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The number of nuclear spins aligned in the lower energy state is slightly greater than those in the higher energy state. In the presence of an external magnetic field, as the spins precess at the Larmor frequency, the excess population results in a net magnetization oriented along the z axis. When a pulse or a short burst of radio waves at the Larmor frequency is applied along the x axis, the coupling of frequencies causes resonance and flips the nuclear spins of the excess population from the...

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Magnetic Fields

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Related Experiment Video

Updated: Jun 5, 2026

All-electronic Nanosecond-resolved Scanning Tunneling Microscopy: Facilitating the Investigation of Single Dopant Charge Dynamics

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Published on: January 19, 2018

"Artificial atoms" in magnetic fields: wave-function shaping and phase-sensitive tunneling.

Wen Lei¹, Christian Notthoff, Jie Peng

¹Department of Physics and CeNIDE, University of Duisburg-Essen, Duisburg, Germany.

Physical Review Letters

|January 15, 2011

Summary

We show how magnetic fields can alter quantum dot wave function shapes. This technique allows for precise control and mapping of electron states within semiconductor nanostructures.

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All-electronic Nanosecond-resolved Scanning Tunneling Microscopy: Facilitating the Investigation of Single Dopant Charge Dynamics

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Published on: January 19, 2018

Optimizing Magnetic Force Microscopy Resolution and Sensitivity to Visualize Nanoscale Magnetic Domains

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Published on: July 20, 2022

Area of Science:

Condensed Matter Physics
Quantum Mechanics
Materials Science

Background:

Semiconductor quantum dots exhibit unique quantum mechanical properties.
Wave function symmetry in quantum dots is crucial for device applications.
External fields can modify electronic states in nanostructures.

Purpose of the Study:

To investigate the influence of external magnetic fields on semiconductor quantum dot wave function shapes.
To demonstrate the control over the symmetry of p-shell states using magnetic fields.
To utilize magnetotunneling wave function mapping for experimental verification.

Main Methods:

Application of an external magnetic field (B(z)) to semiconductor quantum dots.
Monitoring changes in wave function probability density via magnetotunneling.
Theoretical calculations of magnetotunneling signals for comparison with experimental data.

Main Results:

External magnetic fields can transform distinct p-shell wave function orientations into circularly symmetric states.
Magnetotunneling wave function mapping successfully visualizes the changing probability densities.
Calculated magnetotunneling signals accurately reproduce experimental observations, explaining phase factor differences.

Conclusions:

External magnetic fields offer a method to tune quantum dot wave function symmetry.
Magnetotunneling is an effective technique for probing and understanding electron wave functions in quantum dots.
The observed differences in tunneling maps for p(+) and p⁻ states are attributed to their phase factors.