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<p>We study the optical absorption coefficient in a Hartmann potential-confined quantum dot (QD), demonstrating that accounting for angular-radial coupling and excited states is important for the optical response. We solve the Schrödinger equation analytically, obtain a discrete spectrum, and use it to calculate intra- and inter-band transitions. The absorption spectra are determined by the structure of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(E_{n\ell }\)</EquationSource> </InlineEquation> and its position with respect to the Fermi level, as well as temperature through Pauli blocking and thermal broadening. Larger angular quantum number <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\ell \)</EquationSource> </InlineEquation> leads to narrower radial level spacing and a systematic red-shift of the resonance peaks. We also demonstrate that <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(r_0\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(V_0\)</EquationSource> </InlineEquation> are useful tuning parameters: increasing <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(r_0\)</EquationSource> </InlineEquation> diminishes confinement and leads to reduced level spacing, while increasing <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(V_0\)</EquationSource> </InlineEquation> strengthens both the radial and angular components, with an increase in transition energies. These results show the flexibility of Hartmann confinement for tuning optical properties in non-central QD systems.</p>

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Excited-states optical transitions in Hartmann quantum dots

  • 期刊论文

  • 发表日期：

    2026年5月11日

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  • Huynh V. Phuc

摘要

We study the optical absorption coefficient in a Hartmann potential-confined quantum dot (QD), demonstrating that accounting for angular-radial coupling and excited states is important for the optical response. We solve the Schrödinger equation analytically, obtain a discrete spectrum, and use it to calculate intra- and inter-band transitions. The absorption spectra are determined by the structure of \(E_{n\ell }\) and its position with respect to the Fermi level, as well as temperature through Pauli blocking and thermal broadening. Larger angular quantum number \(\ell \) leads to narrower radial level spacing and a systematic red-shift of the resonance peaks. We also demonstrate that \(r_0\) and \(V_0\) are useful tuning parameters: increasing \(r_0\) diminishes confinement and leads to reduced level spacing, while increasing \(V_0\) strengthens both the radial and angular components, with an increase in transition energies. These results show the flexibility of Hartmann confinement for tuning optical properties in non-central QD systems.