Pseudogap and Unconventional Pairing in the Hubbard Model

1998 ◽  
Vol 12 (29n31) ◽  
pp. 2939-2945 ◽  
Author(s):  
Y. M. Malozovsky ◽  
J. D. Fan
Keyword(s):  
Hubbard Model ◽  
P Wave ◽  
Perturbation Approach ◽  
S Wave ◽  
Orbital State ◽  
Adequate Model ◽  
Hubbard Models ◽  
Spin Singlet ◽  
Spin Triplet ◽  
Spin Response

The attractive (U < 0) and repulsive (U > 0) Hubbard models have been studied using the Fermi liquid perturbation approach. The attractive Hubbard model (U < 0) is an adequate model for 3 He , an incompressible and strongly paramagnetic liquid [Formula: see text], [Formula: see text] for |U|N F = 0.9) with a pseudogap in the charge response. A pairing instability and superfluidity for U < 0 exists in the spin channel only: spin-triplet with l = 0, or spin-singlet with l = 1 (p-wave orbital state j = s + l = 1), where l is the orbital momentum of a pair. The repulsive Hubbard model (U > 0) represents a highly compressible and nearly antiferromagnetic liquid [Formula: see text], [Formula: see text] for UN F = 0.9) with a pseudogap in the spin response. However, for U > 0 a pairing instability and superconductivity exist in the charge channel only: spin-singlet with l = 0 (s-wave), or with l = 2 (d-wave) in the case of an anisotropic Fermi surface.

Coexistence of spin-singlet s- and d-wave and spin-triplet p-wave order parameters in anisotropic superconductors

2007 ◽  
Vol 244 (10) ◽  
pp. 3559-3571 ◽  
Author(s):  
R. Gonczarek ◽  
M. Krzyzosiak ◽  
L. Jacak ◽  
A. Gonczarek
Keyword(s):  
Order Parameters ◽  
P Wave ◽  
Spin Singlet ◽  
Anisotropic Superconductors ◽  
Spin Triplet ◽  
D Wave

scholarly journals p-Wave Superconductivity and d-Vector Representation

2021 ◽  
pp. 165-204
Author(s):  
Jean-Pascal Brison
Keyword(s):  
Electron System ◽  
P Wave ◽  
Strongly Correlated ◽  
Vector Representation ◽  
Strongly Correlated Electron ◽  
Correlated Electron Systems ◽  
Orbital State ◽  
Correlated Electron ◽  
Ion Interactions ◽  
Spin Triplet

AbstractSince the mid-80s, new classes of superconductors have been discovered in which the origin of superconductivity cannot be attributed to the electron–ion interactions at the heart of conventional superconductivity. Most of these unconventional superconductors are strongly correlated electron systems, and identifying (or even more difficult, predicting) the precise superconducting state has been, and sometimes remains, an actual challenge. However, in most cases, it has been demonstrated that in these materials the spin state of the Cooper pairs is a singlet state, often associated with a ‘d-wave’ or ‘$$s +/-$$ s + / - ’ orbital state. For a few systems, a spin-triplet state is strongly suspected, like in superfluid $$^3$$ 3 He; this leads to a much more complex superconducting order parameter. This was long supposed to be the case for the d-electron system Sr$$_2$$ 2 RuO$$_4$$ 4 , and is very likely realized in some uranium-based (f-electron) ‘heavy fermions’ like UPt$$_3$$ 3 (with multiple superconducting phases) or UGe$$_2$$ 2 (with coexisting ferromagnetic order). Beyond the interest for these materials, p-wave superconductivity is presently quite fashionable for its topological properties and the prediction that it could host Majorana-like low energy excitations, seen as a route towards robust (topologically protected) qubits. The aim of these notes is to make students and experimentalists more familiar with the d-vector representation used to describe p-wave (spin triplet) superconductivity. The interest of this formalism will be illustrated on some systems where p-wave superconductivity is the prime suspect.

scholarly journals P-wave Cooper pair splitting

2012 ◽  
Vol 3 ◽  
pp. 493-500 ◽  
Author(s):  
Henning Soller ◽  
Andreas Komnik
Keyword(s):  
Andreev Reflection ◽  
Cooper Pair ◽  
Hamiltonian Formalism ◽  
P Wave ◽  
Cooper Pairs ◽  
S Wave ◽  
Spin Singlet ◽  
Cross Correlations ◽  
On Chip ◽  
Crossed Andreev Reflection

Background: Splitting of Cooper pairs has recently been realized experimentally for s-wave Cooper pairs. A split Cooper pair represents an entangled two-electron pair state, which has possible application in on-chip quantum computation. Likewise the spin-activity of interfaces in nanoscale tunnel junctions has been investigated theoretically and experimentally in recent years. However, the possible implications of spin-active interfaces in Cooper pair splitters so far have not been investigated. Results: We analyze the current and the cross correlation of currents in a superconductor–ferromagnet beam splitter, including spin-active scattering. Using the Hamiltonian formalism, we calculate the cumulant-generating function of charge transfer. As a first step, we discuss characteristics of the conductance for crossed Andreev reflection in superconductor–ferromagnet beam splitters with s-wave and p-wave superconductors and no spin-active scattering. In a second step, we consider spin-active scattering and show how to realize p-wave splitting using only an s-wave superconductor, through the process of spin-flipped crossed Andreev reflection. We present results for the conductance and cross correlations. Conclusion: Spin-activity of interfaces in Cooper pair splitters allows for new features in ordinary s-wave Cooper pair splitters, that can otherwise only be realized by using p-wave superconductors. In particular, it provides access to Bell states that are different from the typical spin singlet state.

