Modelling magnetic confinement in two-dimensional quantum dots via gauge-invariant imaginary-time propagation

Area of Science:

• Condensed Matter Physics
• Quantum Computing
• Materials Science

Background:

• Two-dimensional quantum dots are crucial for quantum technology, electronics, and magneto-sensing.
• Accurate modeling of magnetic confinement is essential for understanding their behavior.
• Existing methods can suffer from gauge-dependent artifacts and limitations in handling confinement potentials.

Purpose of the Study:

• To develop a robust real-space framework for modeling magnetically confined states in 2D quantum dots.
• To eliminate gauge-dependent artifacts and accurately treat arbitrary confinement potentials.
• To provide a versatile tool for exploring electronic structures in quantum dots and related nanomaterials.

Main Methods:

• Integration of Wilson-type finite-difference discretization (Wilson Hamiltonian - WH) for exact local U(1) gauge invariance.
• Employment of imaginary-time propagation (ITP) as an efficient and numerically stable eigensolver.
• Application to GaAs and monolayer phosphorene quantum dots with various confinement potentials.

Main Results:

• The WH-ITP method achieves sub-cm⁻¹ agreement with benchmarks for GaAs quantum dots across various magnetic fields.
• Accurate reproduction of magnetic-field-induced effects like wavefunction contraction and nodal structure changes.
• Demonstration of characteristic level shifts and reordering in phosphorene quantum dots due to anisotropic properties.

Conclusions:

• The WH-ITP method is a robust and versatile tool for modeling magnetic confinement and electronic structure in 2D quantum dots.
• The framework accurately captures complex phenomena, including gauge invariance and anisotropic effects.
• This approach facilitates the design and understanding of quantum materials for advanced technological applications.