Black phosphorus （BP） is a good candidate for studying strain effects on two- dimensional （2D） materials beyond graphene and transition-metal dichalcogenides. This is because of its particular ability to sustain h...Black phosphorus （BP） is a good candidate for studying strain effects on two- dimensional （2D） materials beyond graphene and transition-metal dichalcogenides. This is because of its particular ability to sustain high strain and remarkably anisotropic mechanical properties resulting from its unique puckered structure. We here investigate the dependence of lattice vibrational frequencies on cry- stallographic orientations in uniaxially strained few-layer BP by in-situ strained Raman spectroscopy. The out-of-plane A1 mode is sensitive to uniaxial strain along the near-armchair direction whereas the in-plane B2g and A2 modes are sensitive to strain in the near-zigzag direction. For uniaxial strains applied away from these directions, all three phonon modes are linearly redshifted. Our experimental observation is explained by the anisotropic influence of uniaxial tensile strain on structural properties of BP using density functional theory. This study demonstrates the possibility of selective tuning of in-plane and out-of-plane phonon modes in BP by uniaxial strain and makes strain engineering a promising avenue for extensively modulating the optical and mechanical properties of 2D materials.展开更多
The structural and vibrational properties of two-dimensional hexagonal silicon （silicene） and germanium （germanene） are investigated by means of first-principles calculations. It is predicted that the silicene （g...The structural and vibrational properties of two-dimensional hexagonal silicon （silicene） and germanium （germanene） are investigated by means of first-principles calculations. It is predicted that the silicene （germanene） structure with a small buckling of 0.44 ,~ （0.7/k） and bond lengths of 2.28 ,~ （2.44 .~） is energetically the most favorable, and it does not exhibit imaginary phonon mode. The calculated non-resonance Raman spectra of silicene are characterized by a main peak at about 575 cm-1, namely the G-like peak. For germanene, the highest peak is at about 290 cm-1. Extensive calculations on armchair silicene nanoribbons and armchair germanene nanoribbons are also performed, with and without hydrogenation of the edges. The studies reveal other Raman peaks mainly distributed at lower frequencies than the G-like peak which could be attributed to the defects at the edges of the ribbons, thus not present in the Raman spectra of non-defective silicene and germanene. Particularly the Raman peak corresponding to the D mode is found to be located at around 515 cm-1 for silicene and 270 cm-1 for germanene. The calculated G-like and the D peaks are likely the fingerprints of the Raman spectra of the low-buckled structures of silicene and germanene.展开更多
The interface-optical-propagating （IO-PR） mixing phonon modes of a quasi-zero-dimensional （QOD） wurtzite cylindrical quantum dot （QD） structure are derived and studied by employing the macroscopic dielectric con...The interface-optical-propagating （IO-PR） mixing phonon modes of a quasi-zero-dimensional （QOD） wurtzite cylindrical quantum dot （QD） structure are derived and studied by employing the macroscopic dielectric continuum model. The analytical phonon states of IO-PR mixing modes are given. It is found that there are two types of IO-PR mixing phonon modes, i.e. p-IO//z-PR mixing modes and the z-IO//p-PR mixing modes existing in QOD wurtzite QDs. And each IO-PR mixing modes also have symmetrical and antisymmetrieal forms. Via a standard procedure of field quantization, the Frohlich Hamiltonians of electron-（IO-PR） mixing phonons interaction are obtained. Numerical calculations on a wurtzite GaN cylindrical QD are performed. The results reveal that both the radial-direction size and the axial-direction size as well as the dielectric matrix have great influence on the dispersive frequencies of the IO-PR mixing phonon modes. The limiting features of dispersive curves of these phonon modes are discussed in depth. The phonon modes ＂reducing＂ behavior of wurtzite quantum confined systems has been observed obviously in the structures. Moreover, the degenerating behaviors of the IO-PR mixing phonon modes in wurtzite QOD QDs to the IO modes and PR modes in wurtzite Q2D QW and QID QWR systems are analyzed deeply from both of the viewpoints of physics and mathematics.展开更多
An improved valence force field model (VFFM) is suggested to calculate the phonon modes in both bulk specimens and quantum dots (QDs) of AlAs taking account of the effect of transverse effective charges (TCs) correctl...An improved valence force field model (VFFM) is suggested to calculate the phonon modes in both bulk specimens and quantum dots (QDs) of AlAs taking account of the effect of transverse effective charges (TCs) correctly.The resultant dispersions of AlAs bulk phonons are in accord better with the results carefully fitted to the experimental data by using 11-parameters rigid-ion model, than those got by ordinary VFFM, especially in the region of near F point. For AlAs QDs, TCs are evaluated bond by bond for each phonon mode of QD and its effect on the change of the force on atoms is taken into account to modify further the phonon spectrum. The frequency spectra and densities of phonon states of different irreducible representations calculated by using improved VFFM are compared with the results of ordinary VFFM. The correct evaluation of the TCs is not only important in calculating the phonon spectrum of both bulk and QD specimens accurately, but is also in the further discussion of the electron-phonon (e-ph) interaction, which can be directly related to TCs of ions in QD.展开更多
The dispersions of the top interface optical phonons and the side interface optical phonons in cylindrical quantum dots are solved by using the dielectric continuum model. Our calculation mainly focuses on the frequen...The dispersions of the top interface optical phonons and the side interface optical phonons in cylindrical quantum dots are solved by using the dielectric continuum model. Our calculation mainly focuses on the frequency dependence of the IO phonon modes on the wave-vector and quantum number in the cylindrical quantum dot system.Results reveal that the frequency of top interface optical phonon sensitively depends on the discrete wave-vector in z direction and the azimuthal quantum number, while that of the side interface optical phonon mode depends on the radial and azimuthal quantum numbers. These features are obviously different from those in quantum well, quantum well wire,and spherical quantum dot systems. The limited frequencies of interface optical modes for the large wave-vector or quantum number approach two certain constant values, and the math and physical reasons for this feature have been explained reasonably.展开更多
文摘Black phosphorus （BP） is a good candidate for studying strain effects on two- dimensional （2D） materials beyond graphene and transition-metal dichalcogenides. This is because of its particular ability to sustain high strain and remarkably anisotropic mechanical properties resulting from its unique puckered structure. We here investigate the dependence of lattice vibrational frequencies on cry- stallographic orientations in uniaxially strained few-layer BP by in-situ strained Raman spectroscopy. The out-of-plane A1 mode is sensitive to uniaxial strain along the near-armchair direction whereas the in-plane B2g and A2 modes are sensitive to strain in the near-zigzag direction. For uniaxial strains applied away from these directions, all three phonon modes are linearly redshifted. Our experimental observation is explained by the anisotropic influence of uniaxial tensile strain on structural properties of BP using density functional theory. This study demonstrates the possibility of selective tuning of in-plane and out-of-plane phonon modes in BP by uniaxial strain and makes strain engineering a promising avenue for extensively modulating the optical and mechanical properties of 2D materials.
