|
== Referencias ==
<references/>
<!--[[Polaron]] is a [[quasiparticle]] composed of an [[electron]] plus its accompanying [[polarization]] [[Field (physics)|field]]. A slow moving electron in a [[dielectric]] [[crystal]], interacting with [[lattice]] [[ion]]s through long-range [[force]]s will permanently be surrounded by a region of [[lattice]] [[polarization]] and [[deformation]] caused by the moving electron. Moving through the crystal, the electron carries the lattice distortion with it, thus one may speak of a cloud of [[phonon]]s accompanying the electron.
The resulting lattice polarization acts as a [[potential well]] that hinders the movements of the [[charge]], thus decreasing its mobility. Polarons have [[Spin (physics)|spin]], though two close-by polarons are spinless. The latter is called a [[bipolaron]].
In [[materials science]], a polaron is formed when a charge within a molecular chain influences the local [[Atomic nucleus|nuclear]] geometry, causing an attenuation (or even reversal) of nearby bond alternation amplitudes. This "[[excited state]]" possesses an energy level between the lower and upper bands.
The concept of a polaron is used while discussing ways for making a polymer electrically conductive. As an example, PPV (poly paraphenylenevinylene), is presently the most popular commercially available conducting polymer.
In this it is tried to create an excited state which is then eventually relaxed and the energy is emitted either in a radiative manner (emitting light) or a non radiative manner (vibration etc). One of the simplest ways to create such an "excited state" (i.e. a polaron) is by alternating the bond geometry which is done by doping the polymer. In a [[bipolaron]] two charged units exist within a molecular chain. A [[polaron liquid]] has been found in doped cuprate perovskites showing high Tc superconductivity.
The polaron, a [[Fermion|fermionic]] quasiparticle, should not be mixed-up with the [[polariton]], a
[[Boson|bosonic]] one, corresponding, e.g., to a hybridized state between a photon and an optical phonon.
== Polaron theory==
[[L. D. Landau]] <ref name="Landau1933">
{{cite journal
| author = Landau LD
| title = Über die Bewegung der Elektronen in Kristalgitter
| journal = Phys. Z. Sowjetunion
| volume = 3
| pages = 644-645
| year = 1933
}}
</ref> and S. I. Pekar <ref name="Pekar1951">
{{cite journal
| author = Pekar SI
| title = Issledovanija po Ekektronnoj Teorii Kristallov
| journal = Gostekhizdat, Moskva
| volume =
| pages =
| year = 1951
}}
</ref> were at the basis of polaron theory. A charge placed in a polarizable medium will be screened. [[Dielectric]] theory describes the phenomenon by the induction of a polarization around the charge carrier. The induced polarization will follow the charge carrier when it is moving through the medium. The carrier together with the induced polarization is considered as one entity, which is called a [[polaron]] (see Fig. 1).
[[Imagen:Polaron scheme1.jpg|thumb|left|150px|Fig. 1: Artist view of a polaron <ref name="Devreese1979">
{{cite journal
| author = [[Jozef T. Devreese|Devreese JTL]]
| title = Moles agitat mentem. Ontwikkelingen in de fysica van de vaste stof
| journal = Rede uitgesproken bij de aanvaarding van het ambt van buitengewoon hoogleraar in de fysica van de vaste stof, in het bijzonder de theorie van de vaste stof, bij de afdeling der technische natuurkunde aan de Technische Hogeschool Eindhoven
| volume =
| pages =
| year = 1979
}}
</ref>. A conduction electron in an ionic crystal or a polar semiconductor repels the negative ions and attracts the positive ions. A self-induced potential arises, which acts back on the electron and modifies its physical properties.]]
