Unity in the Diversity

The Superstripes 2008 conference has been focused on the discovery of the amplification of the superconducting critical temperature T _c in a novel realization (iron pnictides) of metallic heterostructures at the atomic limit called superstripes. These are formed by superlattices of superconducting units (layers, or stripes, or wires, or spheres or balls) separated by an intercalated material. Superstripes show multiband high T _c superconductivity driven by the shape resonance or Feshbach resonance in the interband pairing that occurs by tuning the chemical potential at an electronic topological transition where the Fermi surface topology of one of the bands changes its dimensionality. The maximum T _c amplification is reached by tuning the chemical potential to “shape resonance” by changing: the charge density and/or the superlattice structural parameters.     

Lifshitz Transitions,Type-II Dirac and Weyl Fermions,Event Horizon and All That

The type-II Weyl and type-II Dirac points emerge in semimetals and also in relativistic systems. In particular, the type-II Weyl fermions may emerge behind the event horizon of black holes. In this case the horizon with Painlevé–Gullstrand metric serves as the surface of the Lifshitz transition. This relativistic analogy allows us to simulate the black hole horizon and Hawking radiation using the fermionic superfluid with supercritical velocity, and the Dirac and Weyl semimetals with the interface separating the type-I and type-II states. The difference between such type of the artificial event horizon and that which arises in acoustic metric is discussed. At the Lifshitz transition between type-I and type-II fermions the Dirac lines may also emerge, which are supported by the combined action of topology and symmetry. The type-II Weyl and Dirac points also emerge as the intermediate states of the topological Lifshitz transitions. Different configurations of the Fermi surfaces, involved in such Lifshitz transition, are discussed. In one case the type-II Weyl point connects the Fermi pockets and the Lifshitz transition corresponds to the transfer of the Berry flux between the Fermi pockets. In the other case the type-II Weyl point connects the outer and inner Fermi surfaces. At the Lifshitz transition the Weyl point is released from both Fermi surfaces. They loose their Berry flux, which guarantees the global stability, and without the topological support the inner surface disappears after shrinking to a point at the second Lifshitz transition. These examples reveal the complexity and universality of topological Lifshitz transitions, which originate from the ubiquitous interplay of a variety of topological characters of the momentum-space manifolds. For the interacting electrons, the Lifshitz transitions may lead to the formation of the dispersionless (flat) band with zero energy and singular density of states, which opens the route to room-temperature superconductivity. Originally, the idea of the enhancement of \(T_\mathrm{c}\) due to flat band has been put forward by the nuclear physics community, and this also demonstrates the close connections between different areas of physics.     

Multiband Superconductors Close to a 3D–2D Electronic Topological Transition

Within the two-band model of superconductivity, we study the dependence of the critical temperature T _c and of the isotope exponent α in the proximity to an electronic topological transition (ETT). The ETT is associated with a 3D–2D crossover of the Fermi surface of one of the two bands: the σ subband of the diborides. Our results agree with the observed dependence of T _c on Mg content in A $_{1-x}{\rm Mg}_x{\rm B}_2$ (A?=?Al or Sc), where an enhancement of T _c can be interpreted as due to the proximity to a ‘shape resonance.’ Moreover we have calculated a possible variation of the isotope effect on the superconducting critical temperature by tuning the chemical potential.     

Feshbach Shape Resonance in Multiband Superconductivity in Heterostructures

We report experimental data showing the Feshbach shape resonance in the electron doped MgB₂ where the chemical potential is tuned by Al, Sc, and C substitutions. The scaling of the critical temperature T _c as a function of the Lifshitz parameter z = E _Γ−E _F, where E _F is the chemical potential and E _Γ is the energy of the Γ critical point where the σ Fermi surface changes from the 3D to a 2D topology, is reported. The resonant amplification of T _c(z) driven by the interband pairing is assigned to a Feshbach shape resonance characterized by quantum superposition of pairs in states corresponding to different spatial location and different parity. It is centered at z = 0 where the chemical potential is tuned to a Van Hove-Lifshits feature for the change of Fermi surface dimensionality in the electronic energy spectrum in one of the subbands. In this heterostructure at atomic limit the multiband superconductivity is in the clean limit because the disparity and negligible overlap between electron wavefunctions in different subbands suppresses the single electron interband impurity scattering rate. The emerging scenario from these experimental data suggests that the Feshbach shape resonance could be the mechanism for high T _c in particular nanostructured architectures.     

