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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...
P-N junction01:11

P-N junction

A p-n junction is formed when p-type and n-type semiconductor materials are joined together. At the interface of the p-n junction, holes from the p-side and electrons from the n-side begin to diffuse into the opposite sides due to the concentration gradient. This diffusion of carriers leads to a region around the junction where there are no free charge carriers, known as the depletion region. The charge density within the depletion region for the n-side and p-side can be described by the...
Metal-Semiconductor Junctions01:24

Metal-Semiconductor Junctions

The contact of metal and semiconductor can lead to the formation of a junction with either Schottky or Ohmic behavior.
Schottky Barriers
Schottky barriers arise when a metal with a work function (Φm) contacts a semiconductor with a different work function (Φs). Initially, electrons transfer until the Fermi levels of the metal and semiconductor align at equilibrium. For instance, if Φm > Φs, the semiconductor Fermi level is higher than the metal's before contact. The semiconductor's...
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...
Junction Potentials in Galvanic Cells01:21

Junction Potentials in Galvanic Cells

The Nernst equation, derived under the assumption of thermodynamic equilibrium, calculates the electromotive force (emf) as the sum of potential differences at phase boundaries in a reversible cell without a liquid junction. However, in irreversible cells such as the Daniell cell, an additional potential difference named the liquid-junction potential (EJ) arises across the interface of two electrolyte solutions due to different ion diffusion rates. This EJ represents the potential difference...
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,...

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Updated: May 11, 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

Multiterminal Coulomb-Majorana junction.

Alexander Altland1, Reinhold Egger

  • 1Institut für Theoretische Physik, Universität zu Köln, Zülpicher Strasse 77, D-50937 Köln, Germany.

Physical Review Letters
|May 28, 2013
PubMed
Summary
This summary is machine-generated.

Finite charging energy in superconducting systems with helical nanowires can destabilize Majorana fermion states. Even weak interactions shift system behavior, potentially leading to exotic Kondo physics instead of ideal Andreev reflection.

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Single-Molecule Förster Resonance Energy Transfer Methods for Real-Time Investigation of the Holliday Junction Resolution by GEN1
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Single-Molecule Förster Resonance Energy Transfer Methods for Real-Time Investigation of the Holliday Junction Resolution by GEN1

Published on: September 18, 2019

Area of Science:

  • Condensed Matter Physics
  • Quantum Phenomena
  • Nanotechnology

Background:

  • Majorana fermion bound states are crucial for topological quantum computing.
  • Superconducting islands coupled to nanowires are a promising platform for realizing these states.
  • The influence of charging effects on these systems is not fully understood.

Purpose of the Study:

  • To investigate the impact of finite charging energy on Majorana fermion bound states in mesoscopic superconducting systems.
  • To explore how charging interactions affect the low-energy behavior and stability of these states.
  • To identify conditions that lead to exotic quantum phenomena.

Main Methods:

  • Theoretical modeling of multiple helical nanowires coupled to a mesoscopic superconducting island.
  • Analysis of low-energy effective Hamiltonians considering finite charging energy.
  • Renormalization group techniques to study fixed points and phase transitions.

Main Results:

  • Weak finite charging energy significantly alters the system's low-energy behavior.
  • Interactions below a critical threshold can drive the system towards an exotic Kondo fixed point.
  • The ideally Andreev reflecting fixed point, expected for infinite capacitance, is destabilized by charging interactions.

Conclusions:

  • Finite charging energy is a critical parameter that can destabilize topological states in superconducting nanowire systems.
  • The system's behavior can transition from decoupled wires to exotic Kondo physics depending on interaction strength.
  • These findings highlight the importance of considering charging effects for practical applications of Majorana fermions.