Nonequilibrium Quasiparticles and Electron Cooling by Normal Metal — Superconductor Tunnel Junctions

  • Dmitri Golubev
  • Andrei Vasenko


It is known that Normal metal - Insulator - Superconductor (NIS) tunnel junction in a certain range of bias voltages cools the normal metal electrode. Within a simple “semiconductor model” of a superconductor one can derive a cooling power of a single NIS junction [11]:
$$ P = {1 \over {{e^2}R}}\int {dE{{\theta \left( {{E^2} - {^2}} \right)\left| E \right|} \over {\sqrt {{E^2} - {^2}} }}\left( {E - eV} \right)\left[ {{f_{\rm{N}}}\left( {E - eV} \right) - {f_S}\left( E \right)} \right].} $$
Here e is a positive absolute value of the electron charge, R is the normal state resistance of the NIS junction, V is the bias voltage, E is the energy of quasiparticles in the superconductor, Δ is the superconducting gap. f N and f S are distribution functions in normal metal and superconductor respectively. In equilibrium these are Fermi functions. The cooling power (1) turns out to be positive if V < Δ/e.


Bias Voltage Tunnel Junction Normal Metal Cooling Power Equilibrium Distribution Function 
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© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Dmitri Golubev
    • 1
  • Andrei Vasenko
    • 2
  1. 1.Institut für Theoretische FestkörperphysikUniversität KarlsruheKarlsruheGermany
  2. 2.Department of PhysicsMoscow State UniversityMoscowRussia

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