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Theory of anharmonic phonons in two-dimensional crystals

机译：二维晶体中的非谐声子理论

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摘要

Anharmonic effects in an atomic monolayer thin crystal with honeycomb lattice structure are investigated by analytical and numerical lattice dynamical methods. Starting from a semiempirical model for anharmonic couplings of third and fourth orders, we study the in-plane and out-of-plane (flexural) mode components of the generalized wave vector dependent Griineisen parameters, the thermal tension and the thermal expansion coefficients as a function of temperature and crystal size. From the resonances of the displacement-displacement correlation functions, we obtain the renormalization and decay rate of in-plane and fiexural phonons as a function of temperature, wave vector, and crystal size in the classical and in the quantum regime. Quantitative results are presented for graphene. There, we find that the transition temperature T_α from negative to positive thermal expansion is lowered with smaller system size. Renormalization of the flexural mode has the opposite effect and leads to values of T_α ≈ 300 K for systems of macroscopic size. Extensive numerical analysis throughout the Brillouin zone explores various decay and scattering channels. The relative importance of normal and umklapp processes is investigated. The work is complementary to crystalline membrane theory and computational studies of anharmonic effects in two-dimensional crystals.
机译：通过解析和数值晶格动力学方法研究了具有蜂窝晶格结构的原子单层薄晶体中的非谐效应。从三阶和四阶非谐耦合的半经验模型出发，我们研究了广义波矢量相关的Griineisen参数的面内和面外（挠曲）模式分量，将热张力和热膨胀系数视为温度和晶体尺寸的函数。从位移-位移相关函数的共振中，我们获得了平面内和挠性声子的重归一化和衰减率，它们是温度，波矢和晶体尺寸在经典和量子状态下的函数。给出了石墨烯的定量结果。在那里，我们发现系统尺寸较小时，从负热膨胀到正热膨胀的转变温度T_α降低。弯曲模式的重新归一化具有相反的效果，并导致宏观尺寸系统的T_α≈300K。整个布里渊区的广泛数值分析探索了各种衰减和散射通道。正常和umklapp过程的相对重要性进行了调查。这项工作是对晶体膜理论和二维晶体非谐效应计算研究的补充。

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  • 来源
    《Physical review》 |2015年第13期|134302.1-134302.20|共20页
  • 作者

    K. H. Michel; S. Costamagna; F. M. Peeters;

  • 作者单位

    Universiteit Antwerpen, Department of Physics, Groenenborgerlaan 171, BE-2020 Antwerpen, Belgium;

    Universiteit Antwerpen, Department of Physics, Groenenborgerlaan 171, BE-2020 Antwerpen, Belgium ,Instituto de Fisica Rosario, Bv. 27 de Febrero 210 bis, 2000 Rosario, Argentina;

    Universiteit Antwerpen, Department of Physics, Groenenborgerlaan 171, BE-2020 Antwerpen, Belgium;

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