### Abstract

We consider a disordered tight-binding model for particle transport in a periodic lattice. We present a parameter that quantifies the effective hopping strength between the single-particle energy eigenstates in neighbouring supercells that each contains a relatively large number of basic unit cells. We investigate the properties of this parameter in the analysis of long-range transport, in particular the suppression of conductivity as a result of disorder. We perform the analysis for two different crystal structures: simple cubic and perovskite. In each simulation we generate two disordered supercells and treat them as neighbouring supercells in the bulk of the material. Because the two supercells have different disorder patterns, the energies and wave functions are not perfectly matched at the boundary between the supercells, resulting in reduced effective coupling between them. We compare these results for the effective hopping strength with those obtained using the inverse participation ratio, which quantifies the spatial extension of the energy eigenstates. We show that there is a close, though not perfect, correspondence between the disorder effects as reflected in the effective hopping strength and in the inverse participation ratio, and hence the new parameter gives additional information in the study of quantum transport in tight-binding models.

Original language | English |
---|---|

Pages (from-to) | 534-540 |

Number of pages | 7 |

Journal | Computational Materials Science |

Volume | 155 |

DOIs | |

Publication status | Published - 1 Dec 2018 |

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### Keywords

- Disordered systems
- Electronic transport
- Localization

### ASJC Scopus subject areas

- Computer Science(all)
- Chemistry(all)
- Materials Science(all)
- Mechanics of Materials
- Physics and Astronomy(all)
- Computational Mathematics

### Cite this

**Effective hopping strength between supercells in a disordered tight-binding model.** / Ashhab, Sahel; Madjet, Mohamed.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Effective hopping strength between supercells in a disordered tight-binding model

AU - Ashhab, Sahel

AU - Madjet, Mohamed

PY - 2018/12/1

Y1 - 2018/12/1

N2 - We consider a disordered tight-binding model for particle transport in a periodic lattice. We present a parameter that quantifies the effective hopping strength between the single-particle energy eigenstates in neighbouring supercells that each contains a relatively large number of basic unit cells. We investigate the properties of this parameter in the analysis of long-range transport, in particular the suppression of conductivity as a result of disorder. We perform the analysis for two different crystal structures: simple cubic and perovskite. In each simulation we generate two disordered supercells and treat them as neighbouring supercells in the bulk of the material. Because the two supercells have different disorder patterns, the energies and wave functions are not perfectly matched at the boundary between the supercells, resulting in reduced effective coupling between them. We compare these results for the effective hopping strength with those obtained using the inverse participation ratio, which quantifies the spatial extension of the energy eigenstates. We show that there is a close, though not perfect, correspondence between the disorder effects as reflected in the effective hopping strength and in the inverse participation ratio, and hence the new parameter gives additional information in the study of quantum transport in tight-binding models.

AB - We consider a disordered tight-binding model for particle transport in a periodic lattice. We present a parameter that quantifies the effective hopping strength between the single-particle energy eigenstates in neighbouring supercells that each contains a relatively large number of basic unit cells. We investigate the properties of this parameter in the analysis of long-range transport, in particular the suppression of conductivity as a result of disorder. We perform the analysis for two different crystal structures: simple cubic and perovskite. In each simulation we generate two disordered supercells and treat them as neighbouring supercells in the bulk of the material. Because the two supercells have different disorder patterns, the energies and wave functions are not perfectly matched at the boundary between the supercells, resulting in reduced effective coupling between them. We compare these results for the effective hopping strength with those obtained using the inverse participation ratio, which quantifies the spatial extension of the energy eigenstates. We show that there is a close, though not perfect, correspondence between the disorder effects as reflected in the effective hopping strength and in the inverse participation ratio, and hence the new parameter gives additional information in the study of quantum transport in tight-binding models.

KW - Disordered systems

KW - Electronic transport

KW - Localization

UR - http://www.scopus.com/inward/record.url?scp=85053392788&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85053392788&partnerID=8YFLogxK

U2 - 10.1016/j.commatsci.2018.09.023

DO - 10.1016/j.commatsci.2018.09.023

M3 - Article

AN - SCOPUS:85053392788

VL - 155

SP - 534

EP - 540

JO - Computational Materials Science

JF - Computational Materials Science

SN - 0927-0256

ER -