the electron  phonon interaction in semiconductor heterostructures is of greater interest in comparison to bulk materials .
this is due to the fact that the quasi - particle space localization leads to the modifications of the energy spectrum .
the all - important factor is the rise of new vibration branches of optical spectrum , namely , the interface optical phonon .
this interaction is of considerable importance in the understanding of the properties of heterostructures based on material with high ionicity .
it can lead to self - consistent bond state of a charge particle and phonons , that is , the large radius polaron .
currently , an investigation on the part played by interface phonons has attracted considerable interest in polaron state formation study .
the contributions to polaron binding energy both of interface and of bulk optical phonons are the same value order in the quantum dots [ 3 - 5 ] . taking into account ,
alternatively , the interface phonon role dominates in polaron binding energy for quantum well case . in response to this fact , the strong electron 
phonon interaction can be realized in the quantum wells based on non - polar material with high iconicity barrier material .
in addition , from the results , it follows that profound polaron effects should be expected , e.g. , in the si / sio2 compounds .
although there are no polar optical phonons in the material of such quantum well , these may be produced at the heteroboundary . as a result , the strong interaction of charged particles with interface phonons becomes possible .
phonon interaction is possible when the quantum well is made of polar material and for the barriers is taken non - polar material . in recent years , varied technologies of semiconductor quantum wire growth with assorted barriers are progressing rapidly .
the most success has been achieved for the quantum wires based on iii  v compounds [ 8 - 12 ] .
it is in these structures that the polaron states can arise . at the same time , no extended theoretical study of the polaron states in such structures is available .
proper allowance must be made for the interaction of charge particles with interface optical phonons for an understanding of this problem . in this paper
, we develop a theory of polarons in the quantum wires , taking into account the interaction of charged particles with all branches of the optical phonon spectrum .
the general equations have been obtained to describe the phonon spectrum taking into account the interaction of polarization and deformation potentials . in materials with high ionicity degree , the charge particle interaction with polar optical phonons is of crucial importance in polaron state formation .
this has led us to use the model which takes into account this phonon type in the quantum wire .
optical - phonon modes in the quantum wire are determined using the classical electrostatics equations : together with conventional boundary conditions at heterointerfaces , where   is the polarization field ,   the electric field ,   the scalar potential ,   the total charge density , and   is the dielectric susceptibility of the material i ( i = 1 , 2 ) . the dielectric function   is given by : where   and   are the frequencies of longitudinal - optical ( lo ) phonons and transverse - optical ( to ) phonons , respectively , and   is the high - frequency dielectric constant .
1 ) for the cylindrical quantum wire leads to the equation defining the dispersion law for interface optical phonons : here , i m is the m - th order modified bessel function of the first kind , km is the m - th order modified bessel function of the second kind , k is the wave vector , 0 is the quantum wire radius .
3 . in fig . 1 is shown the wave - vector dependence of the interface phonon frequencies .
this dependence is calculated for the quantum wire based on cdse surrounded by znse barriers with m = 0 in eq .
the wave - vector dependence of interface optical phonon frequencies for znse / cdse / znse quantum wire the hamiltonian operator for phonon subsystem is conveniently written in terms of the phonon creation and annihilation operators : where the operators   describe the creation of bulk phonons localized inside the quantum wire ,   are the interface phonon creation operators .
phonon interaction for the cylindrical quantum wire can be represented by the method supposed in : here , the coefficients   are defined as : here , n(m ) is n - th order root of the equation jm( ) = 0 , jm is the m - th order bessel function of the first kind .
the interaction parameters m(k ) have the form : the expressions ( 6 ) , ( 7 ) do not require in the region .
the reason is that we suppose the total electron localization within the quantum wire . in eq
the general equations have been obtained to describe the phonon spectrum taking into account the interaction of polarization and deformation potentials . in materials with high ionicity degree ,
the charge particle interaction with polar optical phonons is of crucial importance in polaron state formation .
this has led us to use the model which takes into account this phonon type in the quantum wire .
optical - phonon modes in the quantum wire are determined using the classical electrostatics equations : together with conventional boundary conditions at heterointerfaces , where   is the polarization field ,   the electric field ,   the scalar potential ,   the total charge density , and   is the dielectric susceptibility of the material i ( i = 1 , 2 ) . the dielectric function   is given by : where   and   are the frequencies of longitudinal - optical ( lo ) phonons and transverse - optical ( to ) phonons , respectively , and   is the high - frequency dielectric constant .
1 ) for the cylindrical quantum wire leads to the equation defining the dispersion law for interface optical phonons : here , i m is the m - th order modified bessel function of the first kind , km is the m - th order modified bessel function of the second kind , k is the wave vector , 0 is the quantum wire radius .
