi energy). Differences are, for the multi-band case, we can exploit large entanglement associated with topological states, while for the one-band case a transition between different (d and p) wave pairings can arise. These hint at some future directions.

Unusual boundary effect on coherency in two-band superconductors

We demonstrate that restoration of two-band superconductivity near the surface of the system is governed by length scales which are drastically different from correlation lengths. Similar to the one-band case, one of the characteristic lengths diverges at critical temperature Tc, while another one shows unusual behaviour having singularity at Tc+<Tc. By moving away from the boundary, these scales approach correlation lengths in the bulk state, where the divergence at Tc+ is removed by arbitrary weak interband coupling. The peculiarity can be manifested in proximity sandwich where Tc+ becomes an inflection point for critical temperature being a function of superconducting layer thickness.

Quantifying Envelope and Fine-Structure Coding in Auditory Nerve Responses to Chimaeric Speech

Any sound can be separated mathematically into a slowly varying envelope and rapidly varying fine-structure component. This property has motivated numerous perceptual studies to understand the relative importance of each component for speech and music perception. Specialized acoustic stimuli, such as auditory chimaeras with the envelope of one sound and fine structure of another have been used to separate the perceptual roles for envelope and fine structure. Cochlear narrowband filtering limits the ability to isolate fine structure from envelope; however, envelope recovery from fine structure has been difficult to evaluate physiologically. To evaluate envelope recovery at the output of the cochlea, neural cross-correlation coefficients were developed that quantify the similarity between two sets of spike-train responses. Shuffled auto- and cross-correlogram analyses were used to compute separate correlations for responses to envelope and fine structure based on both model and recorded spike trains from auditory nerve fibers. Previous correlogram analyses were extended to isolate envelope coding more effectively in auditory nerve fibers with low center frequencies, which are particularly important for speech coding. Recovered speech envelopes were present in both model and recorded responses to one- and 16-band speech fine-structure chimaeras and were significantly greater for the one-band case, consistent with perceptual studies. Model predictions suggest that cochlear recovered envelopes are reduced following sensorineural hearing loss due to broadened tuning associated with outer-hair cell dysfunction. In addition to the within-fiber cross-stimulus cases considered here, these neural cross-correlation coefficients can also be used to evaluate spatiotemporal coding by applying them to cross-fiber within-stimulus conditions. Thus, these neural metrics can be used to quantitatively evaluate a wide range of perceptually significant temporal coding issues relevant to normal and impaired hearing.

Conductance characteristics between a normal metal and a two-band superconductor carrying a supercurrent

The conductance is calculated for a point contact junction between a normal metal and a two-band superconductor with a supercurrent applied parallel to the junction interface. Predictions are made for the case of $\mathrm{Mg}{\mathrm{B}}_{2}$, which would allow for the determination of the two energy scales and interband coupling. In addition, the generic features of two-band superconductivity in this configuration are studied and contrasted with the one-band case. It is found that two peaks are possible in the zero bias conductance as a function of superfluid momentum ${q}_{s}$ for the case of two-band superconductivity, whereas only one could occur in the one-band case. We analyze the case of highly decoupled bands to examine further the potential signatures of interband coupling.

Two-band superconductor–normal metal point contact junction conductance with a transverse current

We calculate the conductance of a point contact junction between a normal metal and a two-band superconductor in the presence of a transverse supercurrent. We show that there is a region of parameter space which can be probed that is not accessible to the one-band case. It is proposed that this experiment may be used as a probe of interband coupling.

Phase transitions due to the formation of polarons in colossal magnetoresistive manganites: Monte Carlo simulations

A previously studied single-orbital double-exchange model coupled to phonons [J. A. Verg\'es, V. Mart\'{\i}n-Mayor, and L. Brey, Phys. Rev. Lett. 88, 136401 (2002)] is extended, both to include the $d$-orbital degeneracy and a direct superexchange interaction among Mn atoms, in an attempt to extend the amount of doping allowed for the model. This model, as the previously studied one-band double exchange, shows a first-order metal-insulator phase transition that, for certain ranges of doping, coincides with the paramagnetic-ferromagnetic phase transition. We show that the strong interaction between polarons destroys the insulating phase for a number of carriers similar to the one-band case. For a higher number of carriers, not even the consideration of direct superexchange is enough to localize the carriers at the ferromagnetic-paramagnetic transition. Several phases appearing in experiments as ferromagnetic metal, paramagnetic metal, ferromagnetic insulator, paramagnetic insulator, and antiferromagnetic insulator are also found in the simulations.