{| class="wikitable" style="margin: 1em auto"
|+ Table 1: Fröhlich coupling constants <ref name="Devreese2005">
{{cite journal
| author = [[Jozef T. Devreese|Devreese JTL]]
| title = Polarons
| journal = In: Encyclopedia of Physics, R.G. Lerner and G.L. Trigg (eds.), Wiley-VCH, Weinheim
| volume = vol.2
| pages = pp.2004-2027
| year = 2005
}}
</ref>
! Material
! α
! Material
! α
|-
| InSb
| 0.023
| KI
| 2.5
|-
| InAs
| 0.052
| TlBr
| 2.55
|-
| GaAs
| 0.068
| KBr
| 3.05
|-
| GaP
| 0.20
| RbI
| 3.16
|-
| CdTe
| 0.29
| Bi<sub>12</sub>SiO<sub>20</sub>
| 3.18
|-
| ZnSe
| 0.43
| CdF<sub>2</sub>
| 3.2
|-
| CdS
| 0.53
| KCl
| 3.44
|-
| AgBr
| 1.53
| CsI
| 3.67
|-
| AgCl
| 1.84
| SrTiO<sub>3</sub>
| 3.77
|-
| α-Al<sub>2</sub>O<sub>3</sub>
| 2.40
| RbCl
| 3.81
|-
|}
{{clr}}
A conduction electron in an ionic crystal or a polar semiconductor is the prototype of a polaron. [[Herbert Fröhlich]] proposed a model [[Hamiltonian]] for this polaron through which its dynamics is treated quantum mechanically (Fröhlich Hamiltonian) <ref name="Fröhlich1950">
{{cite journal
| author = [[Herbert Fröhlich|Fröhlich H]], Pelzer H, Zienau S
| title =
| journal = Phil. Mag.
| volume = 41
| pages = 221
| year = 1950
}}
</ref><ref name="Fröhlich1954">
{{cite journal
| author = [[Herbert Fröhlich|Fröhlich H]]
| title =
| journal = Adv. Phys.
| volume = 3
| pages = 325
| year = 1954
}}
</ref>. If the spatial extension of a polaron is large compared to the lattice parameter of the solid, the latter can be treated as a polarizable continuum. This is the case of a ''large a.k.a. Fröhlich polaron''. When the self-induced polarization caused by an electron or hole becomes of the order of the lattice parameter, a ''small a.k.a. Holstein polaron'' can arise. As distinct from large polarons, small polarons are governed by short-range interactions.
The polarization, carried by the longitudinal optical (LO) [[phonons]], is represented by a set of quantum [[oscillators]] with frequency ω, the long-wavelength LO-phonon frequency, and the interaction between the charge and the polarization field is linear in the field. This model (which up to now has not been solved exactly) has been the subject of extensive investigations <ref name="Pekar1951"/><ref name="Devreese2005"/><ref name="Fröhlich1950"/><ref name="Fröhlich1954"><ref name="Kuper1963">
{{cite journal
| author = Kuper GC, Whitfield GD (eds.)
| title = Polarons and Excitons
| journal = Oliver and Boyd, Edinburgh
| volume =
| pages =
| year = 1963
}}
</ref><ref name="Appel1968">
{{cite journal
| author = Appel J
| title =
| journal = In: Solid State Physics, F. Seitz, D. Turnbull, and H. Ehrenreich (eds.), Academic Press, New York
| volume = vol.21
| pages = pp.193-391
| year = 1968
}}
</ref><ref name="Devreese1972">
{{cite journal
| author = [[Jozef T. Devreese|Devreese JTL]] (ed.)
| title = Polarons in Ionic Crystals and Polar Semiconductors
| journal = North-Holland, Amsterdam
| volume =
| pages =
| year = 1972
}}
</ref><ref name="Mitra1987">
{{cite journal
| author = Mitra TK, Chatterjee A, Mukhopadhyay S
| title =
| journal = Phys. Rep.
| volume = 153
| pages = 91
| year = 1987
| title = Polarons
| doi = 10.1016/0370-1573(87)90087-1
}}
</ref><ref name="Devreese1996">
{{cite journal
| author = [[Jozef T. Devreese|Devreese JTL]]
| title =
| journal = In" Encyclopedia of Applied Physics, G. L. Trigg (ed.), VCH, Weinheim
| volume = vol.14
| pages = pp.383-413
| year = 1996
}}
</ref><ref name="Alexandrov1996">
{{cite journal
| author = Alexandrov AS, Mott N
| title = Polarons and Bipolarons
| journal = World Scientific, Singapore
| volume =
| pages =
| year = 1996
}}
</ref>.
The strength of the electron-phonon interaction is expressed by a dimensionless coupling constant α introduced by Fröhlich <ref name="Fröhlich1954"/>. In Table 1 the Fröhlich coupling constant is given for a few solids.