Isotope Effect at the Fano Resonance in Superconducting Gaps for Multiband Superconductors at a 2.5 Lifshitz Transition

The doping dependent isotope effect in cuprates is explained in the framework of shape resonances in the superconducting gaps (belonging to the class of Fano resonances) in multicondensate superconductors. This new paradigm for high temperature superconductivity is based on the recent Fermiology scenario emerging from dHvA and quantum oscillation data showing a 2.5 Lifshitz topological transition due to the appearance of new small Fermi surface in the underdoped regime. The isotope effect is calculated for an electronic system near a band edge for a superlattice of stripes. The model reproduces the doping dependence of the isotope exponent behavior in cuprates and allows to identify the relative role of the intraband Cooper pairing and the configuration interaction between pairing channels from experimental data.     

Anomalous Thermal Expansion in Superconducting Mg1?xAlxB2 System

The thermal lattice expansion in the superconducting Mg_{1− x} Al _x B₂ system (x = 0, 0.13, and 0.59) has been measured using high-resolution X-ray powder diffraction. An unusual large negative thermal expansion (NTE) appears for temperatures below T ^* = 60 K in the MgB₂. The NTE effect increases in Mg_0.87Al_0.13B₂ and disappears at high Al content in the Mg_0.59Al_0.41B₂ where the temperature dependence of volume follows a standard Einstein model in the whole temperature range. The anomalous behavior of the thermal expansion provides a direct evidence in the physics of diborides for the relevance of the proximity to the 2.5 Lifshitz electronic topological transition where the Fermi surface of the σband changes from a two-dimensional (2D) to a three-dimensional (3D) topology.     

Electronic Structure of HgBa<Subscript>2</Subscript>CuO<Subscript>4+<Emphasis Type="Italic">δ</Emphasis></Subscript> with Self-organized Interstitial Oxygen Wires in the Hg Spacer Planes

While recent experiments have found that at optimum doping for the highest critical temperature in HgBa₂CuO_{4 + y} (Hg1201) the oxygen interstitials (O-i) are not homogeneously distributed but form one-dimensional atomic wires, there are no available information of its electronic structure considering self-organized O-i atomic wires. Here we report the calculated electronic structure of HgBa₂CuO_{4 + y} where oxygen interstitials form atomic wires along (1,0,0) crystal direction in the Hg layer. We find that at optimum doping for superconductivity the chemical potential is tuned near an electronic topological Lifshitz transition for the appearing of a second quasi 1D Fermi surface. A first large Fermi surface coexists with a second incipient quasi one-dimensional (1D) Fermi surface related with atomic wires of oxygen interstitials. Increasing oxygen doping the chemical potential is driven to the band edge of the second 1D-band giving a peak in the density-of-states. The new 1D electronic states are confined near the oxygen interstitial wires with a small spread only on nearby sites. Spin-polarized calculations show that the magnetic response is confined in the oxygen-poor domains free of oxygen interstitials wires and it is quite insensitive to the density of O-i wires.     

Superconductivity of Topological Surface States and Strong Proximity Effect in Sn1−xPbxTe–Pb Heterostructures

Superconducting topological crystalline insulators are expected to form a new type of topological superconductors to host Majorana zero modes under the protection of lattice symmetries. The bulk superconductivity of topological crystalline insulators can be induced through chemical doping and the proximity effect. However, only conventional full gaps are observed, so the existence of topological superconductivity in topological crystalline insulators is still controversial. Here, the successful fabrication of atomically flat lateral and vertical Sn_1?xPb_xTe–Pb heterostructures by molecular beam epitaxy is reported. The superconductivity of the Sn_1?xPb_xTe–Pb heterostructures can be directly investigated by scanning tunneling spectroscopy. Unconventional peak–dip–hump gap features and fourfold symmetric quasiparticle interference patterns taken at the zero energy in the superconducting gap support the presence of the topological superconductivity in superconducting Sn_1?xPb_xTe. Strong superconducting proximity effect and easy preparation of various constructions between Sn_1?xPb_xTe and Pb make the heterostructures to be a promising candidate for topological superconducting devices to detect and manipulate Majorana zero modes in the future.     