3 . in fig . 1 is shown the wave - vector dependence of the interface phonon frequencies .
this dependence is calculated for the quantum wire based on cdse surrounded by znse barriers with m = 0 in eq .
the wave - vector dependence of interface optical phonon frequencies for znse / cdse / znse quantum wire the hamiltonian operator for phonon subsystem is conveniently written in terms of the phonon creation and annihilation operators : where the operators   describe the creation of bulk phonons localized inside the quantum wire ,   are the interface phonon creation operators .
phonon interaction for the cylindrical quantum wire can be represented by the method supposed in : here , the coefficients   are defined as : here , n(m ) is n - th order root of the equation jm( ) = 0 , jm is the m - th order bessel function of the first kind .
the interaction parameters m(k ) have the form : the expressions ( 6 ) , ( 7 ) do not require in the region .
the reason is that we suppose the total electron localization within the quantum wire . in eq .
let the quantum wire be surrounded with compositionally identical barriers . in order to separate the effect of exactly dielectric irregularities , we assume that the potential well for electrons is rather deep , so that the penetration of the wave functions under the barrier can be disregarded . in this case , the interaction of charged particles with barrier phonons is weak .
we write the hamiltonian of the system as here ,   is the electron hamiltonian for which the interaction of the electron with phonons is disregarded .
the hamiltonian is given by where   is the quantum wire potential and m is the electron effective mass .
if the interaction of an electron with polar optical phonons is strong , the polaron binding energy can be determined with the use of adiabatic approximation . in so doing ,
the adiabatic parameter here is the ratio of the quantum wire radius 0 to the polaron radius a0 : the exact expression for polaron radius a0 is obtained below . the condition ( eq .
13 ) implies that the main contribution to the polaron binding energy is given by small values of the wave vector k such that if condition ( eq .
13 ) is satisfied , the wave function of an electron localized in the n - th size - quantization level can be represented as : where the wave function   describes the two - dimensional electron motion not disturbed by electron 
the wave function   represents the electron localization in the self - consistent potential well created by phonons .
the quantum numbers n , m define not disturbed electron state in the quantum wire . in the case of total electron localization in the cylindrical quantum wire , the wave function   has the form : here   is n - th root of m - th order bessel function .
the wave function   is to be obtained by solving self - consistent problem . in so doing , the total wave function from eq .
12 ) takes the form after this procedure : here   is the energy of an electron on relevant size - quantization level , m is the electron mass inside the quantum wire .
phonon interaction   can be written as : here ,   and   are the coefficients   and m(k ) from eq .
we obtain average hamiltonian   it can be brought to the form diagonal in phonon variables by the unitary transformation   where the unitary transformation application gives the following equation : from expression ( eq .
21 ) , we can see that , in the adiabatic approximation used here , the bulk phonon spectrum and the interface phonon spectrum remain unchanged .
21 ) presents the energy of a large radius polaron . in the general case , the energy   involved in ( eq .
21 ) depends on the dielectric properties of the materials of both the quantum wire and the barriers . in the general case ,
the polaron binding energy ee depends on electron size - quantization level number and on optical - phonon spectrum properties .
after the procedure of angle averaging which is expressible in explicit form , we obtain this energy ee as : the energy ( eq .
22 ) is defined by the electron interaction with phonon modes correspond to m = 0 only . this equation ( eq .
this contribution is caused by the interaction of localized electron with confined and interface phonons .
however , the electron energy and wave function can be obtained analytically on condition the unequality ( eq .
the most significant contribution to the polaron binding energy in the parameter ( eq . 14 ) gives the interaction of an electron with interface phonon mode of the frequency close to barrier frequency   the largest contribution to the energy in the parameter ( eq .
this quantity comes about from taking into account the interaction of an electron with interface optical phonons .
23 that the quantum wire material properties have no effect on the polaron state formation .
the part of quantum wire material dielectric properties can be obtained in higher orders in the parameter ( eq .
23 that the characteristic values of the phonon wave vector k which describe the value of electron 
phonon interaction is of the order reciprocal to polaron radius a0 the logarithmic function changes weakly in this region .
therefore , we can consider with the same accuracy in parameter ( 14 ) that the energy is equal to : the substitution of the energy from eq .
19 leads to the expression for polaron binding energy as the functional of unknown yet wave function (z ) .
it can be written as : the following equation is obtained by variational method using wave functions (z ) : this nonlinear eq .
26 has the solutions which can be written in the form with any energy values epol : the polaron binding energy is found by substitution of eq . 27 to 26 : the polaron radius a0 is obtained by solving the transcendental equation .
it has the form : it is this quantity from eq . 29 which contains the adiabatic parameter ( eq .
13 ) . substituting material parameters   into eq . 29 for the quantum wire znse
/ cdse / znse leads one to expect that the strong polaron effects for these structure should be observed when the quantum wire radius 0 < 40  .
it might be well to point out that both the polaron binding energy ( eq .
29 ) depend on effective electron mass inside the quantum wire and barrier dielectric properties .
this clearly demonstrates the prevailing role of the interaction of an electron with interface optical phonons .
the availability of the surface phonons leads to widening the range of materials in which the strong polaron effect should be expected .
phonon interaction may exist near the interface between polar and non - polar materials . among other things
phonon interaction is determined significantly by interface optical phonons in narrow quantum wires corresponding to the condition ( eq .
is meant that the interface phonons can produce the effective canal of excitation transfer in the structures with several quantum wires .
this work was supported by russian foundation for basic research , grant 09 - 02 - 00902-a and the program of presidium of ras  the fundamental study of nanotechnologies and nanomaterials  no . 27 .
this article is distributed under the terms of the creative commons attribution noncommercial license which permits any noncommercial use , distribution , and reproduction in any medium , provided the original author(s ) and source are credited .
 the theory of large radius polaron in the quantum wire is developed . 
 the interaction of charge particles with interface optical phonons as well as with optical phonons localized in the quantum wire is taken into account . 
 the interface phonon contribution is shown to be dominant for narrow quantum wires . 
 the wave functions and polaron binding energy are found . 
 it is determined that polaron binding energy depends on the electron mass inside the wire and on the polarization properties of the barrier material . 
Introduction
Interface Phonons in the Quantum Wire
The Polaron in the Quantum Wire
Results and Discussion
Open Access