Oleg Yazyev

Solid State Physics

Python3

Interactive textbook

English

This notebook illustrates the concept of Landau levels by examining the density of states in magnetic fields. It includes a method for computing the density of states at various external fields, allowing visualization of the de Haas-van Alphen effect.

Oleg Yazyev

Solid State Physics

Python3

Interactive textbook

English

This notebook introduces the concept of lattice structures with periodic boundary conditions, specifically the Born-von Karman boundary condition. It explains the transformation from real lattice vectors to reciprocal lattice vectors in two dimensions.

Oleg Yazyev

Solid State Physics

Python3

Exercise worksheets

English

This notebook demonstrates the tight-binding approximation applied to four common two-dimensional (2D) lattice structures: square, triangular, Lieb, and honeycomb lattices. Through detailed calculations, it examines the electronic band structures of each lattice, highlighting key differences in their dispersion relations and energy bands.

Oleg Yazyev

Solid State Physics

Python3

Interactive textbook

English

This notebook illustrates the evolution of the density of states in two-dimensional systems by analyzing all allowed states in an electron shell between consecutive kx values. It includes graphs depicting electron energy dispersion, allowed k states for a specific k shell, and the corresponding density of states.

Oleg Yazyev

Solid State Physics

Python3

Interactive textbook

English

This notebook explores the band structure of monolayer and bilayer graphene using the tight binding model. It provides an overview of the hexagonal lattice structure of monolayer graphene and the interactions between its carbon atoms. The notebook discusses the construction of the Hamiltonian matrix based on nearest neighbor interactions and aims to solve the tight binding problem to understand the electronic properties of graphene.

Oleg Yazyev

Solid State Physics

Python3

Exercise worksheets

English

This notebook presents a simple example of Anderson localization in a one-dimensional system, using a chain of atoms with periodic boundary conditions. It demonstrates how disorder, introduced through random on-site potentials, affects the system's eigenstates.

Oleg Yazyev

Solid State Physics

Python3

Interactive textbook

English

This notebook provides an interactive platform for visualizing transverse and longitudinal wave modes. Users can explore the characteristics of these wave types through dynamic simulations.

Oleg Yazyev

Solid State Physics

Python3

Exercise worksheets

English

The purpose of this notebook is to estimate the values of electron density and mean free time for materials suitable for use as transparent conductors. The focus is on determining the order of magnitude for these two parameters.

Oleg Yazyev

Solid State Physics

Python3

Exercise worksheets

English

This notebook demonstrates the construction of the first three Brillouin zones for a two-dimensional square lattice. It includes the Wigner-Seitz cell for the first Brillouin zone and explains how subsequent zones are defined by Bragg planes relative to the origin. The construction extends to the third Brillouin zone by considering third-nearest neighbors.

Oleg Yazyev

Solid State Physics

Python3

Interactive textbook

English

This notebook applies Bloch's theorem to explain how electron behavior in a crystal is influenced by a periodic external potential. It walks through the process of partitioning the electron wavefunction, solving the Schrödinger-like equation for the periodic component, and visualizing the probability distribution and external potential using numerical methods.