Anomalous Thermal Expansion in Superconducting Mg1− x Al x B2 System

The thermal lattice expansion in the superconducting Mg_{1? x} Al _x B₂ system (x = 0, 0.13, and 0.59) has been measured using high-resolution X-ray powder diffraction. An unusual large negative thermal expansion (NTE) appears for temperatures below T ^* = 60 K in the MgB₂. The NTE effect increases in Mg_0.87Al_0.13B₂ and disappears at high Al content in the Mg_0.59Al_0.41B₂ where the temperature dependence of volume follows a standard Einstein model in the whole temperature range. The anomalous behavior of the thermal expansion provides a direct evidence in the physics of diborides for the relevance of the proximity to the 2.5 Lifshitz electronic topological transition where the Fermi surface of the σband changes from a two-dimensional (2D) to a three-dimensional (3D) topology.     

T c amplication and pseudogap at a shape resonance in a superlattice of quantum stripes

The shape resonance of the superconducting gap for a 2D electron gas in a superlattice of quantum stripes with a finite 1 D periodic potential barrier is studied when the Fermi level is tuned near the bottom of the third superlattice subband. The maximumT _c . appears at a critical charge densityT _c . Forp > p _c (in the underdoped regime) the chemical potential is tuned in a pseudogap region characterized by a decrease of the density of states and an opening of the partial gap at the Fermi surface. The pseudogap is closed forp< p _c (in the overdoped regime).     

Influence of La and Gd Impurities on the Two Phase Transitions in U0.97Th0.03Be13

The phase diagram of U _1–x Th _x Be ₁₃ exhibits two irregular points at x _C1=1.9 at.% and x _C2=4.55 at.% which mark the endpoints of the concentration range where two phase transitions in specific heat measurements are observed. While it is clear that the upper one belongs to a superconducting phase transition, there are different interpretations for the lower one. It has been suggested that the lower transition involves magnetic correlations which coexist with a single superconducting state or that the lower transition separates two different superconducting states (one or both are probably non-s-wave like). In this scenario the onset of local magnetic order is discussed as being due to an accompanied antiferromagnetic transition or as a product of broken time reversal symmetry. To get more information about the nature of the two superconducting phases, substitution experiments with non-magnetic La and magnetic Gd on the U sites in U _0.97 Th _0.03 Be ₁₃ were performed. From specific heat measurements we argue that the upper transition behaves with La/Gd doping like a conventional s-wave superconductor, whereas the lower transition cannot be brought in line with common pictures of superconducting transitions. Also at the     

A Critical Examination of the Spin Dynamics in High-Tc Cuprates

A critical examination of the spin dynamics in high-T _c cuprates is made in the light of recent inelastic neutron scattering results obtained by different groups. The neutron data show that incommensurate magnetic peaks in YBCO belong to the same excitation as the resonance peak observed at (/a, /a). Being observed only in the superconducting state, the incommensurability is rather difficult to reconcile with a stripe picture. We also discuss the link between the resonance peak spectral weight and the superconducting condensation energy.     

Modified BCS Mechanism of Cooper Pair Formation in Narrow Energy Bands of Special Symmetry II. Matthias Rule Reconsidered

In part I of this paper a modified BCS mechanism of Cooper pair formation of electrons was proposed. This mechanism is connected with the existence of a narrow, roughly half-filled superconducting energy band of given symmetry. The special symmetry of the superconducting band was interpreted within a nonadiabatic extension of the Heisenberg model of magnetism. Within this nonadiabatic Heisenberg model, the electrons of the superconducting band are constrained to form Cooper pairs at zero temperature because in any normal conducting state the conservation of crystal-spin angular momentum would be violated. Except for this participation of the angular momentum, the pair formation is mediated in the familiar way by phonons. Superconducting bands can be identified even within a free-electron band structure. Therefore, in this paper the band structures of the bcc and hcp solid solution alloys composed of transition elements are approximated by appropriate free-electron band structures with s–d symmetry. From the free-electron bands, the number n of valence electrons per atom related to the maxima of the superconducting transition temperature T _c in these solid solutions is calculated within the nonadiabatic Heisenberg model. The two observed maxima of T _c are reproduced without any adjustable parameter at valence numbers n approximately equal to 4.9 and 6.5 in bcc and 4.7 and 6.7 in hcp solid solutions. This result is in good agreement with the measured values of 4.7 and 6.4 of Hulm and Blaugher. The upper maximum is predicted not to exist in bcc transition elements but to occur in several ordered structures of bcc solid solution alloys.     

