## Theoretical aspects of conducting polymers: electronic structure and defect states |

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Page 19

Inserting the Ansatz r = r + (-l)n y into the ir-electron Hamiltonian, no Eq.(l), and

using the parametrization (15) the electronic

Inserting the Ansatz r = r + (-l)n y into the ir-electron Hamiltonian, no Eq.(l), and

using the parametrization (15) the electronic

**spectrum**is - 19 -Page 20

electronic structure and defect states Dionys Baeriswyl. Eq.(l), and using the

parametrization (15) the electronic

2cos2ka + A2sin2kaJ% where 2ay. It exhibits a gap 2AQat the two Fermi points,

the size of which is determined by minimalizing the total energy V \ NV2 + 2 I ek |k

|<kF = ^to[^-E(l-52)] where 6= AQ/(2to) is the ratio between bandgap Eg =

2A0and bandwidth W = 4tQ, X is given by Eq. (20) 9 and E(l- 6 ) is a complete

elliptic integral.

electronic structure and defect states Dionys Baeriswyl. Eq.(l), and using the

parametrization (15) the electronic

**spectrum**is obtained as ek = sign e° | (2tQ)2cos2ka + A2sin2kaJ% where 2ay. It exhibits a gap 2AQat the two Fermi points,

the size of which is determined by minimalizing the total energy V \ NV2 + 2 I ek |k

|<kF = ^to[^-E(l-52)] where 6= AQ/(2to) is the ratio between bandgap Eg =

2A0and bandwidth W = 4tQ, X is given by Eq. (20) 9 and E(l- 6 ) is a complete

elliptic integral.

Page 39

In order to get the

if written in terms of internal coordinates, depends on the geometrical structure of

the polymer. For trans <CH)x we use the continuum limit of the SSH Hamiltonian (

27) to get Ekin = (^nVpA<^)-1 | dx A2 (55) where a)Q is the bare phonon

frequency, as in Eq. (28) . Together with Eqs. (48) and (52) this yields a

«2 = u2 irhvFX D(q) ~ 2X<d2 (l + i{V) for |5q| << 1 (56) in agreement with Eq. (28)

and ...

In order to get the

**spectrum**we have to add the kinetic energy of the lattice which,if written in terms of internal coordinates, depends on the geometrical structure of

the polymer. For trans <CH)x we use the continuum limit of the SSH Hamiltonian (

27) to get Ekin = (^nVpA<^)-1 | dx A2 (55) where a)Q is the bare phonon

frequency, as in Eq. (28) . Together with Eqs. (48) and (52) this yields a

**spectrum**«2 = u2 irhvFX D(q) ~ 2X<d2 (l + i{V) for |5q| << 1 (56) in agreement with Eq. (28)

and ...

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