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Magnetic Field Due to Two Straight Wires01:18

Magnetic Field Due to Two Straight Wires

Consider two parallel straight wires carrying a current of 10 A and 20 A in the same direction and separated by a distance of 20 cm. Calculate the magnetic field at a point "P2", midway between the wires. Also, evaluate the magnetic field when the direction of the current is reversed in the second wire.
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
Magnetic Field Due To A Thin Straight Wire01:27

Magnetic Field Due To A Thin Straight Wire

Consider an infinitely long straight wire carrying a current I. The magnetic field at point P at a distance a from the origin can be calculated using the Biot-Savart law.
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)

Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must have a...

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Related Experiment Video

Updated: May 20, 2026

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
05:39

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

Strong-coupling topological Josephson effect in quantum wires.

Flavio S Nogueira1, Ilya Eremin

  • 1Institut für Theoretische Physik III, Ruhr-Universität Bochum, Universitätsstraße 150, 44801 Bochum, Germany. flavio.nogueira@fu-berlin.de

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|July 13, 2012
PubMed
Summary

We explored the Josephson effect in quantum wires with Majorana fermions. A critical point was found where energy levels close, revealing new degeneracies and a 4π-periodic Josephson current.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Mesoscopic Physics

Background:

  • The Josephson effect describes the supercurrent between two superconductors separated by a thin barrier.
  • Majorana zero energy boundary modes are exotic quasiparticles with potential applications in topological quantum computing.

Purpose of the Study:

  • To investigate the Josephson effect in a system of two lattice quantum wires hosting Majorana zero energy boundary modes.
  • To analyze the energy spectrum and Josephson current in the presence of these topological modes.

Main Methods:

  • Exact analytical solution for the Josephson effect in the weak-coupling regime.
  • Analysis of energy level behavior as a function of tunnel amplitude.
  • Calculation of exact tunnel currents for fixed eigenstate parity.

Main Results:

  • The energy spectrum exhibits a ± cos(ϕ/2) contribution in the weak-coupling limit, consistent with perturbative results.
  • A critical tunnel amplitude (gc) is identified where the energy gap closes, leading to new degeneracies and principal values for Josephson energies.
  • The Josephson current displays a 4π periodicity, characteristic of the topological Josephson effect, with additional features upon gap closure.

Conclusions:

  • The study provides an exact solution for the topological Josephson effect in a Majorana-based system.
  • The findings reveal a transparent regime with merged Bogoliubov states and enhanced ground state degeneracies.
  • The results offer insights into the behavior of topological quantum systems and their potential for novel electronic properties.