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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.20162 |
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Table of Contents:
- In bilayer graphene the exact energy levels of quantum dots can be derived from the four-component continuum Hamiltonian. Here, we study the quantum dot energy levels with approximate equations and compare them with the exact levels. The starting point of our approach is the four-component continuum model and the quantum dot is defined by a continuous potential well in a uniform magnetic field. Using some simple arguments we demonstrate realistic regimes where approximate quantum dot equations can be derived. Interestingly these approximate equations can be solved semi-analytically, in the same context as a single-component Schrödinger equation. The approximate equations provide valuable insight into the physics with minimal numerical effort compared with the four-component quantum dot model. We show that the approximate quantum dot energy levels agree very well with the exact levels in a broad range of parameters and find realistic regimes where the relative error is vanishingly small.