scholarly journals Odd-frequency Cooper-pair amplitude around a vortex core in a chiralp-wave superconductor in the quantum limit

2012 ◽  
Vol 86 (6) ◽  
Author(s):  
Takeshi Daino ◽  
Masanori Ichioka ◽  
Takeshi Mizushima ◽  
Yukio Tanaka
Keyword(s):  
Vortex Core ◽  
Cooper Pair ◽  
Quantum Limit ◽  
Pair Amplitude

scholarly journals VORTEX IN CHIRAL SUPERCONDUCTING STATE

2001 ◽  
Vol 15 (10n11) ◽  
pp. 1617-1620
Author(s):  
J. GORYO
Keyword(s):  
Angular Momentum ◽  
Electric Field ◽  
Superconducting State ◽  
Time Reversal ◽  
Vortex Core ◽  
Cooper Pair ◽  
P Wave ◽  
Time Reversal Symmetry ◽  
Fractional Charge ◽  
T Violation

We have investigated the vortex in chiral superconductors, especially in p-wave case. In chiral superconductors the Cooper pair has orbital angular momentum hence U(1), parity (P) and time reversal symmetry (T) are broken simultaneously. We have found that the vortex has fractional charge and fractional angular momentum which comes from P- and T-violation. The fractionalization of the angular momentum suggests that the vortex could be an anyon which obeys the fractional statistics. We have also pointed out that the electric field is induced near the vortex core and non-trivial electromagnetic phenomena are expected to occur.

scholarly journals Low-Lying Quasiparticle Excitations around a Vortex Core in Quantum Limit

1998 ◽  
Vol 80 (13) ◽  
pp. 2921-2924 ◽  
Author(s):  
N. Hayashi ◽  
T. Isoshima ◽  
M. Ichioka ◽  
K. Machida
Keyword(s):  
Vortex Core ◽  
Quantum Limit ◽  
Quasiparticle Excitations

Stagnation point flow in a vortex core

Tellus ◽  
1975 ◽  
Vol 27 (3) ◽  
pp. 269-280 ◽  
Author(s):  
L. Hatton
Keyword(s):  
Stagnation Point ◽  
Vortex Core ◽  
Stagnation Point Flow

Superfluidity and Superconductivity

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Wave Packet ◽  
Long Range ◽  
Cooper Pair ◽  
Bose Condensation ◽  
Range Order ◽  
Condensed State ◽  
Long Range Order ◽  
Coherent Wave

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.

scholarly journals Thermoelectric current in a graphene Cooper pair splitter

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.

scholarly journals Particle simulation of plasmons

Nanophotonics ◽  
2020 ◽  
Vol 9 (10) ◽  
pp. 3303-3313 ◽  
Author(s):  
Wen Jun Ding ◽  
Jeremy Zhen Jie Lim ◽  
Hue Thi Bich Do ◽  
Xiao Xiong ◽  
Zackaria Mahfoud ◽  
...  
Keyword(s):  
Simulation Method ◽  
Electron Excitation ◽  
Particle Simulation ◽  
Quantum Limit ◽  
Free Electrons ◽  
Theoretical Approaches ◽  
Electromagnetic Responses ◽  
Electric And Magnetic Fields ◽  
Particle Simulations ◽  
Collective Oscillations

AbstractParticle simulation has been widely used in studying plasmas. The technique follows the motion of a large assembly of charged particles in their self-consistent electric and magnetic fields. Plasmons, collective oscillations of the free electrons in conducting media such as metals, are connected to plasmas by very similar physics, in particular, the notion of collective charge oscillations. In many cases of interest, plasmons are theoretically characterized by solving the classical Maxwell’s equations, where the electromagnetic responses can be described by bulk permittivity. That approach pays more attention to fields rather than motion of electrons. In this work, however, we apply the particle simulation method to model the kinetics of plasmons, by updating both particle position and momentum (Newton–Lorentz equation) and electromagnetic fields (Ampere and Faraday laws) that are connected by current. Particle simulation of plasmons can offer insights and information that supplement those gained by traditional experimental and theoretical approaches. Specifically, we present two case studies to show its capabilities of modeling single-electron excitation of plasmons, tracing instantaneous movements of electrons to elucidate the physical dynamics of plasmons, and revealing electron spill-out effects of ultrasmall nanoparticles approaching the quantum limit. These preliminary demonstrations open the door to realistic particle simulations of plasmons.

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