The physical properties of a polaron differ from those of a band-carrier. A polaron is characterized by its ''self-energy'' <math>\Delta E</math>, an ''effective mass'' <math>m*</math> and by its characteristic ''response'' to external electric and magnetic fields (e. g. dc mobility and optical absorption coefficient).
When the coupling is weak (<math>\alpha</math> small), the self-energy of the polaron can be approximated as <ref name="Smondyrev1986">
{{cite journal
| author = Smondyrev MA
| title =
| journal = Theor. Math. Phys.
| volume = 68
| pages = 653
| year = 1986
| title = Diagrams in the polaron model
| doi = 10.1007/BF01017794
}}
</ref>:
{|
|width=500|<math>
\frac{\Delta E}{\hbar\omega } \approx -\alpha -0.015919622\alpha^2,
</math>
|<math>(1)\,</math>
|}
and the polaron mass <math>m*</math>, which can be measured by cyclotron resonance experiments, is larger than the band mass m of the charge carrier without self-induced polarization <ref name="Röseler1968">
{{cite journal
| author = Röseler J
| title =
| journal = Phys. Stat. Sol. (b)
| volume = 25
| pages = 311
| year = 1968
| title = A new variational ansatz in the polaron theory
| doi = 10.1002/pssb.19680250129
}}
</ref>:
{|
|width=500|<math>
\frac{m^*}{m} \approx 1+\frac{\alpha}{6}+0.0236\alpha^2.
</math>
|<math>(2)\,</math>
|}
When the coupling is strong (α large), a variational approach due to Landau and Pekar indicates that the self-energy is proportional to α² and the polaron mass scales as α⁴.
[[Feynman]] <ref name="Feynman1955">
{{cite journal
| author = [[Richard Feynman|Feynman RP]]
| title =
| journal = Phys. Rev.
| volume = 97
| pages = 660
| year = 1955
}}
</ref> introduced a [[variational principle]] for path integrals to study the polaron. He simulated the interaction between the electron and the polarization modes by a harmonic interaction between a hypothetical particle and the electron. The analysis of an exactly solvable ("symmetrical") 1D-polaron model <ref name="Devreese1964">
{{cite journal
| author = [[Jozef T. Devreese|Devreese JTL]], Evrard R
| title =
| journal = Phys. Lett.
| volume = 11
| pages = 278
| year = 1964
}}
</ref><ref name="Devreese1968">
{{cite journal
| author = [[Jozef T. Devreese|Devreese JTL]], Evrard R
| title =
| journal = Proceedings of the British Ceramic Society
| volume = 10
| pages = 151
| year = 1968
}}
</ref>, Monte Carlo schemes <ref name="Mishchenko2000">
{{cite journal
| author = Mishchenko AS, Prokof'ev NV, Sakamoto A, Svistunov BV
| title =
| journal = Phys. Rev. B
| volume = 62
| pages = 6317
| year = 2000
| title = Diagrammatic quantum Monte Carlo study of the Fröhlich polaron
| doi = 10.1103/PhysRevB.62.6317
}}
</ref><ref name="Titantah2001">
{{cite journal
| author = Titantah JT, Pierleoni C, Ciuchi S
| title =
| journal = Phys. Rev. Lett.
| volume = 87
| pages = 206406
| year = 2001
| title = Free Energy of the Fröhlich Polaron in Two and Three Dimensions
| doi = 10.1103/PhysRevLett.87.206406
}}
</ref> and other numerical schemes <ref name="DeFilippis2003">
{{cite journal
| author = De Filippis G, Cataudella V, Marigliano Ramaglia V, Perroni CA, Bercioux D
| title =
| journal = Eur. Phys. J. B
| volume = 36
| pages = 65
| year = 2003
}}
</ref> demonstrate the remarkable accuracy of Feynman's path-integral approach to the polaron ground-state energy. Experimentally more directly accessible properties of the polaron, such as its mobility and optical absorption, have been investigated subsequently.
== Polaron optical absorption ==
The expression for the magnetooptical absorption of a polaron is <ref name="Peeters1986">
{{cite journal
| author = Peeters FM, [[Jozef T. Devreese|Devreese JTL]]
| title =
| journal = Phys. Rev. B
| volume = 34
| pages = 7246
| year = 1986
}}
</ref>:
{|
|width=500|<math>
\Gamma(\Omega) \propto -\frac{\mathrm{Im} \Sigma(\Omega)}{\left[\Omega-\omega_{\mathrm{c}}-\mathrm{Re} \Sigma(\Omega)\right]^2 + \left[\mathrm{Im}\Sigma(\Omega)\right]^2} .
