Spectral properties of locally correlated electrons in a Bardeen–Cooper–Schrieffer superconductor

Abstract

We present a detailed study of the spectral properties of a locally correlated site embedded in a BCS superconducting medium. To this end the Anderson impurity model with superconducting bath is analysed by numerical renormalisation group (NRG) calculations. We calculate one and two-particle dynamic response function to elucidate the spectral excitation and the nature of the ground state for different parameter regimes with and without particle-hole symmetry. The position and weight of the Andreev bound states is given for all relevant parameters. We also present phase diagrams for the different ground state parameter regimes. This work is also relevant for dynamical mean field theory extensions with superconducting symmetry breaking.

To Screen or Not to Screen, That is the Question!

“…23 The results obtained reproduced previously reported calculations. 22 When the QD is tuned in an odd valley, the system has two possible ground states (GSs): a magnetic doublet (S = 1 2 ) or a singlet (S = 0). The nature of the singlet has two well-known limiting cases: BCS-like ABS (i.e., a superposition of a zero and double occupancy) or Kondo-like bound state (i.e., a many-body state where the QD's spin is screened by electrons from the metallic reservoir near the Fermi energy), although there is no definite boundary between them.…”

“…The nature of the singlet has two well-known limiting cases: BCS-like ABS (i.e., a superposition of a zero and double occupancy) or Kondo-like bound state (i.e., a many-body state where the QD's spin is screened by electrons from the metallic reservoir near the Fermi energy), although there is no definite boundary between them. 22 The actual GS is determined by the magnitude of the Kondo energy k B T K (which is a function of U, and ε 0 24-27 ) with respect to . For …”

Nonequilibrium transport through a Josephson quantum dot

“…Recent theoretical [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] and experimental progress [40][41][42][43][44][45][46] added a quantitative understanding for mesoscopic systems including the effect of finite but equal temperatures (∆T = 0). 29,36,38 It was even possible to achieve a satisfying agreement between experimental data for the critical current obtained with a carbon nanotube as the quantum dot 44 and model calculations.…”

Nonequilibrium transport theory of the singlet-triplet transition: Perturbative approach

“…Therefore, both phase shifts are close to δ ± ≈ π/2 by the Friedel sum rule. 13 While for a vertical dot the contributions of the channels i = ± add up to the conductance, and amount in a total conductance of G lin = 4e 2 /h, for lateral dots there is a destructive interference (see Eq. 30), which finally amounts in a complete back-reflection of electrons and no conductance, G ≈ 0.…”

“…These devices are promising candidates for our future electronics, and might possibly be used as building blocks of spintronics devices and spin-based quantum computers, too. 8 Moreover, the unprecedented control of these minuscule structures opens new and fascinating possibilities to build and study hybrid structures, [9][10][11][12][13] entangle electron spins, 14 and also to realize and study simple quantum systems in the close vicinity of quantum phase transitions under non-equlibrium conditions. [15][16][17][18][19] Understanding the physical properties of these tiny electronic circuits represents a major challenge to theoretical as well as to experimental physicists.…”