Superconductivity in Small Systems.

We have proposed a theory called the resonating Hartree-Bogoliubov (Res HB) theory to describe large quantum fluctuations in a superconducting Fermion system. One needs also to deal with small quantum fluctuations which correspond to those described by the conventional random phase approximation (RPA). We can derive a new approximation called the Res HB RPA from time dependent small fluctuations of the Res HB ground state. The theory can give a unified description of collective excitations arising from large and small quantum fluctuations and their coupling in a superconducting system. For instance it may be applicable to rotational and vibrational excitations in nuclei with resonance of different deformed shapes.We have proposed a theory called the resonating Hartree-Bogoliubov (Res HB) theory to describe large quantum fluctuations in a superconducting Fermion system. One needs also to deal with small quantum fluctuations which correspond to those described by the conventional random phase approximation (RPA). We can derive a new approximation called the Res HB RPA from time dependent small fluctuations of the Res HB ground state. The theory can give a unified description of collective excitations arising from large and small quantum fluctuations and their coupling in a superconducting system. For instance it may be applicable to rotational and vibrational excitations in nuclei with resonance of different deformed shapes.

Progress of Theoretical PhysicsAug 1, 19916 citations

Superconductivity

David S. Simon

Undergraduate texts in physicsJan 1, 20250 citations

Superconductivity from repulsion: Variational results for the two-dimensional Hubbard model in the limit of weak interaction

D. Baeriswyl

The two-dimensional Hubbard model is studied for small values of the interaction strength ( $U$ of the order of the hopping amplitude $t$ ), using a variational ansatz well suited for this regime. The wave function, a refined Gutzwiller ansatz, has a BCS mean-field state with $d$ -wave symmetry as its reference state. Superconducting order is found for densities $n<1$ (but not for $n=1$ ). This resolves a discrepancy between results obtained with the functional renormalization group, which do predict superconducting order for small values of $U$ , and numerical simulations, which did not find superconductivity for $U\ensuremath{\lesssim}4t$. Both the gap parameter and the order parameter have a domelike shape as a function of $n$ with a maximum for $n\ensuremath{\approx}0.8$. Expectation values for the energy, the particle number, and the superconducting order parameter are calculated using a linked-cluster expansion up to second order in $U$ . In this way large systems (millions of sites) can be readily treated and well converged results are obtained. A big size is indeed required to see that the gap becomes very small at half filling and probably tends to zero in the thermodynamic limit, whereas away from half filling a finite asymptotic limit is reached. For a lattice of a given size the order parameter becomes finite only above a minimal coupling strength ${U}_{c}$ . This threshold value decreases steadily with increasing system size, which indicates that superconductivity exists for arbitrarily small $U$ for an infinite system. For moderately large systems the size dependence is quite irregular, due to variations in level spacings at the Fermi energy. The fluctuations die out if the gap parameter spans several level spacings.The two-dimensional Hubbard model is studied for small values of the interaction strength ($U$ of the order of the hopping amplitude $t$), using a variational ansatz well suited for this regime. The wave function, a refined Gutzwiller ansatz, has a BCS mean-field state with $d$-wave symmetry as its reference state. Superconducting order is found for densities $n<1$ (but not for $n=1$). This resolves a discrepancy between results obtained with the functional renormalization group, which do predict superconducting order for small values of $U$, and numerical simulations, which did not find superconductivity for $U\ensuremath{\lesssim}4t$. Both the gap parameter and the order parameter have a domelike shape as a function of $n$ with a maximum for $n\ensuremath{\approx}0.8$. Expectation values for the energy, the particle number, and the superconducting order parameter are calculated using a linked-cluster expansion up to second order in $U$. In this way large systems (millions of sites) can be readily treated and well converged results are obtained. A big size is indeed required to see that the gap becomes very small at half filling and probably tends to zero in the thermodynamic limit, whereas away from half filling a finite asymptotic limit is reached. For a lattice of a given size the order parameter becomes finite only above a minimal coupling strength ${U}_{c}$. This threshold value decreases steadily with increasing system size, which indicates that superconductivity exists for arbitrarily small $U$ for an infinite system. For moderately large systems the size dependence is quite irregular, due to variations in level spacings at the Fermi energy. The fluctuations die out if the gap parameter spans several level spacings.

arXiv:1809.04916Physical review. B./Physical review. BJun 27, 20196 citations

Superconducting Quantum Arrays for Broadband RF Systems

Victor K. Kornev, Aleksei Sharafiev, Igor I. Soloviev +2 more

Superconducting Quantum Arrays (SQAs), homogenous arrays of Superconducting Quantum Cells, are developed for implementation of broadband radio frequency (RF) systems capable of providing highly linear magnetic signal to voltage transfer with high dynamic range, including active electrically small antennas (ESAs). Among the proposed quantum cells which are bi-SQUID and Differential Quantum Cell (DQC), the latter delivered better performance for SQAs. A prototype of the transformer-less active ESA based on a 2D SQA with nonsuperconducting electric connection of the DQCs was fabricated using HYPRES niobium process with critical current density 4.5 kA/cm 2 . The measured voltage response is characterized by a peak-to-peak swing of ~100 mV and steepness of ~6500 μV/μT.Superconducting Quantum Arrays (SQAs), homogenous arrays of Superconducting Quantum Cells, are developed for implementation of broadband radio frequency (RF) systems capable of providing highly linear magnetic signal to voltage transfer with high dynamic range, including active electrically small antennas (ESAs). Among the proposed quantum cells which are bi-SQUID and Differential Quantum Cell (DQC), the latter delivered better performance for SQAs. A prototype of the transformer-less active ESA based on a 2D SQA with nonsuperconducting electric connection of the DQCs was fabricated using HYPRES niobium process with critical current density 4.5 kA/cm 2 . The measured voltage response is characterized by a peak-to-peak swing of ~100 mV and steepness of ~6500 μV/μT.

Journal of Physics Conference SeriesMay 12, 20143 citations

A New Spin on Superconductivity

Marric Stephens

PhysicsAug 19, 20260 citations

The two-dimensional Hubbard model is studied for small values of the interaction strength (

U

of the order of the hopping amplitude

t

), using a variational ansatz well suited for this regime. The wave function, a refined Gutzwiller ansatz, has a BCS mean-field state with

d

-wave symmetry as its reference state. Superconducting order is found for densities

n<1

(but not for

n=1

). This resolves a discrepancy between results obtained with the functional renormalization group, which do predict superconducting order for small values of

U

, and numerical simulations, which did not find superconductivity for $U\ensuremath{\lesssim}4t$. Both the gap parameter and the order parameter have a domelike shape as a function of

n

with a maximum for $n\ensuremath{\approx}0.8$. Expectation values for the energy, the particle number, and the superconducting order parameter are calculated using a linked-cluster expansion up to second order in

U

. In this way large systems (millions of sites) can be readily treated and well converged results are obtained. A big size is indeed required to see that the gap becomes very small at half filling and probably tends to zero in the thermodynamic limit, whereas away from half filling a finite asymptotic limit is reached. For a lattice of a given size the order parameter becomes finite only above a minimal coupling strength

{U}_{c}

. This threshold value decreases steadily with increasing system size, which indicates that superconductivity exists for arbitrarily small

U

for an infinite system. For moderately large systems the size dependence is quite irregular, due to variations in level spacings at the Fermi energy. The fluctuations die out if the gap parameter spans several level spacings.