</math>
|<math>(3)\,</math>
|}
Here, <math>\omega_{c}</math> is the [[Cyclotron_frequency|cyclotron frequency]] for a rigid-band electron. The magnetooptical absorption Γ(Ω) at the frequency Ω takes the form Σ(Ω) is the so-called "memory function", which describes the dynamics of the polaron. Σ(Ω) depends also on α, β and <math>\omega_{c}</math>.
In the absence of an external magnetic field (<math>\omega_{c}=0</math>) the optical absorption spectrum (3) of the polaron at weak coupling is determined by the absorption of radiation energy, which is reemitted in the form of LO phonons. At larger coupling, <math>\alpha \ge 5.9</math>, the polaron can undergo transitions toward a relatively stable internal excited state called the "relaxed excited state" (RES) (see Fig. 2). The RES peak in the spectrum also has a phonon sideband, which is related to a Franck-Condon-type transition.
[[Imagen:FigP24-2.jpg|thumb|200px|left|Fig.2. Optical absorption of a polaron at <math>\alpha = 5</math> and 6. The RES peak is very intense compared with the Franck-Condon (FC) peak <ref name="Devreese1972"/><ref name="Devreese1972b">
{{cite journal
| author = [[Jozef T. Devreese|Devreese JTL]], De Sitter J, Goovaerts M
| title =
| journal = Phys. Rev. B
| volume = 5
| pages = 2367
| year = 1972
}}
</ref>.]]
A comparison of the DSG results <ref name="Devreese1972b"/> with the optical conductivity spectra given by approximation-free numerical <ref name="Mishchenko2003">
{{cite journal
| author = Mishchenko AS, Nagaosa N, Prokof'ev NV, Sakamoto A, Svistunov BV
| title =
| journal = Phys. Rev. Lett.
| volume = 91
| pages = 236401
| year = 2003
| title = Optical Conductivity of the Fröhlich Polaron
| doi = 10.1103/PhysRevLett.91.236401
}}
</ref> and approximate analytical approaches is given in ref. <ref name="DeFilippis2006">
{{cite journal
| author = De Filippis G, Cataudella V, Mishchenko AS, Perroni CA, [[Jozef T. Devreese|Devreese JTL]]
| title =
| journal = Phys. Rev. Lett.
| volume = 96
| pages = 136405
| year = 2006
}}
</ref>.
Calculations of the optical conductivity for the Fröhlich polaron performed within the Diagrammatic Quantum Monte Carlo method <ref name="Mishchenko2003"/>, see Fig. 3, fully confirm the results of the path-integral variational approach <ref name="Devreese1972b"/> at <math>\alpha \lesssim 3.</math> In the intermediate coupling regime <math>3<\alpha <6,</math> the low-energy behavior and the position of the maximum of the optical conductivity spectrum of ref. <ref name="Mishchenko2003"/> follow well the prediction of ref. <ref name="Devreese1972b"/>. There are the following qualitative differences between the two approaches in the intermediate and strong coupling regime: in ref. <ref name="Mishchenko2003"/>, the dominant peak broadens and the second peak does not develop, giving instead rise to a flat shoulder in the optical conductivity spectrum at <math>\alpha =6</math>. This behavior can be attributed to the optical processes with participation of two <ref name="Goovaerts1973">
{{cite journal
| author = Goovaerts MJ, De Sitter J, [[Jozef T. Devreese|Devreese JTL]]
| title =
| journal = Phys. Rev.
| volume = 7
| pages = 2639
| year = 1973
}}
</ref> or more phonons. The nature of the excited states of a polaron needs further study.
[[Imagen:PolaronOptCond.jpg|thumb|right|200px|Fig. 3: Optical conductivity spectra calculated within the Diagrammatic Quantum Monte Carlo method (open circles) compared to the DSG calculations (solid lines) <ref name="Devreese1972b"/><ref name="Mishchenko2003"/>.]]
