Thermodynamic properties of an electron gas in a two-dimensional quantum dot: an approach using density of states

TL;DR

This work develops a density‑of‑states–based description of a two‑dimensional electron gas confined in a quantum dot under a perpendicular magnetic field and computes thermodynamic properties across temperatures. By deriving the single‑particle spectrum for a radial parabolic confinement and expressing the subband DOS as $D(E)$, the authors evaluate the chemical potential, magnetization, entropy, and heat capacity as functions of magnetic field and temperature, highlighting de Haas–van Alphen–type oscillations due to subband depopulation. Temperature broadening modifies these oscillations and reveals magnetocaloric effects, with strong fields pushing the system toward Landau‑like quantization and saturating magnetization. The results offer insights for nanostructured devices and deepen understanding of confined electron thermodynamics in quantum dots.

Abstract

Potential applications of quantum dots in the nanotechnology industry make these systems an important field of study in various areas of physics. In particular, thermodynamics has a significant role in technological innovations. With this in mind, we studied some thermodynamic properties in quantum dots, such as entropy and heat capacity, as a function of the magnetic field over a wide range of temperatures. The density of states plays an important role in our analyses. At low temperatures, the variation in the magnetic field induces an oscillatory behavior in all thermodynamic properties. The depopulation of subbands is the trigger for the appearance of the oscillations.

Figures (5)

• Figure 1: (a) The black line corresponds to the chemical potential at $T=0$ computed from Eq. (\ref{['Eq:Fermi 1']}). To compare with exact results, we also plot the Fermi energy computes self-consistently (line brown). In (b) and (c), the red and blue lines correspond to the chemical potential at finite temperatures obtained from Eq. (\ref{['Eq:N']}). We plot the chemical potential at $T=0$ (black line) to better visualize the temperature effect. The dashed lines in (a), (b), and (c) show the position at which subbands with $n=1,2,3,4,5$ are depopulated. The corresponding magnetic fields are obtained from Eq. (\ref{['Eq:B-maximos']}).
• Figure 2: (a) The black line corresponds to the magnetization at $T=0$ computed from Eq. (\ref{['Eq:Mag1']}). We also plot the exact magnetization results (line brown) for comparison. In (b) and (c), the red and blue lines correspond to the magnetization at finite temperatures obtained from Eq. (\ref{['Eq:Mag3']}). The dashed lines in (a), (b), and (c) show the position at which subbands with $n=1,2,3,4,5$ are depopulated. The corresponding magnetic fields are obtained from Eq. (\ref{['Eq:B-maximos']}).
• Figure 3: Entropy (Eq. (\ref{['Eq:entropia']})) as a function of the magnetic field in a wide range temperature. The dashed lines in (a) and (b) show the position at which subbands with $n=1,2,3,4,5$ are depopulated. The corresponding magnetic fields are obtained from Eq. (\ref{['Eq:B-maximos']}). In (c), temperatures vary from $1.0$ K to $30.0$ K, with a range of $1.0$ K. The curves highlighted in red and blue correspond to temperatures of $1.0$ K and $5.0$ K, respectively.
• Figure 4: Temperature as a function of the magnetic field. The dashed lines in (a) and (b) show the position at which subbands with $n=1,2,3,4,5$ are depopulated. The corresponding magnetic fields are obtained from Eq. (\ref{['Eq:B-maximos']}).
• Figure 5: Heat capacity (Eq. (\ref{['Eq:calorespecifico2']})) as a function of the magnetic field in a wide range temperature. The dashed lines in (a), (b), and (c) show the position at which subbands with $n=1,2,3,4,5$ are depopulated. The corresponding magnetic fields are obtained from Eq. (\ref{['Eq:B-maximos']}). In (d), temperatures vary from $1.0$ K to $30.0$ K, with a range of $1.0$ K. The curves highlighted in red and blue correspond to temperatures of $2.0$ K and $5.0$ K, respectively.