文摘The structural and vibrational properties of two-dimensional hexagonal silicon （silicene） and germanium （germanene） are investigated by means of first-principles calculations. It is predicted that the silicene （germanene） structure with a small buckling of 0.44 ,~ （0.7/k） and bond lengths of 2.28 ,~ （2.44 .~） is energetically the most favorable, and it does not exhibit imaginary phonon mode. The calculated non-resonance Raman spectra of silicene are characterized by a main peak at about 575 cm-1, namely the G-like peak. For germanene, the highest peak is at about 290 cm-1. Extensive calculations on armchair silicene nanoribbons and armchair germanene nanoribbons are also performed, with and without hydrogenation of the edges. The studies reveal other Raman peaks mainly distributed at lower frequencies than the G-like peak which could be attributed to the defects at the edges of the ribbons, thus not present in the Raman spectra of non-defective silicene and germanene. Particularly the Raman peak corresponding to the D mode is found to be located at around 515 cm-1 for silicene and 270 cm-1 for germanene. The calculated G-like and the D peaks are likely the fingerprints of the Raman spectra of the low-buckled structures of silicene and germanene.
基金Supported by National Natural Science Foundation of China under Grant Nos. 60711120203, 60890193STPAA of Guangzhou City under Grant No. 2060
文摘The interface-optical-propagating （IO-PR） mixing phonon modes of a quasi-zero-dimensional （QOD） wurtzite cylindrical quantum dot （QD） structure are derived and studied by employing the macroscopic dielectric continuum model. The analytical phonon states of IO-PR mixing modes are given. It is found that there are two types of IO-PR mixing phonon modes, i.e. p-IO//z-PR mixing modes and the z-IO//p-PR mixing modes existing in QOD wurtzite QDs. And each IO-PR mixing modes also have symmetrical and antisymmetrieal forms. Via a standard procedure of field quantization, the Frohlich Hamiltonians of electron-（IO-PR） mixing phonons interaction are obtained. Numerical calculations on a wurtzite GaN cylindrical QD are performed. The results reveal that both the radial-direction size and the axial-direction size as well as the dielectric matrix have great influence on the dispersive frequencies of the IO-PR mixing phonon modes. The limiting features of dispersive curves of these phonon modes are discussed in depth. The phonon modes ＂reducing＂ behavior of wurtzite quantum confined systems has been observed obviously in the structures. Moreover, the degenerating behaviors of the IO-PR mixing phonon modes in wurtzite QOD QDs to the IO modes and PR modes in wurtzite Q2D QW and QID QWR systems are analyzed deeply from both of the viewpoints of physics and mathematics.
文摘An improved valence force field model (VFFM) is suggested to calculate the phonon modes in both bulk specimens and quantum dots (QDs) of AlAs taking account of the effect of transverse effective charges (TCs) correctly.The resultant dispersions of AlAs bulk phonons are in accord better with the results carefully fitted to the experimental data by using 11-parameters rigid-ion model, than those got by ordinary VFFM, especially in the region of near F point. For AlAs QDs, TCs are evaluated bond by bond for each phonon mode of QD and its effect on the change of the force on atoms is taken into account to modify further the phonon spectrum. The frequency spectra and densities of phonon states of different irreducible representations calculated by using improved VFFM are compared with the results of ordinary VFFM. The correct evaluation of the TCs is not only important in calculating the phonon spectrum of both bulk and QD specimens accurately, but is also in the further discussion of the electron-phonon (e-ph) interaction, which can be directly related to TCs of ions in QD.
文摘The dispersions of the top interface optical phonons and the side interface optical phonons in cylindrical quantum dots are solved by using the dielectric continuum model. Our calculation mainly focuses on the frequency dependence of the IO phonon modes on the wave-vector and quantum number in the cylindrical quantum dot system.Results reveal that the frequency of top interface optical phonon sensitively depends on the discrete wave-vector in z direction and the azimuthal quantum number, while that of the side interface optical phonon mode depends on the radial and azimuthal quantum numbers. These features are obviously different from those in quantum well, quantum well wire,and spherical quantum dot systems. The limited frequencies of interface optical modes for the large wave-vector or quantum number approach two certain constant values, and the math and physical reasons for this feature have been explained reasonably.
基金Ministry of Science and Technology of China(National Key Scientific Instrument and Equipment Development Projects)(2011YQ130018)Department of Science and Technology of Yunnan Province
