BN nanotubes are pyroelectric, piezoelectric and photogalvanic media. The photogalvanic effects occurs because excitation of the electrons with light polarized along the tube direction produces a charge current on the tube wall with a direction determined by the tube chirality.
Boron-Nitride is a III-V analog to graphene; it can be formed in
a two dimensional honeycomb lattice with the inequivalent sublattice sites occupied by the group III (B) and group V (N)
elements. This sublattice symmetry breaking allows for new electronic phenomena not found in graphene or carbon nanotubes.
Although the BN bond is partially ionic, there is no net electric polarization of the BN sheet because of its threefold symmetry. When the sheet is wrapped to form a tube, the threefold
symmetry is lifted and an electric polarization is allowed. There are two types of effects that produce a net electric polarization of the BN nanotube. Short range (chemical) effects occur because of perturbations to the electronic Hamiltonian due to the curvature of the tube. This modifies the "hybridization" of the molecular orbitals and the matrix elements
for hopping between atomic sites. Global (physical) effects occur because of the requirement that the electronic wavefunctions match continuously around the tube circumference. Interestingly, the Berry's phase approach to the electric polarization
demonstrates that the latter physical effects completely dominate the predicted electric polarization. Because of this
the electric polarization is predicted to show a "period 3" dependence on the tube's wrapping vector, and nearby
wrappings whose structure is nearly identical in the tangent plane can exhibit widely different electric polarizations.
This is the III-V analog of the structure specific variation of conducting and nonconducting behavior of the carbon nanotubes.
The electric polarization can be modified by any perturbation that couples to the bandgap, e.g. an elastic mechanical strain. Thus the BN nanotubes are piezoelectric materials. The strains that
can modulate the electric polarization depend on the tube wrapping vector. For the armchair structure shown on the right,
uniaxial strain (stretch) and bend do not linearly couple, but tube torsion does. Thus twisting an armchair BN tube
generates a voltage between its ends and conversely, an applied voltage induces torsion.
The piezoelectric properties of the BN tube can be understood
by analyzing the piezoelectric response of a flat BN sheet. Although threefold symmetry prohibits an electric dipole
moment in the equilibrium state, the symmetry is lowered by an elastic deformation. Thus
the isolated BN sheet is a piezoelectric medium. A uniaxial strain (stretching the sheet as shown)
produces an electric polarization aligned with the stretching direction.
A shear strain (as shown) produces a polarization perpendicular
to the direction of the atomic displacements. Because of the threefold symmetry there is a single piezoelectric coefficient for the sheet
that controls all the symmetry allowed linear piezoelectric constants.
The piezoelectric properties of the BN nanotube are accurately described by mapping this response of the sheet into
the tangent plane of the tube. In this way, one finds that the armchair structures have a dipole moment coupled
to twist (but not stretch) and the zigzag structures have a dipole coupled to stretch (but not twist). Intermediate
tube wrapping couple to both elastic strains. This implies that twist and stretch are linearly coupled together
in the elastic theory of the tube, an anomalous situation that reflects the underlying microscopic chirality of
the structure. Na Sai's work (see the reference below) developed the scaling relations required to understand
tube piezoelectricity in terms of the piezo-response of the two dimensional sheet.
The photogalvanic properties follow from the pyroelectric behavior. At low energy optical excitation of the electrons produces a perturbation to the charge density that opposes the ground state polarization, and acts as a pump. Thus as shown in the figure at the top of the page, a charge current can be produced along the tube axis (left), in a circulating azimuthal direction (center) or in a chiral pattern (right).
E.J. Mele and P. Kral "Electric Polarization in Heteropolar Nanotubes as a Geometric Phase"
Physical Review Letters 88, 056803 (2002)
Na Sai and E.J. Mele "Nanotube Piezoelectricity" cond-mat/0308583