# Questions tagged [josephson-junction]

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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 ...
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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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### 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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### 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 ...
664 views

### 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 ...
309 views

### 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 ...
1 vote
26 views

### 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 ...
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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 ...
1 vote
96 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 ...
1 vote
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 ...
1 vote
85 views

### 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?...
515 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 ...
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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 ...
1 vote
339 views

### 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 ...
1 vote
699 views

### 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 ...
283 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 ...
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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.
1k views

### 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 ...
1 vote