In search of the vortex charge and the Cooper pair mass

Chapter 13 addresses Bose condensation in superfluids (and superconductors), which involves the field operator ψ‎ having a c-number component (<ψ(x,t)>≠0), challenging number conservation. The nonlinear Gross-Pitaevskii equation is derived for this condensate wave function<ψ>=ψ−ψ˜, facilitating identification of the coherence length and the core region of vortex motion. The noncondensate Green’s function G˜1(1,1′)=−i<(ψ˜(1)ψ˜+(1′))+> and the nonvanishing anomalous correlation function F˜∗(2,1′)=−i<(ψ˜+(2)ψ˜+(1′))+> describe the dynamics and elementary excitations of the non-condensate states and are discussed in conjunction with Landau’s criterion for viscosity. Associated concepts of off-diagonal long-range order and the interpretation of <ψ> as a superfluid order parameter are also introduced. Anderson’s Bose-condensed state, as a phase-coherent wave packet superposition of number states, resolves issues of number conservation. Superconductivity involves bound Cooper pairs of electrons capable of Bose condensation and superfluid behavior. Correspondingly, the two-particle Green’s function has a term involving a product of anomalous bound-Cooper-pair condensate wave functions of the type F(1,2)=−i<(ψ(1)ψ(2))+>≠0, such that G2(1,2;1′,2′)=F(1,2)F+(1′,2′)+G˜2(1,2;1′,2′). Here, G˜2 describes the dynamics/excitations of the non-superfluid-condensate states, while nonvanishing F,F+ represent a phase-coherent wave packet superposition of Cooper-pair number states and off-diagonal long range order. Employing this form of G2 in the G1-equation couples the condensed state with the non-condensate excitations. Taken jointly with the dynamical equation for F(1,2), this leads to the Gorkov equations, encompassing the Bardeen–Cooper–Schrieffer (BCS) energy gap, critical temperature, and Bogoliubov-de Gennes eigenfunction Bogoliubons. Superconductor thermodynamics and critical magnetic field are discussed. For a weak magnetic field, the Gorkov-equations lead to Ginzburg–Landau theory and a nonlinear Schrödinger-like equation for the pair wave function and the associated supercurrent, along with identification of the Cooper pair density. Furthermore, Chapter 13 addresses the apparent lack of gauge invariance of London theory with an elegant variational analysis involving re-gauging the potentials, yielding a manifestly gauge invariant generalization of the London equation. Consistency with the equation of continuity implies the existence of Anderson’s acoustic normal mode, which is supplanted by the plasmon for Coulomb interaction. Type II superconductors and the penetration (and interaction) of quantized magnetic flux lines are also discussed. Finally, Chapter 13 addresses Josephson tunneling between superconductors.

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Thermoelectric current in a graphene Cooper pair splitter

Nature Communications ◽

10.1038/s41467-020-20476-7 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Z. B. Tan ◽

A. Laitinen ◽

N. S. Kirsanov ◽

A. Galda ◽

V. M. Vinokur ◽

...

Keyword(s):

Cooper Pair ◽

Theoretical Description ◽

Seebeck Effect ◽

Normal Metal ◽

Electric Voltage ◽

Power Generators ◽

Metal Structures ◽

Fundamental Phenomenon ◽

Non Local ◽

Cooper Pair Splitting

AbstractGeneration of electric voltage in a conductor by applying a temperature gradient is a fundamental phenomenon called the Seebeck effect. This effect and its inverse is widely exploited in diverse applications ranging from thermoelectric power generators to temperature sensing. Recently, a possibility of thermoelectricity arising from the interplay of the non-local Cooper pair splitting and the elastic co-tunneling in the hybrid normal metal-superconductor-normal metal structures was predicted. Here, we report the observation of the non-local Seebeck effect in a graphene-based Cooper pair splitting device comprising two quantum dots connected to an aluminum superconductor and present a theoretical description of this phenomenon. The observed non-local Seebeck effect offers an efficient tool for producing entangled electrons.

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Multiplicity, Parity and Angular Momentum of a Cooper Pair in Unconventional Superconductors of D4h Symmetry: Sr2RuO4 and Fe-Pnictide Materials

Symmetry ◽

10.3390/sym13081435 ◽

2021 ◽

Vol 13 (8) ◽

pp. 1435

Author(s):

Victor G. Yarzhemsky

Keyword(s):