The application of a sufficiently strong external magnetic field allows one to satisfy the resonance condition <math>\Omega =\omega _{\mathrm{c}}+\mathrm{Re} \Sigma (\Omega )</math>, which {(for <math>\omega_c < \omega</math>)} determines the polaron cyclotron resonance frequency. From this condition also the polaron cyclotron mass can be derived. Using the most accurate theoretical polaron models to evaluate <math>\Sigma (\Omega )</math>, the experimental cyclotron data can be well accounted for.
Evidence for the polaron character of charge carriers in AgBr and AgCl was obtained through high-precision cyclotron resonance experiments in external magnetic fields up to 16 T <ref name="Hodby1987">
{{cite journal
| author = Hodby JW, Russell GP, Peeters F, [[Jozef T. Devreese|Devreese JTL]], Larsen DM
| title =
| journal = Phys. Rev. Lett.
| volume = 58
| pages = 1471
| year = 1987
| title = Cyclotron resonance of polarons in the silver halides: AgBr and AgCl
| doi = 10.1103/PhysRevLett.58.1471
}}
</ref>. The all-coupling magneto-absorption calculated in ref. <ref name="Peeter1986">
{{cite journal
| author = Peeters FM, [[Jozef T. Devreese|Devreese JTL]]
| title =
| journal = Phys. Rev. B
| volume = 34
| pages = 7246
| year = 1986
}}
</ref>, leads to the best quantitative agreement between theory and experiment for AgBr and AgCl. This quantitative interpretation of the cyclotron resonance experiment in AgBr and
AgCl <ref name="Hodby1987"/> by the theory of ref. <ref name="Peeter1986"/> provided one of the most convincing and clearest demonstrations of Fröhlich polaron features in solids.
Experimental data on the magnetopolaron effect, obtained using far-infrared photoconductivity techniques, have been applied to study the energy spectrum of shallow donors in polar semiconductor layers of CdTe <ref name="Grynberg1996">
{{cite journal
| author = Grynberg M, Huant S, Martinez G, Kossut J, Wojtowicz T, Karczewski G, Shi JM, Peeters FM, [[Jozef T. Devreese|Devreese JTL]]
| title =
| journal =
| volume =
| pages =
| year = 1996
}}
</ref>.
The polaron effect well above the LO phonon energy was studied through cyclotron resonance measurements, e. g., in II-VI semiconductors, observed in ultra-high magnetic fields <ref name="Miura2003">
{{cite journal
| author = Miura N, Imanaka Y
| title =
| journal = Phys. Stat. Sol. (b)
| volume = 237
| pages = 237
| year = 2003
| title = Polaron cyclotron resonance in II–VI compounds at high magnetic fields
| doi = 10.1002/pssb.200301781
}}
</ref>. The resonant polaron effect manifests itself when the cyclotron frequency approaches the LO phonon energy in sufficiently high magnetic fields.
== Polarons in two dimensions and in quasi-2D structures ==
The great interest in the study of the two-dimensional electron gas (2DEG) has also resulted in many investigations on the properties of polarons in two dimensions <ref name="Devreese1987">
{{cite journal
| author = [[Jozef T. Devreese|Devreese JTL]], Peeters FM (eds.)
| title = The Physics of the Two-Dimensional Electron Gas
| journal = ASI Series, Plenum, New York
| volume = B157
| pages =
| year = 1987
}}
</ref><ref name="Wu1986">
{{cite journal
| author = Wu XG, Peeters FM, [[Jozef T. Devreese|Devreese JTL]]
| title =
| journal = Phys. Rev. B
| volume = 34
| pages = 2621
| year = 1986
}}
</ref><ref name="Peeters1987">
{{cite journal
| author = Peeters FM, [[Jozef T. Devreese|Devreese JTL]]
| title =
| journal = Phys. Rev. B
| volume = 36
| pages = 4442
| year = 1987
}}
</ref>. A simple model for the 2D polaron system consists of an electron confined to a plane, interacting via the Fröhlich interaction with the LO phonons of a 3D surrounding medium. The self-energy and the mass of such a 2D polaron are no longer described by the expressions valid in 3D; for weak coupling they can be approximated as <ref name="Sak1972">
{{cite journal
| author = Sak J
| title =
| journal = Phys. Rev. B
| volume = 6
| pages = 3981
| year = 1972
}}
</ref><ref name="Peeters1988">
{{cite journal
| author = Peeters FM, Wu XG, [[Jozef T. Devreese|Devreese JTL]]
| title =
| journal = Phys. Rev. B
| volume = 37
| pages = 933
| year = 1988
}}
</ref>:
{|
|width=500|<math>
\frac{\Delta E}{\hbar \omega} \approx -\frac{\pi}{2}\alpha\ - 0.06397\alpha^2;
</math>
|<math>(4)\,</math>
|}
{|
|width=500|<math>
\frac{m^*}{m} \approx 1+\frac{\pi}{8}\alpha\ + 0.1272348\alpha^2.
