Quantum Transport through Hierarchical Structures

TL;DR

This paper investigates quantum electron transport in hierarchical Hanoi networks, revealing band gaps in HN3 and contrasting properties with HN5 and linear networks using a renormalization group approach.

Contribution

It introduces a renormalization group method to analyze quantum transport in hierarchical lattices, highlighting the presence of band gaps in HN3.

Findings

Band gaps observed in HN3 network

No band gaps in HN5 or linear networks

Renormalization group approach effectively solves quantum transport equations

Abstract

The transport of quantum electrons through hierarchical lattices is of interest because such lattices have some properties of both regular lattices and random systems. We calculate the electron transmission as a function of energy in the tight binding approximation for two related Hanoi networks. HN3 is a Hanoi network with every site having three bonds. HN5 has additional bonds added to HN3 to make the average number of bonds per site equal to five. We present a renormalization group approach to solve the matrix equation involved in this quantum transport calculation. We observe band gaps in HN3, while no such band gaps are observed in linear networks or in HN5.