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What does the $I$-$V$ curve in josephson junction mean?

According to the $I$-$V$ curve for Josephson junction tunneling for S-I-S (superconductor-insulator-superconductor), Do we have any tunneling current for $0< V\leq V_c$? If yes, then why don't we ...
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1 answer
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Analogies between Fraunhofer diffraction and Josephson junctions

There are several analogies between diffraction patterns and Josephson junctions, especially between a double slit experiment and two Josephson junctions in a superconducting ring (like this): Both ...
bernd's user avatar
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5 votes
2 answers
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The Hamiltonian for Josephson Junctions

In the Feynman Lectures on physics, Feynman says the amplitudes across a Josephson Junction should be related by the following, where the subscript denotes the side of the junction that the amplitude ...
Bob's user avatar
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4 votes
1 answer
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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 ...
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3 votes
1 answer
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Regimes of Josephson junction

There are several formulas to describe critical current in Josepshon S-N-S junction mainly based on Eilenberger and Usadel equations for quasi-classical Green's functions. The starting point is the ...
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3 votes
1 answer
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Lagrangian for a non-linear wave equation

I have the following wave equation that I am trying to understand better: $$\frac{\partial^2 \varphi}{\partial t^2}-\frac{\partial^2 \sin{\varphi}}{\partial x^2}=0.$$ This equation describes an LC ...
S Thomas's user avatar
3 votes
1 answer
1k views

Josephson junction: why do we need a capacitance in parallel to the inductance in the description?

To start: I am really a huge beginner in Josephson junction. I need to understand the electrical equations associated to it, I don't need to go in the superconducting physics and I would like to stick ...
StarBucK's user avatar
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1 answer
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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 ...
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0 answers
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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
  • 3,668
2 votes
1 answer
439 views

Josephson junction characteristics

Is there a physical interpretation for the characteristic frequency and voltage of a josephson junction? $$ \omega_c = \frac{2 \pi I_0 R}{\Phi_0} $$ $$ V_c = I_0 R $$ $I_0$ is the critical current ...
psitae's user avatar
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2 votes
1 answer
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Microscopic derivation of the Josephson effect

In section 18.7 of Bruus & Flensberg the authors provide a microscopic derivation of the Josephson effect. The hamiltonian on both sides of the tunnelling junction is just the typical BCS ...
Kouta Dagnino's user avatar
2 votes
1 answer
262 views

Computing flux modulation of the energy spectrum in a DC SQUID

I've been reading some work by Y. Chen et al's paper on tunable couplers for transmon qubits (you can find the work at https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.113.220502) and wanted to ...
Nathan Holman's user avatar
2 votes
0 answers
89 views

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 ...
SlothForeva's user avatar
2 votes
0 answers
26 views

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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2 votes
1 answer
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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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2 answers
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Resistively and Capacitively Shunted Junction (RCSJ) Model of Josephson Junction Numerical Solution

I'm trying to write a program to plot the I-V charateristics the josephson junction using a python program for some given values of resistance $R$, capacitance $C$, and critical current $I_0$, using ...
L lawliet's user avatar
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1 vote
1 answer
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What makes cooper pairs hop to another superconductor?

I know the derivation and how the Josephson effect works. But if we just have two slabs of superconducting material placed together with an insulator between them, what makes the initial hopping occur?...
mikanim's user avatar
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1 answer
21 views

Thermal Smearing in Josephson Junction

I'm basically trying to simulate a josephson junction at a particular temperature. As per some of the plots I could find, the rise in temperature leads to a rounding of the I - V curve. I was ...
L lawliet's user avatar
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1 vote
1 answer
36 views

Unitary Transformation Taking a 4$\pi$ Periodic Wave Function to 2$\pi$ Periodic Wave Function

I am reading the following paper, which discusses Majorana fermions in Josephson junction arrays. Initially, the paper starts with a model such that the wavefunctions are $4\pi$ periodic. These ...
user avatar
1 vote
1 answer
70 views

Wavefunction used in Derivation of Josephson Effect

In deriving the Josephson Effect, the ansatz wavefunction is given as $\sqrt{n} \exp{(i\delta)}$ which leads to the Josephson Relations. It seems that this wavefunction is used because $<\psi|\psi&...
Rixcrix's user avatar
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What is the temperature dependence of the critical current in weak links?

I am now working on hybrid Josephson junctions that are supposed to be tunnel junctions, so that the temperature dependence of the critical current should be $$ I_c (T)=\frac{\pi}{2}\frac{\Delta(T)}{...
casx's user avatar
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1 vote
1 answer
52 views

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 ...
Dragon123's user avatar
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1 vote
0 answers
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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
1 vote
0 answers
58 views

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
1 vote
0 answers
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
1 vote
0 answers
98 views

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 ...
user333905's user avatar
1 vote
0 answers
166 views

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 ...
user129412's user avatar
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1 vote
1 answer
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Why is Andreev reflection in a NS junction retroreflective?

Background Consider a normal metal (N) - superconductor (S) junction. Assume N is in the region $x<0$ and S is in the region $x>0$. In addition, let us assume that the system is invariant in the ...
MOOSE's user avatar
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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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0 answers
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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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1 vote
0 answers
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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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1 vote
0 answers
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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
  • 367
0 votes
1 answer
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Questions about the SQUID (Superconducting Quantum Interference Device)

If the bias current is approximately 2 Ic (double the critical current), wouldn’t the whole loop become normal? Or do only the Josephson junctions become normal? And when the junctions become ...
Laura's user avatar
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0 votes
3 answers
111 views

Questions regarding the pair of Josephson equations

The Josephson effect was somehow surprising because a current can flow without applying an external voltage. The pair of seminal equations are (I refrain of repeating what symbol is what) \begin{...
user2820579's user avatar
0 votes
1 answer
423 views

Why do excited states of charge qubits have higher charge sensitivity than the ground state?

Lets define charge qubits as two coupled superconductors connected by a Josephson tunnel junction governed by the Hamiltonian \begin{equation} H = 4 E_C \left(n - n_g\right)^2 - E_J \cos{\phi} \end{...
user129412's user avatar
  • 1,521
0 votes
2 answers
517 views

Is there net current through a Josephson junction at zero bias?

It is widely stated that when a Josephson junction is placed in a superconducting circuit, the cooper pairs can tunnel through and create a net current without a bias voltage. However, given that the ...
mactud's user avatar
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0 answers
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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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0 answers
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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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1 answer
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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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0 answers
53 views

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
0 votes
1 answer
286 views

Definition of Josephson current

Consider a system of two superconductors (with Hamiltonian $H_{SC1}$ and $H_{SC2}$) weakly tunnel coupled via some intermediate system, i.e. an insulator, a ferromagnet, a quantum dot, etc. (described ...
IdeA's user avatar
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0 answers
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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