</math>
|<math>(5)\,</math>
|}
It has been shown that simple scaling relations exist, connecting the physical properties of polarons in 2D with those in 3D. An example of such a scaling relation is <ref name="Peeters1987"/>:
{|
|width=500|<math>
\frac{m_{\mathrm{2D}}^*(\alpha)}{m_{\mathrm{2D}}} = \frac{m_{\mathrm{3D}}^*(\frac{3}{4}\alpha)}{m_{\mathrm{3D}}} ,
</math>
|<math>(6)\,</math>
|}
where <math>m_\mathrm{2D}^*</math> (<math>m_\mathrm{3D}^*</math>) and <math>m_\mathrm{2D}^{}</math> (<math>m_\mathrm{3D}^{}</math>) are, respectively, the polaron and the electron-band masses in 2D (3D).
The effect of the confinement of a Fröhlich polaron is to enhance the ''effective'' polaron coupling. However, many-particle effects tend to counterbalance this effect because of screening <ref name="Devreese1987"><ref name="DasSarma1985">
{{cite journal
| author = Das Sarma S, Mason BA
| title =
| journal = Ann. Phys. (New York)
| volume = 163
| pages = 78
| year = 1985
}}
</ref>.
Also in 2D systems [[cyclotron resonance]] is a convenient tool to study polaron effects. Although several other effects have to be taken into account (nonparabolicity of the electron bands, [[many-body]] effects, the nature of the confining potential, etc.), the polaron effect is clearly revealed in the cyclotron mass. An interesting 2D system consists of electrons on films of liquid He <ref name="Shikin1973">
{{cite journal
| author = Shikin VB, Monarkha YP
| title =
| journal = Sov. Phys. - JETP
| volume = 38
| pages = 373
| year = 1973
}}
</ref><ref name="Jackson1981">
{{cite journal
| author = Jackson SA, Platzman PM
| title =
| journal = Phys. Rev. B
| volume = 24
| pages = 499
| year = 1981
}}
</ref>. In this system the electrons couple to the ripplons of the liquid He, forming "ripplopolarons". The effective coupling can be relatively large and, for some values of the parameters, self-trapping can result. The acoustic nature of the ripplon dispersion at long wavelengths is a key aspect of the trapping.
For GaAs/Al<sub>x</sub>Ga<sub>1-x</sub>As quantum wells and superlattices, the polaron effect is found to decrease the energy of the shallow donor states at low magnetic fields and leads to a resonant splitting of the energies at high magnetic fields. The energy spectra of such polaronic systems as shallow donors ("bound polarons"), e. g., the D<sub>0</sub> and D<sup>-</sup> centres, constitute the most complete and detailed polaron spectroscopy realised in the literature <ref name="Shi1993">
{{cite journal
| author = Shi JM, Peeters FM, [[Jozef T. Devreese|Devreese JTL]]
| title =
| journal = Phys. Rev. B
| volume = 48
| pages = 5202
| year = 1993
}}
</ref>.
In GaAs/AlAs quantum wells with sufficiently high electron density, anticrossing of the cyclotron-resonance spectra has been observed near the GaAs transverse optical (TO) phonon frequency rather than near the GaAs LO-phonon frequency <ref name="x">
{{cite journal
| author = Poulter AJL, Zeman J, Maude DK, Potemski M, Martinez G, Riedel A, Hey R, Friedland KJ
| title =
| journal = Phys. Rev. Lett.
| volume = 86
| pages = 336
| year = 2001
| title = Magneto Infrared Absorption in High Electron Density GaAs Quantum Wells
| doi = 10.1103/PhysRevLett.86.336
}}
</ref>. This anticrossing near the TO-phonon frequency was explained in the framework of the polaron theory <ref name="x">
{{cite journal
| author = Klimin SN, [[Jozef T. Devreese|Devreese JTL]]
| title =
| journal = Phys. Rev. B
| volume = 68
| pages = 245303
| year = 2003
}}
</ref>.
