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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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Measuring how one directional quantity affects another along a specific path involves comparing their orientation and strength. When two such quantities are represented using direction and amount, a numerical result is computed to show how much one acts along the path of the other. This result comes from a rule combining both inputs' horizontal and vertical parts and adding the results.This calculation gives a single value that grows larger when both inputs point in similar directions and...
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The dot product is an essential concept in mathematics and physics.
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The dot product is a powerful tool in problem-solving involving vectors, given that the dot product of two vectors is the product of their magnitudes and the cosine of the angle between them measured anti-clockwise. Solving problems involving the dot product requires understanding its properties and developing a step-by-step process to solve them. Here are the main steps to follow when solving any general problem involving the dot product:
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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
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A zero-dimensional topologically nontrivial state in a superconducting quantum dot.

Pasquale Marra1, Alessandro Braggio2, Roberta Citro3

  • 1RIKEN Center for Emergent Matter Science, Wakoshi, Saitama 351-0198, Japan.

Beilstein Journal of Nanotechnology
|July 7, 2018
PubMed
Summary

We demonstrate a zero-dimensional topological superconductor using a quantum dot. Topological phase transitions are revealed by current discontinuities, indicating broken time-reversal symmetry.

Keywords:
Josephson effectJosephson junctionsquantum dotssuperconducting quantum dotstopological statestopological superconductors

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Area of Science:

  • Condensed Matter Physics
  • Quantum Phenomena
  • Topological Matter

Background:

  • Topological states of matter are classified by symmetries and dimensionality.
  • Nontrivial topological states can exist in zero-dimensional systems with discrete energy spectra.

Purpose of the Study:

  • To realize a nontrivial zero-dimensional topological superconductor.
  • To investigate topological phase transitions in such systems.

Main Methods:

  • Coupling a quantum dot with two superconducting leads.
  • Analyzing the system's properties at zero temperature.

Main Results:

  • A quantum dot system realizes a zero-dimensional topological superconductor with broken time-reversal symmetry.
  • Topological phase transitions involve changes in fermion parity.
  • Zero-energy modes and current-phase relation discontinuities signal these transitions.

Conclusions:

  • Fermion parity transitions can be detected via current discontinuities.
  • Measuring critical current at low temperatures can reveal topological phase transitions.