scholarly journals A GENERALIZATION OF THE GINZBURG–LANDAU THEORY TO p-WAVE SUPERCONDUCTORS

2008 ◽  
Vol 22 (18) ◽  
pp. 1709-1716 ◽  
Author(s):  
E. DI GREZIA ◽  
S. ESPOSITO ◽  
G. SALESI
Keyword(s):  
Present Model ◽  
Landau Theory ◽  
Magnetic Behavior ◽  
P Wave ◽  
Cooper Pairs ◽  
S Wave ◽  
Ginzburg Landau ◽  
Original Medium ◽  
Mean Fields ◽  
Spin Triplet

We succeed in building up a straightforward theoretical model for spin-triplet p-wave superconductors, by introducing a second-order parameter and a nonlinear interaction between the two mean fields in the Ginzburg–Landau theory. Such interaction breaks the isotropy of the original medium and allows pairs of electrons to arrange into S = 1 Cooper pairs. The present model predicts a thermodynamical and magnetic behavior analogous to that observed in conventional s-wave superconductors.

PERTURBATION OF PHASE VELOCITIES IN ELASTIC ORTHORHOMBIC MEDIA

Geophysics ◽  
2021 ◽  
pp. 1-109
Author(s):  
Alexey Stovas ◽  
Yuriy Roganov ◽  
Vyacheslav Roganov
Keyword(s):  
Seismic Waves ◽  
Transversely Isotropic ◽  
Second Order ◽  
P Wave ◽  
Order Perturbation ◽  
Perturbation Approach ◽  
S Wave ◽  
Anisotropic Models ◽  
S Waves ◽  
Phase Velocities

The parameterization of anisotropic models is very important when focusing on specific signatures of seismic waves and reducing the parameters crosstalk involved in inverting seismic data. The parameterization is strongly dependent on the problem at hand. We propose a new parameterization for an elastic orthorhombic model with on-axes P- and S-wave velocities and new symmetric anelliptic parameters. The perturbation approach is well defined for P waves in acoustic orthorhombic media. In the elastic orthorhombic media, the P-wave perturbation coefficients are very similar to their acoustic counterparts. However, the S-waves perturbation coefficients are still unknown. The perturbation coefficients can be interpreted as sensitivity coefficients, and they are important in many applications. We apply the second-order perturbation in anelliptic parameters for P, S1 and S2 wave phase velocities in elastic orthorhombic model. We show that using the conventional method some perturbation coefficients for S waves are not defined in the vicinity of the singularity point in an elliptical background model. Thus, we propose an alternative perturbation approach that overcomes this problem. We compute the first- and second-order perturbation coefficients for P and S waves. The perturbation-based approximations are very accurate for P and S waves compared with exact solutions, based on a numerical example. The reductions to transversely isotropic and acoustic orthorhombic models are also considered for analysis. We also show how perturbations in anelliptic parameters affect S-wave triplications in an elastic orthorhombic model.

scholarly journals Spin-orbit coupling suppression and singlet-state blocking of spin-triplet Cooper pairs

2021 ◽  
Vol 7 (3) ◽  
pp. eabe0128
Author(s):  
Sachio Komori ◽  
James M. Devine-Stoneman ◽  
Kohei Ohnishi ◽  
Guang Yang ◽  
Zhanna Devizorova ◽  
...  
Keyword(s):  
Orbit Coupling ◽  
Cooper Pairs ◽  
Triplet States ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
S Wave ◽  
Magnetic Exchange ◽  
Spin Singlet ◽  
Order Of Magnitude ◽  
Spin Triplet

An inhomogeneous magnetic exchange field at a superconductor/ferromagnet interface converts spin-singlet Cooper pairs to a spin-polarized triplet state. Although the decay envelope of triplet pairs within ferromagnetic materials is well studied, little is known about their decay in nonmagnetic metals and superconductors and, in particular, in the presence of spin-orbit coupling (SOC). Here, we investigate devices in which singlet and triplet supercurrents propagate into the s-wave superconductor Nb. In the normal state of Nb, triplet supercurrents decay over a distance of 5 nm, which is an order of magnitude smaller than the decay of spin-singlet pairs due to the SOC. In the superconducting state of Nb, triplet supercurrents are not able to couple with the singlet wave function and are thus blocked by the absence of available equilibrium states in the singlet gap. The results offer insight into the dynamics between s-wave singlet and s-wave triplet states.

ANALYSIS OF PROXIMITY EFFECTS BETWEEN SPIN SINGLET AND SPIN TRIPLET SUPERCONDUCTORS

1978 ◽  
Vol 39 (C6) ◽  
pp. C6-481-C6-483 ◽  
Author(s):  
K. Scharnberg ◽  
D. Fay ◽  
N. Schopohl
Keyword(s):  
Proximity Effects ◽  
Spin Singlet ◽  
Spin Triplet
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