The Study of Effects of Strain on Band Gap of Perovskite Crystal using LDA and LDA+U Method

Table of Contents

1 Introduction

1.1 Introduction to pervoskite structure

1.1.1 Introduction to CaTiO3

1.1.2 Structure

1.1.3 Formation of band gap

1.2 Scope of present study

1.3 How we approach?

2 Theoritical Background

2.1 General Consideration

2.2 Many-Body Hamiltonian and Born-Oppenheimer Approximation

2.3 Hartree-Fock Method of Self Consistent Fields

2.4 Density Functional Theory

2.4.1 General Consideration

2.4.2 Thomas-Fermi Model

2.4.3 Hohenberg-Kohn Theorem

2.4.4 The Kohn-Sham Formalism

2.5 The Exchange -Correlation Functional

2.5.1 Local Density Approximation

2.5.2 Generalized Gradient Approximation

2.5.3 Solution of the Kohn-Sham equations: Self-consistency iteration procedure

2.6 LDA+U Method

3 Computational Details

3.1 General Consideration

3.1.1 PWscf

3.1.2 Post Processing

4 Results and Discussion

4.1 Convergence Tests

4.1.1 Kinetic energy cut-off(ecutwfc)

4.1.2 K-points grid

4.1.3 Lattice parameter

4.1.4 Band structure

4.2 LDA Method

4.2.1 Calculation of band structure of perovskite CaTiO3 by LDA method

4.2.2 Effect of strain on atomic displacement by LDA method

4.2.3 Effect of strain on indirect band gap by LDA method

4.2.4 Effect of strain on direct band gap by LDA method

4.2.5 Partial density of states of perovskite structure of CaTiO3 by LDA method

4.3 LDA+U Method

4.3.1 Determination of Hubbard potential

4.3.2 Calculation of band structure of perovskite CaTiO3 by LDA+U method

4.3.3 Effect of strain on indirect band gap by LDA+U method

4.3.4 Effect of strain on direct band gap by LDA+U method

4.3.5 Partial density of states of perovskite structure of CaTiO3 by LDA+U method

4.3.6 Comparision of band gap between LDA and LDA+U method

5 Conclusions and Concluding Remarks

Objectives & Topics

This dissertation focuses on the investigation of the electronic and structural properties of perovskite Calcium Titanate (CaTiO3) using first-principles calculations. The primary research goal is to determine the effects of in-plane strain on the band gap and atomic displacements, while addressing the limitations of standard density functional theory (DFT) methods by employing the LDA+U approach to obtain accurate band gap predictions.

• Investigation of perovskite CaTiO3 structural properties.
• Application of Density Functional Theory (DFT) using LDA and LDA+U methods.
• Calculation of electronic band structures and Partial Density of States (PDOS).
• Evaluation of the effects of external strain (from -5% to +5%) on band gaps and atomic displacements.
• Comparative analysis of LDA and LDA+U results against experimental data.

Excerpt from the book

Summary of Chapters

1 Introduction: Provides an overview of the perovskite structure, the properties of CaTiO3, and the scope and approach of this research.

2 Theoritical Background: Discusses the fundamental physics behind the many-body system, the Born-Oppenheimer approximation, and the development of Density Functional Theory and the LDA+U method.

3 Computational Details: Details the simulation environment, specifically the Quantum ESPRESSO suite and the specific parameters used for the calculations.

4 Results and Discussion: Presents the convergence tests, the calculation results of band structures and PDOS, and the investigation of strain effects on band gaps.

5 Conclusions and Concluding Remarks: Summarizes the key findings, confirming that LDA+U provides more accurate results for CaTiO3 compared to standard LDA methods.

Keywords

Perovskite, CaTiO3, Density Functional Theory, LDA, LDA+U, Hubbard potential, Band gap, Electronic properties, Quantum ESPRESSO, Atomic displacement, Strain, Semiconductor, Insulator, Lattice parameter, First-principles calculation

Frequently Asked Questions

What is the primary subject of this research?

This work is a scientific study on the effects of strain on the band gap and electronic properties of perovskite Calcium Titanate (CaTiO3) crystals.

What is the main objective of the study?

The objective is to accurately model the electronic properties of CaTiO3 using first-principles calculations and to demonstrate that the LDA+U method provides better results for this material than the standard LDA method.

Which scientific method is employed?

The study utilizes Density Functional Theory (DFT) within the Quantum ESPRESSO computational suite, specifically comparing Local Density Approximation (LDA) and LDA with Hubbard potential (LDA+U).

What are the central thematic areas?

The research covers crystal structure, band gap formation, the impact of atomic displacement under strain, and the electronic behavior of transition metal oxides.

What does the main body of the work address?

It details the theoretical background of the methods used, describes the computational simulation setup, presents the results of convergence tests, and analyzes data on band structures, PDOS, and the variation of band gaps under strain.

Which keywords characterize this work?

Key terms include CaTiO3, Density Functional Theory, Hubbard potential, band gap, and strain analysis.

How does strain affect the band gap of CaTiO3?

The study finds that the band gap generally increases with contraction and decreases with the expansion of the crystal lattice compared to its equilibrium value.

Why is the LDA+U method used instead of only LDA?

Standard LDA significantly underestimates the band gap of CaTiO3, predicting a semiconductor state when the material is actually an insulator; the LDA+U method is used to obtain results that are in closer agreement with experimental data.

What is the value of the Hubbard potential used in the calculations?

The study determines that a Hubbard potential (U) of 10.6 eV provides the best fit to the experimental band gap value for CaTiO3.

What is the conclusion regarding the nature of CaTiO3?

The calculations confirm that CaTiO3 acts as an indirect band gap insulator, a result correctly captured by the LDA+U method.