[Paper Review] Impact of a topological defect and Rashba spin-orbit interaction on the thermo-magnetic and optical properties of a 2D semiconductor quantum dot with Gaussian confinement

Jorge David Castaño‐Yepes, D. A. Amor-Quiroz+2 more|arXiv (Cornell University)|Sep 13, 2018

Quantum and electron transport phenomena68 references42 citations

TL;DR

The paper analyzes a single-electron GaAs 2D quantum dot with Gaussian confinement under a conical disclination and Rashba spin-orbit interaction, computing thermo-magnetic properties and optical responses via the canonical partition function and density-matrix formalism.

ABSTRACT

In this paper, we examine the effect of introducing a conical disclination on the thermal and optical properties of a two dimensional GaAs quantum dot in the presence of a uniform and constant magnetic field. In particular, our model consists of a single-electron subject to a confining Gaussian potential with a spin-orbit interaction in the Rashba approach. We compute the specific heat and the magnetic susceptibility from the exact solution of the Schr\\"odinger equation via the canonical partition function, and it is shown that the peak structure of the Schottky anomaly is linearly displaced as a function of the topological defect. We found that such defect and the Rashba coupling modify the values of the temperature and magnetic field in which the system behaves as a paramagnetic material. Remarkably, the introduction of a conical disclination in the quantum dot relaxes the selection rules for the electronic transitions when an external electromagnetic field is applied. This creates a new set of allowed transitions causing the emergence of semi-suppressed resonances in the absorption coefficient as well as in the refractive index changes which are blue-shifted with respect to the regular transitions for a quantum dot without the defect.

Motivation & Objective

• Motivate understanding of how topological defects (conical disclination) affect thermo-magnetic behavior in 2D quantum dots.
• Investigate the influence of Rashba spin-orbit interaction on energy spectra, specific heat, and magnetic susceptibility.
• Examine how defect and SOI alter optical transitions, absorption, and refractive index via dipole matrix elements.

Proposed method

• Model a single electron in a 2D quantum dot with Gaussian confinement and Rashba SOI under a uniform magnetic field.
• Incorporate a conical disclination by using a kink parameter alpha and transform to an equivalent coordinate system.
• Solve the Schrödinger equation to obtain exact eigenvalues and eigenfunctions (R_{nls}, E_{nls}) with Rashba and Zeeman terms.
• Compute the canonical partition function from the spectrum to derive C_v and χ.
• Use density-matrix formalism to obtain linear and third-order nonlinear optical coefficients and total refractive index changes.
• Analyze dipole transition selection rules and compute absorption/refractive index changes from dipole moments.

Experimental results

Research questions

• RQ1 How does a conical disclination (topological defect) shift the Schottky anomaly peak in the specific heat of a GaAs 2D-QD?
• RQ2 What is the impact of Rashba spin-orbit interaction on the energy spectrum, magnetic susceptibility, and phase diagram of the system?
• RQ3 How does the topological defect modify optical transition selection rules and the absorption/refractive index spectra under external fields?
• RQ4 How do Gaussian confinement parameters (via the interpolation parameter kappa) and the kink parameter p affect thermo-magnetic and optical properties?

Key findings

• Schottky anomaly peaks in specific heat are linearly displaced by the topological defect; Rashba coupling further sharpens and shifts peaks to lower temperatures.
• Rashba SOI reduces the temperature and magnetic field required for the paramagnetic phase, and the conical disclination yields an asymmetric paramagnetic region in the B–T plane.
• Topological defect relaxes optical selection rules, enabling transitions with Δl not equal to ±1 and producing semi-suppressed resonances in absorption and refractive index changes that blue-shift relative to defect-free transitions.
• The defect and SOI broaden the set of allowed dipolar transitions, with diagonal (Δl=0) transitions dominating for certain parameter regimes, and higher |n−m| transitions being progressively suppressed.
• Total absorption and refractive index changes depend on intensity via the third-order nonlinear term, enhancing nonlinearity and enabling tunable optical responses.
• Increasing the inverse kink parameter p modifies the angular selection rules and results in a blue shift of the refractive index changes for fixed transitions.