Angular Momentum ◽

Cooper Pair ◽

Point Group ◽

Group Symmetry ◽

Cooper Pairs ◽

Group Approach ◽

Angular Momentum Projection ◽

Space Group ◽

Unconventional Superconductors ◽

Even Pairs

Sr2RuO4 and Fe-pnictide superconductors belong to the same point group symmetry D4h. Many experimental data confirm odd pairs in Sr2RuO4 and even pairs in Fe-pnictides, but opposite conclusions also exist. Recent NMR results of Pustogow et al., which revealed even Cooper pairs in Sr2RuO4, require reconsideration of symmetry treatment of its SOP (superconducting order parameter). In the present work making use of the Mackey–Bradley theorem on symmetrized squares, a group theoretical investigation of possible pairing states in D4h symmetry is performed. It is obtained for I4/mmm , i.e., space group of Sr2RuO4, that triplet pairs with even spatial parts are possible in kz direction and in points M and Y. For the two latter cases pairing of equivalent electrons with nonzero total momentum is proposed. In P4/nmm space group of Fe- pnictides in point M, even and odd pairs are possible for singlet and triplet cases. It it shown that even and odd chiral states with angular momentum projection m=±1 have nodes in vertical planes, but Eg is nodal , whereas Eu is nodeless in the basal plane. It is also shown that the widely accepted assertion that the parity of angular momentum value is directly connected with the spatial parity of a pair is not valid in a space-group approach to the wavefunction of a Cooper pair.

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Single-photon pump by Cooper-pair splitting

Physical Review Research ◽

10.1103/physrevresearch.1.033098 ◽

2019 ◽

Vol 1 (3) ◽

Cited By ~ 2

Author(s):

Mattia Mantovani ◽

Wolfgang Belzig ◽

Gianluca Rastelli ◽

Robert Hussein

Keyword(s):

Cooper Pair ◽

Single Photon ◽

Cooper Pair Splitting

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Cooper Pair-Like Systems at High Temperature and their Role on Fluctuations Near the Critical Temperature

International Journal of Modern Physics B ◽

10.1142/s0217979298002349 ◽

1998 ◽

Vol 12 (29n31) ◽

pp. 3216-3219 ◽

Cited By ~ 2

Author(s):

M. Ausloos ◽

S. Dorbolo

Keyword(s):

Phase Transition ◽

Electrical Resistivity ◽

High Temperature ◽

Critical Temperature ◽

Oxygen Diffusion ◽

Cooper Pair ◽

Anomalous Behavior ◽

Anomalous Effect ◽

Linear Temperature ◽

Ybco Sample

A logarithmic behavior is hidden in the linear temperature regime of the electrical resistivity R(T) of some YBCO sample below 2T c where "pairs" break apart, fluctuations occur and "a gap is opening". An anomalous effect also occurs near 200 K in the normal state Hall coefficient. In a simulation of oxygen diffusion in planar 123 YBCO, an anomalous behavior is found in the oxygen-vacancy motion near such a temperature. We claim that the behavior of the specific heat above and near the critical temperature should be reexamined in order to show the influence and implications of fluctuations and dimensionality on the nature of the phase transition and on the true onset temperature.

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Entanglement from a nanomechanical resonator weakly coupled to a single Cooper-pair box

Physical Review B ◽

10.1103/physrevb.72.195411 ◽

2005 ◽

Vol 72 (19) ◽

Cited By ~ 48

Author(s):

L. Tian

Keyword(s):

Cooper Pair ◽

Nanomechanical Resonator ◽

Cooper Pair Box ◽

Weakly Coupled

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Superconducting coherence length of hole-doped cuprates obtained from electron–boson spectral density function

Scientific Reports ◽

10.1038/s41598-021-91163-w ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Jungseek Hwang

Keyword(s):

Spectral Density ◽

Coherence Length ◽

Cooper Pair ◽

Average Frequency ◽

Spin Fluctuations ◽

Fermi Velocity ◽

Cooper Pairs ◽

Spectroscopic Techniques ◽

Microscopic Mechanism ◽

Superconducting Coherence Length

AbstractElectron–boson spectral density functions (EBSDFs) can be obtained from measured spectra using various spectroscopic techniques, including optical spectroscopy. EBSDFs, known as glue functions, are suggested to have a magnetic origin. Here, we investigated EBSDFs obtained from the measured optical spectra of hole-doped cuprates with wide doping levels, from underdoped to overdoped cuprates. The average frequency of an EBSDF provides the timescale for the spin fluctuations to form Cooper pairs. This timescale is directly associated with retarded interactions between electrons. Using this timescale and Fermi velocity, a reasonable superconducting coherence length, which reflects the size of the Cooper pair, can be extracted. The obtained coherence lengths were consistent with those measured via other experimental techniques. Therefore, the formation of Cooper pairs in cuprates can be explained by spin fluctuations, the timescales of which appear in EBSDFs. Consequently, EBSDFs provide crucial information on the timescale of the microscopic mechanism of Cooper pair formation.

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