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Register a new userCooper instability and superconductivity on the Penrose lattice
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Bulk SC has recently been observed in the Al-Zn-Mg QC. To settle the several fundamental issues on the SC on the QC, we perform a systematic study on an attractive Hubbard model on the Penrose lattice. The first issue is the Cooper instability under an infinitesimal attractive interaction on the QC without a Fermi surface. We start from the two-electron problem outside the filled Fermi-sea, where we analytically prove that an infinitesimal Hubbard attraction can lead to the Cooper instability as long as the density of state is nonzero at the Fermi level, which provides the basis for the SC on the QC. Our numerical results yield that the Cooper pairing always takes place between a time-reversal partner, satisfying the Andersons theorem. On this basis, we perform a MF study on the system, at both the zero and finite temperatures. The MF study also shows that an arbitrarily weak attraction can lead to the pairing order, with the resulting pairing state well described by the BCS theory, and the thermal dynamic behaviors well consistent with experiment results. The second issue is about the superfluid density on the QC without translational symmetry. Its clarified that although the normal state of the system locates at the critical point of the metal-insulator transition, the pairing state exhibits real SC, carrying finite superfluid density that can be verified by the Meissner effect. Further more, our study reveals a fundamental difference between the SC on the periodic lattice and that on the QC: while the paramagnetic superfluid density in the former case vanishes at zero temperature, that in the latter case is nonzero due to the lack of translational symmetry, reflecting the consumption of superfluid density from the scattering by the non-periodic structure. These properties of the SC on the Penrose lattice revealed here are universal for all QCs.
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We study a possible superconductivity in quasiperiodic systems, by portraying the issue within the attractive Hubbard model on a Penrose lattice. Applying a real-space dynamical mean-field theory to the model consisting of 4181 sites, we find a superconducting phase at low temperatures. Reflecting the nonperiodicity of the Penrose lattice, the superconducting state exhibits an inhomogeneity. According to the type of the inhomogeneity, the superconducting phase is categorized into three different regions which cross over each other. Among them, the weak-coupling region exhibits spatially extended Cooper pairs, which are nevertheless distinct from the conventional pairing of two electrons with opposite momenta.
The superconducting and normal state characteristics of yttrium hexaboride (YB$_6$) have been investigated for the single crystals with a transition temperatures $T_c$ ranging between 6 K and 7.6 K. The extracted set of microscopic parameters [the coherence length $xi$(0) $sim$ 320$div$340 ${AA}$, the penetration depth $lambda$(0) $sim$ 1100$div$1600 ${AA}$ and the mean free path of charge carriers $l$ = 31$div$58 ${AA}$, the Ginzburg-Landau-Maki parameters $kappa$$_{1,2}$(0) $sim$ 3.3$div$4.8 and the superconducting gap $Delta$(0) $sim$ 10.3$div$14.8 K] confirms the type II superconductivity in dirty limit ($xi$$gg$ $l$) with a medium to strong electron-phonon interaction (the electron-phonon interaction constant $lambda_{e-ph}$ = 0.93$div$0.96) and $s$-type pairing of charge carriers in this compound [2$Delta$(0)$/k_BT_c$ $approx$ 4]. The comparative analysis of charge transport (resistivity, Hall and Seebeck coefficients) and thermodynamic (heat capacity, magnetization) properties in the normal state in YB$_6$ allowed to detect a transition into the cage-glass state at $T^*$ $sim$ 50 K with a static disorder in the arrangement of the Y$^{3+}$ ions. We argue that the significant $T_c$ variations in the YB$_6$ single crystals are determined by two main factors: (i) the superconductivity enhancement is related with the increase of the number of isolated vacancies, both at yttrium and boron sites, which leads to the development of an instability in the hexaboride lattice; (ii) the $T_c$ depression is additionally stimulated by the spin polarization of conduction electrons emerged and enhanced by the magnetic field in the vicinity of defect complexes in the YB$_6$ matrix.
The relation between the polar structural instability and superconductivity in a Weyl semimetal candidate MoTe2 has been clarified by finely controlled physical and chemical pressure. The physical pressure as well as the chemical pressure, i.e., the Se substitution for Te, enhances the superconducting transition temperature Tc at around the critical pressure where the polar structure transition disappears. From the heat capacity and thermopower measurements, we ascribe the significant enhancement of Tc at the critical pressure to a subtle modification of the phonon dispersion or the semimetallic band structure upon the polar-to-nonpolar transition. On the other hand, the physical pressure, which strongly reduces the interlayer distance, is more effective on the suppression of the polar structural transition and the enhancement of Tc as compared with the chemical pressure, which emphasizes the importance of the interlayer coupling on the structural and superconducting instability in MoTe2.
The Kohn-Luttinger mechanism for unconventional superconductivity (SC) driven by weak repulsive electron-electron interactions on a periodic lattice is generalized to the quasicrystal (QC) via a real-space perturbative approach. The repulsive Hubbard model on the Penrose lattice is studied as an example, on which a classification of the pairing symmetries is performed and a pairing phase diagram is obtained. Two remarkable properties of these pairing states are revealed, due to the combination of the presence of the point-group symmetry and the lack of translation symmetry on this lattice. Firstly, the spin and spacial angular momenta of a Cooper pair is de-correlated: for each pairing symmetry, both spin-singlet and spin-triplet pairings are possible even in the weak-pairing limit. Secondly, the pairing states belonging to the 2D irreducible representations of the $D_5$ point group can be time-reversal-symmetry-breaking topological SCs carrying spontaneous bulk super current and spontaneous vortices. These two remarkable properties are general for the SCs on all QCs, and are rare on periodic lattices. Our work starts the new area of unconventional SCs driven by repulsive interactions on the QC.
We investigated the Abrikosov vortex lattice (VL) of a pure Niobium single crystal with the muon spin rotation (mu SR) technique. Analysis of the mu SR data in the framework of the BCS-Gorkov theory allowed us to determine microscopic parameters and the limitations of the theory. With decreasing temperature the field variation around the vortex cores deviates substantially from the predictions of the Ginzburg-Landau theory and adopts a pronounced conical shape. This is evidence of partial diffraction of Cooper pairs on the VL predicted by Delrieu for clean superconductors.
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