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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

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Published on: August 2, 2019

A Parameter-Free Semilocal Exchange Energy Functional for Two-Dimensional Quantum Systems.

Abhilash Patra¹, Subrata Jana¹, Prasanjit Samal¹

¹School of Physical Sciences , National Institute of Science Education and Research, HBNI , Bhubaneswar 752050 , India.

The Journal of Physical Chemistry. A

|March 22, 2018

Summary

A new, parameter-free density functional for two-dimensional systems was developed using density matrix expansion. This accurate and simple functional shows good agreement with exact exchange theory for semiconductor quantum dots.

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Area of Science:

Condensed Matter Physics
Quantum Chemistry
Computational Materials Science

Background:

Accurate density functionals are crucial for electronic structure calculations.
Semilocal density functionals in two dimensions present unique challenges.
The density matrix expansion (DME) is a powerful tool for constructing functionals.

Purpose of the Study:

To revisit and refine the density matrix expansion (DME) method for constructing semilocal density functionals in two dimensions.
To develop a simple, accurate, and parameter-free exchange functional for 2D systems.
To evaluate the performance of the new functional for realistic systems.

Main Methods:

Revisiting the density matrix expansion (DME) approach.
Constructing a parameter-free semilocal exchange functional incorporating kinetic energy-dependent momentum.
Testing the functional using semiconductor quantum dot systems.

Main Results:

An accurate, simple, parameter-free semilocal exchange functional for 2D systems was successfully constructed.
The functional demonstrates good agreement with standard exact exchange theory for multi-electron quantum dots.
The functional satisfies key properties relevant to 2D exchange and its lower bound.

Conclusions:

The developed parameter-free semilocal exchange functional is a promising advancement for 2D electronic structure calculations.
Its simplicity and accuracy make it suitable for studying systems like quantum dots.
The approach validates the effectiveness of DME for creating reliable density functionals.