QUANTUM HONEYCOMP

Aim

This program allows to perform tight binding calculations with a user friendly interface. A generic version of this program is called quantum-lattice, and can be downloaded from https://github.com/joselado/quantum-lattice

How to install

Linux and Mac

The program runs in Linux and Mac machines.

Clone the github repository

git clone https://github.com/joselado/quantum-honeycomp

and execute the script install as

python install.py

The script will install all the required dependencies if they are not already present for the python command used. Afterwards, you can run the program by executing in a terminal

quantum-honeycomp

Windows

For using this program in Windows, the easiest solution is to create a virtual machine using Virtual Box, installing a version of Ubuntu in that virtual machine, and following the previous instructions. Alternatively, you can try this version that was adapted for a Windows system (latest updates may not be included in it).

Examples

This program allows to study a variety of electronic states by means of tight binding models as shown below.

Quantum anomalous Hall state

Honeycomb lattice with Rashba spin-orbit coupling and exchange field, giving rise to a net Chern number and chiral edge states https://journals.aps.org/prb/abstract/10.1103/PhysRevB.82.161414

Quantum Spin Hall state

Honeycomb lattice with Kane-Mele spin-orbit coupling and Rashba spin-orbit coupling, giving rise to a gapped spectra with a non-trivial Z2 invariant and helical edge states https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.226801

Magnetism in graphene zigzag nanoribbons

Self-consistent mean field calculation of a zigzag graphene ribbon, with electronic interactions included as a mean field Hubbard model. Interactions give rise to an edge magnetization in the ribbon, with an antiferromagnetic alignment between edges

Nodal line semimetals

Band structure of a slab of a 3D nodal line semimetal in a diamond lattice, showing the emergence of topological zero energy drumhead states in the surface of the slab https://link.springer.com/article/10.1007%2Fs10909-017-1846-3

Confined modes in 0D systems

Spectra and spatially resolved density of states of a triangular graphene island, showing the emergence of confined modes

Colossal graphene quantum dots

Density of states and spatially resolved density of states of a bg graphene quantum dot. The huge islands module uses special techniques to efficiently solve systems with hundreds of thousands of atoms.

Landau levels

Electronic spectra of a massive honeycomb lattice in the presence of an off-plane magnetic field, giving rise to Landau levels and chiral edge states

Artificial topological superconductors

Bogoliuvov de Gennes band structructure of a two-dimensional gas in a square lattice with Rashba spin-orbit coupling, off-plane exchange field and s-wave superconducting proximity effect. When superconductivity is turned on, a gap opens up in the spectra hosting a non-trivial Chern number, giving rise to propagating Majorana modes in the system

Quantum Valley Hall effect

Band structure of Bernal stacked bilayer graphene, showing the emergence of a gap when an interlayer bias is applied. The previous gap hosts a non-trivial valley Chern number, giving rise to the emergence of pseudo-helical states in the edge of the system

Twisted bilayer graphene

Bandstructure and local density of states of twisted bilayer graphene at the magic angle, showing the emergence of a flat band, with an associated triangular density of states https://journals.aps.org/prb/abstract/10.1103/PhysRevB.82.121407

Capabilities

• Tight binding models in different lattices (triangular, square, honeycomb, Kagome, Lieb, diamond, pyrochlore)
• Possibility of crafting your own lattice interactively
• Tunable parameters in the Hamiltonian (Fermi energy, magnetic order, sublattice imbalance, magnetic field, Rashba spin-orbit coupling, intrinsic spin-orbit coupling, Haldane coupling, anti-Haldane coupling, s-wave superconductivity)
• Different results are automatically plotted from the interface
• Band structure of 0d,1d,2d systems
• Density of states of 0d,1d,2d systems
• Selfconsistent mean-field Hubbard calculations of 0d,1d,2d systems
• Berry curvature, Chern number and Z2 invariant in 2d systems
• Special module to deal with systems with more than 100000 atoms using the Kernel polynomial method
• Special modules to study 1d and 2d study interfaces between different systems
• Special module for single impurities in pristine infinite systems using the embedding technique