### Abstract

An outstanding and fundamental problem in contemporary physics is to include and probe the many-body effect in the study of relativistic quantum manifestations of classical chaos. We address this problem using graphene systems described by the Hubbard Hamiltonian in the setting of resonant tunneling. Such a system consists of two symmetric potential wells separated by a potential barrier, and the geometric shape of the whole domain can be chosen to generate integrable or chaotic dynamics in the classical limit. Employing a standard mean-field approach to calculating a large number of eigenenergies and eigenstates, we uncover a class of localized states with near-zero tunneling in the integrable systems. These states are not the edge states typically seen in graphene systems, and as such they are the consequence of many-body interactions. The physical origin of the non-edge-state type of localized states can be understood by the one-dimensional relativistic quantum tunneling dynamics through the solutions of the Dirac equation with appropriate boundary conditions. We demonstrate that, when the geometry of the system is modified to one with chaos, the localized states are effectively removed, implying that in realistic situations where many-body interactions are present, classical chaos is capable of facilitating greatly quantum tunneling. This result, besides its fundamental importance, can be useful for the development of nanoscale devices such as graphene-based resonant-tunneling diodes.

Original language | English (US) |
---|---|

Article number | 224301 |

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

Volume | 90 |

Issue number | 22 |

DOIs | |

State | Published - Dec 16 2014 |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Electronic, Optical and Magnetic Materials

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*90*(22), [224301]. https://doi.org/10.1103/PhysRevB.90.224301

**Quantum chaotic tunneling in graphene systems with electron-electron interactions.** / Ying, Lei; Wang, Guanglei; Huang, Liang; Lai, Ying-Cheng.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 90, no. 22, 224301. https://doi.org/10.1103/PhysRevB.90.224301

}

TY - JOUR

T1 - Quantum chaotic tunneling in graphene systems with electron-electron interactions

AU - Ying, Lei

AU - Wang, Guanglei

AU - Huang, Liang

AU - Lai, Ying-Cheng

PY - 2014/12/16

Y1 - 2014/12/16

N2 - An outstanding and fundamental problem in contemporary physics is to include and probe the many-body effect in the study of relativistic quantum manifestations of classical chaos. We address this problem using graphene systems described by the Hubbard Hamiltonian in the setting of resonant tunneling. Such a system consists of two symmetric potential wells separated by a potential barrier, and the geometric shape of the whole domain can be chosen to generate integrable or chaotic dynamics in the classical limit. Employing a standard mean-field approach to calculating a large number of eigenenergies and eigenstates, we uncover a class of localized states with near-zero tunneling in the integrable systems. These states are not the edge states typically seen in graphene systems, and as such they are the consequence of many-body interactions. The physical origin of the non-edge-state type of localized states can be understood by the one-dimensional relativistic quantum tunneling dynamics through the solutions of the Dirac equation with appropriate boundary conditions. We demonstrate that, when the geometry of the system is modified to one with chaos, the localized states are effectively removed, implying that in realistic situations where many-body interactions are present, classical chaos is capable of facilitating greatly quantum tunneling. This result, besides its fundamental importance, can be useful for the development of nanoscale devices such as graphene-based resonant-tunneling diodes.

AB - An outstanding and fundamental problem in contemporary physics is to include and probe the many-body effect in the study of relativistic quantum manifestations of classical chaos. We address this problem using graphene systems described by the Hubbard Hamiltonian in the setting of resonant tunneling. Such a system consists of two symmetric potential wells separated by a potential barrier, and the geometric shape of the whole domain can be chosen to generate integrable or chaotic dynamics in the classical limit. Employing a standard mean-field approach to calculating a large number of eigenenergies and eigenstates, we uncover a class of localized states with near-zero tunneling in the integrable systems. These states are not the edge states typically seen in graphene systems, and as such they are the consequence of many-body interactions. The physical origin of the non-edge-state type of localized states can be understood by the one-dimensional relativistic quantum tunneling dynamics through the solutions of the Dirac equation with appropriate boundary conditions. We demonstrate that, when the geometry of the system is modified to one with chaos, the localized states are effectively removed, implying that in realistic situations where many-body interactions are present, classical chaos is capable of facilitating greatly quantum tunneling. This result, besides its fundamental importance, can be useful for the development of nanoscale devices such as graphene-based resonant-tunneling diodes.

UR - http://www.scopus.com/inward/record.url?scp=84919675537&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84919675537&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.90.224301

DO - 10.1103/PhysRevB.90.224301

M3 - Article

AN - SCOPUS:84919675537

VL - 90

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 22

M1 - 224301

ER -