Dynamical mean-field study of the ferromagnetic transition temperature of a two-band model for colossal magnetoresistance materials

The ferromagnetic transition temperature $({T}_{\mathrm{C}})$ of a two-band double-exchange (DE) model for colossal magnetoresistance materials is studied using dynamical mean-field theory in wide ranges of coupling constants, hopping parameters, and carrier densities. The results are shown to be in good agreement with Monte Carlo simulations. When the bands overlap, the value of ${T}_{\mathrm{C}}$ is found to be much larger than in the one-band case, for all values of the chemical potential within the energy overlap interval. A nonzero off-diagonal hopping produces an additional boost of ${T}_{\mathrm{C}}$, showing the importance of these terms, as well as the concomitant use of multiband models, to increase the critical temperatures in DE-based theories.

Dynamical correlations in multiorbital Hubbard models: fluctuation exchangeapproximations

We study the two-band degenerate Hubbard model using the fluctuation exchangeapproximation (FLEX) and compare the results with quantum Monte Carlo (QMC)calculations. Both the self-consistent and the non-self-consistent versions of the FLEX schemeare investigated. We find that, unlike in the one-band case, in the multiband case, goodagreement with the quantum Monte Carlo results is obtained within the electron–electronT-matrix approximation using the full renormalization of the one-particle propagators. Thecrossover to strong coupling and the formation of satellites is more clearly visible in thenon-self-consistent scheme. Finally we discuss the behaviour of the FLEX for higher orbitaldegeneracy.

Kondo Resonance for Orbitally Degenerate Systems

Formation of the Kondo state in the general two-band Anderson model has been investigated within the numerical renormalization group calculations. The Abrikosov-Suhl resonance is essentially asymmetric for the model with one electron per impurity (quarter filling case) in contrast with the one-band case. An external magnetic (pseudomagnetic) field breaking spin (orbital) degeneracy leads to asymmetric splitting and essential broadening of the many-body resonance. Unlike the standard Anderson model, the "spin-up" Kondo peak is pinned against the Fermi level, but not suppressed by the magnetic field.

Ferromagnetic ground state of an orbital degenerate electronic model for transition-metal oxides: Exact solution and physical mechanism

We present an exact ground state solution of a one-dimensional electronic model for transition-metal oxides in the strong coupling limit. The model contains doubly degenerated orbit for itinerant electrons and the Hund coupling between the itinerant electrons and localized spins. The ground state is proven to be a full ferromagnet for any density of electrons. Our model provides a rigorous example for metallic ferromagnetism in narrow band systems. The physical mechanism for ferromagnetism and its relevance to high-dimensional systems, like R$_{1-x}$X$_x$MnO$_3$, are discussed. Due to the orbital degeneracy of itinerant electrons, the superexchange coupling can be ferromagnetic rather than antiferromagnetic in the one-band case.

Effective electron-electron interactions and the theory of superconductivity

Electron pairing is examined from a viewpoint which treats electron-electron interactions first (both in a single band and two-band context) and only later adds in electron-phonon coupling. We report solutions to the Eliashberg equation for the one- and two-band interacting electron gas, in the absence of phonons and then with phonons included, using effective electron-electron interactions that are closely constrained by sum rules. No s-wave pairing is found for the one-band case in the absence of phonons but higher angular momentum pairing is possible. In some contrast, intrinsic s-wave pairing is found for the two-band case, and again nonzero angular momentum pairing may arise. With the subsequent inclusion of phonons, but treated on a completely equal footing with electrons, transition temperatures of several simple metals are determined, and found to agree to within 20% of measured values. For low density systems, significant deviations from the predictions of the McMillan expression assuming \ensuremath{\mu}\ensuremath{\approx}0.1 are found. An important example is Li where we obtain ${\mathrm{T}}_{\mathrm{c}}$\ensuremath{\approx}0.4 mK in sharp contrast with previous approximations which give ${\mathrm{T}}_{\mathrm{c}}$\ensuremath{\sim}1 K, and are not supported by experiment.

