### Abstract

A closed-form algorithm for computing subsurface Green functions-the blocks of a material's Green function between the surface and the bulk-is presented, where we assume the system satisfies a common principal-layer approximation. By exploiting the block tridiagonal and nearly block Toeplitz structure of the Hamiltonian and overlap matrices, this method scales independently of the system size (constant scaling), allowing studies of large systems. As a proof-of-concept example, we investigate the decay of surface effects in an armchair graphene nanoribbon, demonstrating the persistence of surface effects hundreds of atomic layers (~0.5 μm) away from a surface. We finally compare the surface-to-bulk transitions of finite and semi-infinite systems, finding that finite systems exhibit amplified surface effects.

Original language | English |
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Article number | 085412 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 83 |

Issue number | 8 |

DOIs | |

Publication status | Published - Feb 15 2011 |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Electronic, Optical and Magnetic Materials

### Cite this

**Probing the surface-to-bulk transition : A closed-form constant-scaling algorithm for computing subsurface Green functions.** / Reuter, Matthew G.; Seideman, Tamar; Ratner, Mark A.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 83, no. 8, 085412. https://doi.org/10.1103/PhysRevB.83.085412

}

TY - JOUR

T1 - Probing the surface-to-bulk transition

T2 - A closed-form constant-scaling algorithm for computing subsurface Green functions

AU - Reuter, Matthew G.

AU - Seideman, Tamar

AU - Ratner, Mark A

PY - 2011/2/15

Y1 - 2011/2/15

N2 - A closed-form algorithm for computing subsurface Green functions-the blocks of a material's Green function between the surface and the bulk-is presented, where we assume the system satisfies a common principal-layer approximation. By exploiting the block tridiagonal and nearly block Toeplitz structure of the Hamiltonian and overlap matrices, this method scales independently of the system size (constant scaling), allowing studies of large systems. As a proof-of-concept example, we investigate the decay of surface effects in an armchair graphene nanoribbon, demonstrating the persistence of surface effects hundreds of atomic layers (~0.5 μm) away from a surface. We finally compare the surface-to-bulk transitions of finite and semi-infinite systems, finding that finite systems exhibit amplified surface effects.

AB - A closed-form algorithm for computing subsurface Green functions-the blocks of a material's Green function between the surface and the bulk-is presented, where we assume the system satisfies a common principal-layer approximation. By exploiting the block tridiagonal and nearly block Toeplitz structure of the Hamiltonian and overlap matrices, this method scales independently of the system size (constant scaling), allowing studies of large systems. As a proof-of-concept example, we investigate the decay of surface effects in an armchair graphene nanoribbon, demonstrating the persistence of surface effects hundreds of atomic layers (~0.5 μm) away from a surface. We finally compare the surface-to-bulk transitions of finite and semi-infinite systems, finding that finite systems exhibit amplified surface effects.

UR - http://www.scopus.com/inward/record.url?scp=79960992944&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79960992944&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.83.085412

DO - 10.1103/PhysRevB.83.085412

M3 - Article

VL - 83

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 1098-0121

IS - 8

M1 - 085412

ER -