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Inconsistency in microscopic derivation of the Josephson effect?

My question is related to, but different from, other questions in this platform (see this, this and this). One of the few places I have found in literature that provide a microscopic derivation of the ...
Lucas Baldo's user avatar
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Current Voltage characteristic of Josephson Junction

I'm having trouble understanding what the current voltage characteristic of a Josephson Junction looks like. When we first looked at the voltage state of a Josephson Junction we got the following ...
runrun's user avatar
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What can I expect to see in a oscillator exhibiting bifurcation?

I have a program which aims to simulate a Josephson Bifurcation Amplifier. I am currently trying to obtain a plot of the probability of bifurcation as a function of the ratio between the driving and ...
turnip's user avatar
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Josephson supercurrent measurement in a lab

This may be a very trivial question but I am a theoretician and can't find the answer to this question for the life of me. Is it possible to actually measure the Josephson supercurrent flowing through ...
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Equality of Bose Lattice Hamiltonian and Josephson Array Hamiltonian

I am currently reading the paper Boson localization and the superfluid-insulator transition by Fisher, Weichman, and Fisher. Equation 2.1 defines the Hamiltonian of a Bose Lattice gas as $$ H = -\sum_{...
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Normal metal-superconductor action (revealing Andreev reflection)

Short Example A conventional Josephson junction, which consists of a superconductor-insulator-superconductor (SIS) sandwich and is biased by a constant current $I$, has the following action: $$S_{SIS}\...
Olexot's user avatar
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Is Number Operator a Generalized Momentum?

In superconducting circuit, the number operator, $\hat{n}$, and phase operator, $\hat{\varphi}$ are conjugate pairs. Is $\hat{n}$ the canonical momentum, conjugate momentum, and also generalized ...
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Tenfold way symmetry classification for systems with pseudomomentum

For classifying Hamiltonians $H(\vec{k})$ of topological insulators/superconductors in the tenfold way, one has to see whether the Hamiltonians obeys (disobeys) symmetries of the following type (let's ...
Dave Force's user avatar
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Josephson current operator and conjugate variables

I am studying multi-terminal Josephson junctions and encountered the formula \begin{align} \hat{I}_{\alpha} = \frac{2e}{\hbar}\frac{\partial\hat{H}}{\partial\phi_{\alpha}} \end{align} where $\hat{I}_{\...
Lev Teshler's user avatar
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115 views

Lagrangian of a Josephson junction

The lagrangian density of the system, as given in Squeezed-state generation using a Josephson parametric amplifier, B Yurke, is given by $$ L(x) = \delta(x)\ \frac{\hbar}{2e} [I_c Cos(\phi) + \phi \...
Raghav Sah's user avatar
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How to Understand Quantum Phase Slips in Josephson Junction Array in terms of Tunneling?

I am trying to understand quantum phase slips in terms of quantum tunneling between the minima of the Josephson potential (see page 2 right before equation (1)). Consider the following circuit diagram ...
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How asymmetric does a SQUID need to be to characterize the current-phase relationship?

I've been reading the paper Measurement of the Current-Phase Relation of Superconducting Atomic Contacts by Della Rocca et al. from 2007 (PRL, arXiv). Here they do measurements on a DC SQUID ...
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Characteristic lengths in SNS Josephson Junction

An S-N-S Josephson junction is formed by two Superconducting (S) leads separated by a normal metal (N) which acts like the weak link. While studying, I often encounter the words diffusive, long, ...
Krlngc's user avatar
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Original derivation of the Josephson effect

In my efforts to understand Josephson's original derivation of the effect that bears his name, I was led to Eqs. 3.68 on pg. 69 from Tinkham's book (Introduction to Superconductivity, McGraw-Hill, 2nd ...
bk17's user avatar
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Josephson junction exceeding the coherence length of the cooper pair

In this recent paper http://arxiv.org/abs/1504.03286, the authors present the data that they measured Fraunhofer-like diffraction pattern in a Josephson junction with graphene sandwiched between ...
chicane's user avatar
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Why are the Fermi levels of two different superconductors in a Josephson junction the same?

ELECTRON TUNNELING AND SUPERCONDUCTIVITY (Fig. 10A)– This is Giaever's Nobel lecture about how to measure the energy gap of each superconductor using a Josephson junction. I wonder why we can assume ...
isend's user avatar
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Josephson relations when $V$ approaches the superconducting gap

The standard Josephson relations are $I = I_0 \sin(\phi)$ and $V = \phi_0 \dot{\phi} / 2\pi$. However these equations break down when $I$ exceeds $I_0$, or when $V$ exceeds $V_\text{gap} = 2\Delta / e$...
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Second harmonic of Josephoson current

The expression of Josephson current including the second harmonic between two s-wave superconductors is $$ I_{J}=I_{1}sin(\phi)+I_{2}sin(2\phi) $$ I try to calculate $I_{2}$ by following derivation in ...
Hui's user avatar
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Current in a Superconducting Loop Interrupted by a Josephson Junction

Assuming we have the following circuit consisting of a superconducting loop having the same superconductor material everywhere, and interrupted by the short Josephson junction J1 with a phase ...
M B's user avatar
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Josephson Potential Derivations

I am currently reading the following lecture notes to understand phase slips in the Josephson junction (JJ). For now, I am trying to understand how to derive the Josephson potential. I am first given ...
user333905's user avatar
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Origin of Josephson voltage equation?

i cant find a satisfying explanation, and I cant figure it out myself, a derivation for the josephson equation: $$U(t)=\frac{\hbar}{2e}\frac{d\phi}{dt}$$ where $U(t)$ is the voltage, and $\phi$ is the ...
Learn4life's user avatar
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What is the difference between a Josephson junction and a superconducting tunnel junction?

I am wondering if there is any difference between a Josephson junctions and superconducting tunnel junctions. I appreciate a good explanation.
user101464's user avatar