Besides optical properties <ref name="Devreese1996"/><ref name="Devreese2005"/><ref name="Calvani2001">
{{cite journal
| author = Calvani P
| title = Optical Properties of Polarons
| journal = Editrice Compositori, Bologna
| volume =
| pages =
| year = 2001
}}
</ref>, many other physical properties of polarons have been studied, including the possibility of self-trapping, polaron transport <ref name="Feynman1962">
{{cite journal
| author = Feynman RP, Hellwarth RW, Iddings CK, Platzman PM
| title =
| journal = Phys. Rev.
| volume = 127
| pages = 1004
| year = 1962
| title = Mobility of Slow Electrons in a Polar Crystal
| doi = 10.1103/PhysRev.127.1004
}}
</ref>, magnetophonon resonance, etc.
== Extensions of the polaron concept ==
Significant are also the extensions of the polaron concept: acoustic polaron, [[piezoelectric]] polaron, electronic polaron, bound polaron, trapped polaron, [[Spin (physics)|spin]] polaron, molecular polaron, solvated polarons, polaronic exciton, Jahn-Teller polaron, small polaron, [[bipolaron]]s and many-polaron systems <ref name="Devreese2005"/>. These extensions of the concept are invoked, e. g., to study the properties of conjugated polymers, colossal magnetoresistance perovskites, high-<math>T_{c}</math> superconductors, layered MgB<sub>2</sub> superconductors, fullerenes, quasi-1D conductors, semiconductor nanostructures.
The possibility that polarons and bipolarons play a role in high-<math>T_{c}</math> [[superconductors]] has renewed interest in the physical properties of many-polaron systems and, in particular, in their optical properties. Theoretical treatments have been extended from one-polaron to many-polaron systems <ref name="Devreese2005"/><ref name="Bassani2003">
{{cite journal
| author = Bassani FG, Cataudella V, Chiofalo ML, De Filippis G, Iadonisi G, Perroni CA
| title =
| journal = Phys. Stat. Sol. (b)
| volume = 237
| pages = 173
| year = 2003
| title = Electron gas with polaronic effects: beyond the mean-field theory
| doi = 10.1002/pssb.200301763
}}
</ref>.
A new aspect of the polaron concept has been investigated for semiconductor [[nanostructures]]: the exciton-phonon states are not factorizable into an adiabatic product Ansatz, so that a ''non-adiabatic'' treatment is needed <ref name="Fomin1998">
{{cite journal
| author = Fomin VM, Gladilin VN, [[Jozef T. Devreese|Devreese JTL]], Pokatilov EP, Balaban SN, Klimin SN
| title =
| journal = Phys. Rev. B
| volume = 57
| pages = 2415
| year = 1998
| title = Photoluminescence of spherical quantum dots
| doi = 10.1103/PhysRevB.57.2415
}}
</ref>. The ''non-adiabaticity'' of the exciton-phonon systems leads to a strong enhancement of the phonon-assisted transition probabilities (as compared to those treated adiabatically) and to multiphonon optical spectra that are considerably different from the [[Franck-Condon]] progression even for small values of the electron-phonon coupling constant as is the case for typical semiconductor nanostructures <ref name="Fomin1998"/>.
In biophysics [[Davydov soliton]] is a propagating along the [[protein]] [[α-helix]] self-trapped amide I excitation that is a solution of the Davydov Hamiltonian. The mathematical techniques that are used to analyze Davydov's soliton are similar to some that have been developed in polaron theory. In this context the [[Davydov soliton]] corresponds to a ''polaron'' that is (i) ''large'' so the continuum limit approximation in justified, (ii) ''acoustic'' because the self-localization arises from interactions with acoustic modes of the lattice, and (iii) ''weakly coupled'' because the anharmonic energy is small compared with the phonon bandwidth <ref name="Scott1992">
{{cite journal
| author = Scott AS
| title = Davydov's soliton
| journal = Physics Reports
| volume = 217
| pages = 1-67
| year = 1992
| doi = 10.1016/0370-1573(92)90093-F
}}
</ref>.
==See also==
==References and notes==
{{reflist|2}}
==Enlaces externos==
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[[Categoría:Física]]
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