Superconductivity in Itinerant Ferromagnetic Systems

We studied the possible superconducting state in an electronic itinerant ferromagnetic system characterized by a density of states that presents a moderately strong peak that is controlled by a specific parameter a and is positioned near the band edge. Specifically, we investigated the superconducting critical temperature, T _c , and the zero-temperature superconducting gap, ??₀. The analysis is done in a self-consistent way, the BCS mean-field equation being solved together with the electron density equation to trace possible changes in the system??s chemical potential due to the strong correlations between the component electrons. We discussed the density dependence of the superconducting critical temperature and zero-temperature superconducting gap for various values of the control parameter a and of the electron?Celectron attractive interaction. In the zero temperature limit we derive the system??s phase diagram and discuss the possible fermionic and bosonic regimes of the diagram as function of the strength of the attractive interaction.     

Electronic structure and low-temperature properties of V x Nb1−x N alloys

The vanadium and niobium nitrdes V _x Nb_1–x N are studied theoretically and experimentally for varying compositionsx. Self-consistent linear muffin-tin orbital band calculations are performed for various ordered supercells corresponding tox=0.0, 0.25, 0.50, 0.75, and 1.0. The band results are used to calculate electron-phonon coupling and spin susceptibility enhancement factors in order to study the variations of specific heat and superconducting transition temperatures with composition. A relative localization of, in particular, the V 3d states is found for the mixed compositions. The superconducting temperatures are found to be more reduced for intermediate compositions than what is expected from a simple interpolation between pure VN and NbN. Effects of spin fluctuations are important for the alloys containing vanadium, but are probably larger than what has been found in our theoretical study, and also containingq0 contributions. A small peak in the density of states near the Fermi energy is associated with a flat band near theW point, and causes a shoulder in density of state-dependent properties forx near 0.9.     

Superconductivity and the Van Hove Scenario

We give a review of the role of the Van Hove singularities in superconductivity. Van Hove singularities (VHs) are a general feature of low-dimensional systems. They appear as divergences of the electronic density of states (DOS). Jacques Friedel and Jacques Labbé were the first to propose this scenario for the A15 compounds. In NbTi, for example, Nb chains give a quasi-1D electronic structure for the d-band, leading to a VHs. They developed this model and explained the high T _C and the many structural transformations occurring in these compounds. This model was later applied by Jacques Labbé and Julien Bok to the cuprates and developed by Jacqueline Bouvier and Julien Bok. The high T _C superconductors cuprates are quasi-bidimensional (2D) and thus lead to the existence of Van Hove singularities in the band structure. The presence of VHs near the Fermi level in the cuprates is now well established. In this context we show that many physical properties of these materials can be explained, in particular the high critical temperature T _C, the anomalous isotope effect, the superconducting gap and its anisotropy, and the marginal Fermi liquid properties, they studied these properties in the optimum and overdoped regime. These compounds present a topological transition for a critical hole doping p≈0.21 hole per CuO₂ plane.     

Computing Topological Invariants of Triangular Chandelier Lattice

A numerical parameter mathematically derived from the graph structure is a topological index. The topological index is the first actual choice in QSAR research and these indices are used to build the correlation model between the chemical structures of various chemicals compounds. Here, we investigate some old degree-based topological indices like Randic index, sum connectivity index, ABC index, GA index, 1^st and 2^nd Zagreb indices, modified second Zagreb index, redefined version of 1^st, 2^nd and 3^rd Zagreb indices, hyper and augmented Zagreb indices, forgotten index and symmetric division degree index, and some new degree-based indices like SK index, SK₁ index, SK₂ index, and AG₁ index of triangular chandelier-lattice (TCL). The results are generalized by using edge partition and closed formulas for topological indices of triangular chandelier-lattice are analysed.