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Related Concept Videos

Quantum Numbers02:43

Quantum Numbers

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It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
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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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Heteronuclear single-quantum correlation spectroscopy (HSQC) is a 2D NMR technique that reveals one-bond correlations between hydrogen and a heteronucleus. The HSQC experiment is similar to the heteronuclear correlation experiment (HETCOR) but is more sensitive. In the HSQC spectrum, the proton chemical shift is plotted on the horizontal F2 axis, while the 13C chemical shift is plotted on the vertical F1 axis. The corresponding proton and 13C spectra are also shown. The HSQC contour plot does...
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Correlations02:20

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Correlation means that there is a relationship between two or more variables (such as ice cream consumption and crime), but this relationship does not necessarily imply cause and effect. When two variables are correlated, it simply means that as one variable changes, so does the other. We can measure correlation by calculating a statistic known as a correlation coefficient. A correlation coefficient is a number from -1 to +1 that indicates the strength and direction of the relationship between...
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Statistical tests can calculate whether there is a relationship, or correlation, between independent and dependent variables. An indirect relationship of the variables signifies a correlation, while a direct relationship shows causation. If it is determined that no connection exists between the variables, then the correlation is a coincidence.
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The mode is one of the commonly used measures of a central tendency. It is defined as the most frequent value in a data set.
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Correlative Light- and Electron Microscopy Using Quantum Dot Nanoparticles
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Interplay between correlations and Majorana mode in proximitized quantum dot.

G Górski1, J Barański2, I Weymann3

  • 1Faculty of Mathematics and Natural Sciences, University of Rzeszów, 35-310, Rzeszów, Poland.

Scientific Reports
|October 26, 2018
PubMed
Summary

We investigated how Majorana modes affect quantum dot transport. Their influence is spin-dependent, potentially enabling new quantum phase transitions and Kondo effects, verifiable with polarized STM spectroscopy.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Information Science
  • Nanoscale Science and Technology

Background:

  • Quantum dots are crucial for quantum computing and electronics.
  • Topological superconducting nanowires host Majorana end-modes, promising fault-tolerant quantum computation.
  • Interfacing quantum dots with Majorana modes presents opportunities for novel quantum phenomena.

Purpose of the Study:

  • To explore the low-energy spectrum and transport properties of a quantum dot hybridized with a topological superconducting nanowire.
  • To investigate the interplay between Majorana quasiparticles, on-dot correlations, and pairing.
  • To study the quantum phase transition from spinless to spinful configurations and the emergence of subgap Kondo effect.

Main Methods:

  • Self-consistent perturbative treatment for correlations.
  • Unbiased numerical renormalization group (NRG) calculations.
  • Theoretical modeling of a quantum dot coupled to normal/superconducting reservoirs and a topological nanowire.

Main Results:

  • The Majorana mode exhibits a spin-selective influence (constructive or destructive) on the quantum dot's low-energy transport behavior.
  • A quantum phase transition from a spinless (BCS-type) to a spinful (singly occupied) configuration is identified.
  • The subgap Kondo effect is found to arise in the spinful configuration.

Conclusions:

  • The spin of the Majorana mode critically determines its effect on quantum dot transport.
  • This spin-selective influence offers a pathway to control quantum transport and phase transitions.
  • Experimental verification using polarized scanning tunneling microscopy (STM) spectroscopy is proposed.