Intervalley kinetic energy terms in the effective mass equation: a one-dimensional analytical study

We show that a one-dimensional analytical study allows us to test and clarify the derivation, assumptions, and symmetry properties of the intervalley effective mass equation (IVEME). In particular, we show that the IVEME is consistent with a two-band case, and is in fact exact for a model that satisfies exactly all its assumptions. On the other hand, an alternative formulation in k-space that includes intervalley kinetic energy terms is consistent with a one-band case, provided that intra-valley kinetic energy terms are also calculated consistent with one band. We also show that the standard symmetry assumptions for both real space and k-space formulations are not actually exact, but are consistent with a "total symmetric" projection, or with taking spherical averages in a three-dimensional case.

Mobility in a quasi-one-dimensional semiconductor: An analytical approach.

The electron mobility in a quasi-one-dimensional semiconductor is theoretically investigated when the scattering is due to ionized donors in an approximation where (i) the envelope wave function is assumed to be constant inside a cylindrical wire and zero outside and (ii) the finite-temperature effect is taken into account in the static dielectric function. It is shown that for the one-band case (intraband scattering only) this leads to an entirely analytical formula for the mobility at low temperature, for both uniform and modulation doping. For modulation doping, the theoretical mobility is much larger than that obtained in a two-dimensional semiconductor for comparable buffer-layer thicknesses. The main differences between the one- and the two-band cases (intraband and interband scattering) are pointed out. The localization effect is also briefly discussed.

Photoemission from ferromagnetic metals above the Curie temperature. I. Simple models

The authors have calculated the angle-resolved photoemission from metals with a local but spatially varying exchange splitting Delta j on atom j. They have considered magnetic configurations consisting of a simple spiral and ensembles of simple spirals in the one-band case and configurations consisting of simple spirals and double spirals for model transition-metal d bands. They find that electrons whose velocity is such that they see a very rapid change in the direction of Delta j give rise to a central line, while electrons whose velocity is such that they see a slow change in Delta j produce a pair of lines split by approximately mod Delta mod . However, for the regular configurations there is no clear separation between the two regimes and they cannot see the three-peak structure predicted by Korenman and Prange (1980).

Coherent-Potential Approximation in a Two-Band Model: Electronic and Transport Properties of Semiconducting Binary Alloys

The formalism of the coherent-potential approximation is extended to include the two-band case. The single-site energy of the one-band case is replaced by a 2 \ifmmode\times\else\texttimes\fi{} 2 matrix which varies randomly from site to site according to the occupancy of the site. The Kubo formulas for transport are also extended for the two-band model giving a nonvanishing vertex correction as opposed to the zero vertex correction for the single-band model. The cases treated explicitly correspond to fully disordered binary semiconducting alloys. The band gap and bandwidths are chosen as representative of typical semiconductor values, and concentrations, band gaps, gap centers, and band mixing are all varied systematically. Results are reported for densities of states, parentage, dc conductivity, and the imaginary part of the dielectric constant ${\ensuremath{\epsilon}}_{2}(\ensuremath{\omega})$. The analytic behavior of ${\ensuremath{\epsilon}}_{2}(\ensuremath{\omega})$ near threshold corresponds to several experimental situations.

Theory of the decay of excess carrier concentrations in semiconductors

Differential equations are presented for the decay of excess carrier concentrations in semiconductors by Shockley-Read and Auger processes involving recombination centres. An exact solution is obtained for the interaction of centres with the conduction band only and an approximate solution for the interaction with both bands. For the one-band case three ranges of excess concentration can, in principle, be distinguished in one of which the decay is exponential. For the two-band case there are four ranges, in three of which the decay is exponential. The theory applies also in the presence of a constant electric field. For small departures from equilibrium the results agree with those derived earlier by a different method.