Quasiparticle, charge, and energy conservation in weak‐coupling superconductors

Abstract

The conservation of quasiparticles, electric charge, and energy in weak-couplihg superconductors is discussed and correlated with the interpretation of the quasiparticles as particle and hole excitations. The formulation employed is that of the Bogolyubov-de Gennes equations. In the absence of spin-dependent interactions these equations are written in the form of a time-dependent Schrodinger equation with a two-component wave function and a two-by-two matrix Hamiltonian. Accordingly, the desired conservation laws are discussed on much the same basis as in ordinary quantum theory. The generalization to permit nonlocal quasiparticle and pair potentials and spin-dependent interactions is briefly presented.Die Konservierung von Quasipartikeln, elektrischer Ladung und Energie in schwach-gekoppelten Supraleitern wird besprochen und mit der Auslegung von Quasipartikeln als Partikel-und Lijcheranregungen in ffbereinstimmung gebracht. Die angewandten Formulierungen sind diejenigen der Bogolyubov-de Gennes-Gleichungen. Ohne spimbhiingige Wechselwirkungen werden diese Gleichungen als eine zeitabhiingige Schrodinger-Gleichung betrachtet, die als Wellenfunktion mit zwei Komponenten und einer Hamilton-Matrix vom Rang awei behandelt werden. Entsprechend werden die Gesetze der Konservierung auf der gleichen Basis wie in der iiblichen Quantentheorie besprochen. Die Verallgemeinerung auf nichtlokale Quasipartikelpotentiale und Paarpotentiale und auf spinabhiingige Wechselwirkungen wird kura besprochen.

Dynamics of conversion of supercurrents into normal currents and vice versa

“…AS and the associated formation and destruction of Cooper pairs and supercurrents can be calculated from the Time-dependent Bogoliubov-de Gennes Equations (TdBdGE) [18,19,9,23]. They describe the evolution of the spinor quasiparticle (q.p.)…”

“…This equation [18,19,9,23] has a non-vanishing right-hand side if the u l and v l describe quasiparticles that decay exponentially in the superconductor during total Andreev reflection, because their energies are less than the maximum value of ∆. In this case the source equation yields a finite supercurrent j sl .…”

“…While the conversion of a normal current into a supercurrent by electron → hole scattering in the interface between an N and an S region of semi-infinite lengths has been described before [18,19,9], the reverse process has not. Thus, it is the purpose of this paper to analyze the normal-current ←→ supercurrent conversion processes in a superconducting layer of finite length L z between two normal current leads.…”

Asymmetric Andreev reflection induced electrical and thermal Hall-like effects in metal/anisotropic superconductor junctions

“…By substituting these definitions into the Bogoliubov-de Gennes equation, we have two conservation laws: [16][17][18] …”

Excess currents larger than the point contact limit in normal-metal/superconducting junctions

“…This conversion process is known as Andreev reflection [1]. When the NS junction carries an electrical current, Andreev reflection is accompanied by the conversion of normal current to supercurrent [2,3]. This supercurrent flow modifies the currentvoltage relation in NS and NSN junctions [4][5][6], superconducting wires [7,8], SNS junctions [9], and NS junctions with a supercurrent parallel to the NS interface [10].…”