Electric Polarization of Heteropolar Nanotubes as a Geometric Phase

Abstract

The three-fold symmetry of planar boron nitride, the III-V analog to graphene, prohibits an electric polarization in its ground state, but this symmetry is broken when the sheet is wrapped to form a BN nanotube. We show that this leads to an electric polarization along the nanotube axis which is controlled by the quantum mechanical boundary conditions on its electronic states around the tube circumference. Thus the macroscopic dipole moment has an intrinsically nonlocal quantum mechanical origin from the wrapped dimension. We formulate this novel phenomenon using the Berry's phase approach and discuss its experimental consequences. 72.40.+w, 78.20.Jq, 61.48.+c, 85.40.Ux Physical properties of materials at the nanoscale can differ dramatically from their bulk counterparts. This is especially evident in the electronic properties, since the quantum behavior of electrons on this scale is sensitive to the size, shape and symmetry of the sample. Recent discovery of carbon nanotubes [1] provides a striking example, where metallic or semiconducting tubes of identical compositions have only slightly different radii [2][3][4]. Layered BN provides a III-V analog to these materials; it can be formed in single and multiwall nanotubes that have the same Bravais lattice as their graphene counterparts, but with inequivalent atomic species on its two sublattices [5,6].Here we show that the broken sublattice symmetry produces a macroscopic electric polarization in BN nanotubes, dependent on their topology. Remarkably, this ground state polarization is an intrinsically nonlocal quantum effect that cannot be described by a classical theory. The sign and size of the longitudinal polarization of the heteropolar tube are controlled by the boundary conditions on its electronic wave functions along its wrapped compact dimensions. We analyze this novel phenomenon by developing a quantum theory of the nanotube polarization in terms of a geometric phase [7][8][9].A natural description of the electronic properties of this system is developed from an expansion of the tight binding Hamiltonian for the π electrons at small wavevectors q around the K and K ′ points at the corners of the Brillouin zone of the 2D hexagonal lattice [10,11]. Introducing index α = ±1 for these points then leads to the long wavelength Hamiltonians [10][11][12]

Spontaneous polarization and piezoelectricity in boron nitride nanotubes

“…These data suggest a natural division of the nanotubes into three families with different ⌬ el : /3 for n ϭ3lϪ1, Ϫ /3 for nϭ3lϩ1, and Ϫ for nϭ3l, where l is an integer, 21 which is similar to the result obtained by Mele and Král. 7 However, the existence of such three classes of behavior is surprising, given that the ionic character of the electronic charge density ͑associated with the B-N bond͒ does not change with the nanotube index. Additionally, there is an important difference between our results and those of Ref.…”

“…Recently, these properties have been partially explored by Mele and Král, using a model electronic Hamiltonian. 7 They predicted that BNNT's are piezoelectric and pyroelectric, with the direction of the spontaneous electric field that changes with the index of the tubes. The ab initio calculations presented in this paper provide a much fuller description and show that BNNT systems are indeed excellent lightweight piezoelectrics, with comparable or better piezoelectric response and superior mechanical properties than in piezoelectric polymers.…”

Piezoelectricity in two-dimensional materials: Comparative study between lattice dynamics andab initiocalculations

“…The synthesis of hexagonal boron-nitride (h-BN) nanotubes 2,3 has stimulated theoretical work on polarization and piezoelectricity in BN nanotubes and its dependence on their topology [4][5][6][7] . Even more the discovery of graphene and other 2D crystals like h-BN and MoS 2 has opened the road for the study of mechanical and electric properties of a new class of materials with controlled composition and number of atomic layers (i.e.…”

Comparative high pressure Raman study of boron nitride nanotubes and hexagonal boron nitride

“…BNNT have wide band gap (~5.7 eV), which is very weakly dependent on the chirality and the tube Page 2 of 13 diameter; hence they are promising materials for applications in nano-electronics and optoelectronics. Theoretically it has been predicted [5][6][7] that BNNT are excellent piezoelectric systems with better response and superior mechanical properties than the usual piezoelectric polymers. On doping BNNT with transition metals, they become halfmetallic ferromagnet and hence are potential candidates for spintronics applications, e.g.…”