Vacuum Polarization (and Zitterbewegung), Polaron, and Polariton.
１．Vacuum Polarization
The elementary electric charge, e = 1.6 x 10^-19 C, is the shielded or renormalized value. The electron interacts with the vacuum via its electric field producing electron-positron pairs in the vacuum.
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半導体の電気伝導におけるZitterbewegung（ジグザグ運動） 中村壮智、勝本信吾（2018）
「狭ギャップ半導体である InAs 量子井戸中の二次元電子系に生じる ZB を，量子ポイントコンタクト（QPC）を電子の注入電極と収集電極に使い，比較的大きな試料に生じる再現性のある伝導度ゆらぎ（不規則な磁気抵抗）として検証した．」
「QPC では伝導度が量子化伝導度 Gq≡2e^2/h 単位で量子化される．QPC を構成する系が Rashba型スピン軌道相互作用を有していると，QPC の伝導度がちょうど Gq である時，これを通過する電子のスピンは高い偏極度で偏極される．これを注入時の初期状態準備に用いた．」
「また，結晶や構造の乱れから来る散乱により ZB の蛇行を増幅して収集電極での分解能を補強している．以上の道具立ての上で，二次元電子面に平行な磁場の Zeeman 効果によりギャップを変調することで，ZB の振動数を変調したところ，磁場に対して再現性を持つ電気伝導度のゆらぎ（不規則な振動）を観測した．」
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２．Polaron
The electron mass in the vacuum, m = 9.109 x 10^-31 kg, is the shielded or renormalized value via above-mentioned vacuum polarization.
The electron mass in the material is the shielded value. The electron interact with the material particularly when the material has electric dipoles, which is called the electron-lattice interaction.
When the electron-lattice interaction is strong, electron can propagate through the material while changing the atom positions from the equlibrium ones, which is called the polaron.
As a result, the effective mass of an electron in some solid materials can differ from the rest mass of an electron, 9.11×10^−31 kg).
In Cu-based perovskites, the strong electron correlation enhances the electron-lattice coupling.
The crystalline structure, which can be observed as the time spacial average, does not tell the dynamic lattice vibration; however, EXAFS or Atomic Pair Distribution Function (PDF) Analysis can observe it.
EXAFS results show that the axial oxygens' vibration changes at Tc in YBa2Cu307 (YBCO-1237). This may be due to charge density wave (CDW) or due to polaron that means the electron move is slowing down because of the electron-lattice coupling.
Particularly in underdoped Cu-based perovskites, EXAFS shows the dynamic structural change with the slow down of the nuclear spin-lattice relaxation time, T1 that means the spin-gap generation. The T1 slow down may be due to bipolaron.
PDF analysis results shows the ferroelectric-like polarization, although the domain size is 1.0 to 1.5 nm. In addition, the structure changes with temperature; thus, it is not the result of defects.
Electron propagation along the n-type semiconductor surface is influenced by the adsorbed oxygen molecules, particularly when the n-type semiconductor has a polaronic nature, such as a slightly electron-doped (underdoped) SrTiO3. Note that in an heavily electron-doped SrTiO3 the electron-lattice interaction can be shielded.
In the epitaxially grown n-SrTiO3 thin films, the electrical resistance can be influenced by oxygen concentration in helium down to P(O2) = 1 x 10^-20: Effect of Oxygen Adsorption on Polaron Conduction in Nanometer-Scale Nb5+-, Fe3+-, and Cr3+-Doped SrTiO3 Thin Films.
The dopants are Cr3+ (and oxygen vacancy), Fe3+ (and oxygen vacancy), Nb5+; all of the dopants are B-site dopants.
The polaron diameter and the spacial distribution of B-site dopants are comparable, thus, an electron can be weakly bound within the space.
The deposition temperature is 940 degrees Celsius, thus, the lattice constant of the film is a bit larger than that of the single crystal.
The thickness of the conductive film must be nearly the same as the polaron diameter.
３．Polariton
The electromagnetic wave propagating through the material can interact with electric dipoles in the material, e.g., copper (I) oxide in a resonating manner. This is called the polariton.
The electromagnetic wave can interact with dipoles resulting from electron-hole pairs; this is called the exiton-polariton.
The transition from supersonic to superfluid flow has been observed at room temperature in a polariton condensate by using an organic microcavity supporting stable Frenkel exciton-polaritons.
"Polaritons are confined to two dimensions and the reduced dimensionality introduces an additional element of interest for the topological ordering mechanism leading to condensation, as recently evidenced in ref. 21. However, until now, such phenomena have mainly been observed in microcavities embedding quantum wells of III–V or II–VI semiconductors. As a result, experiments must be performed at low temperatures (below ∼20 K), beyond which excitons autoionize. This is a consequence of the low binding energy typical of Wannier–Mott excitons."
"Our sample consists of an optical microcavity composed of two dielectric mirrors surrounding a thin film of 2,7-Bis[9,9-di(4-methylphenyl)-fluoren-2-yl]-9,9-di(4-methylphenyl)fluorene (TDAF) organic molecules. Light–matter interaction in this system is so strong that it leads to the formation of hybrid light–matter modes (polaritons), with a Rabi energy 2ΩR ∼ 0.6 eV. A similar structure has been used previously to demonstrate polariton condensation under high-energy non-resonant excitation."
"Upon resonant excitation, it allows for the injection and flow of polaritons with a well-defined density, polarization and group velocity."
"When the pump power is increased such that the polariton density reaches values close to 10^7 pol μm−2, the shadow cone and the waves upstream vanish almost completely, as expected for a superfluid. This is confirmed by the image in momentum space (Fig. 2f), in which the scattering ring disappears almost fully."
"A Bose–Einstein condensate (BEC) is a state of matter in which extensive collective coherence leads to intriguing macroscopic quantum phenomena."
"In crystalline semiconductor microcavities, bosonic quasiparticles, known as exciton–polaritons, can be created through strong coupling between bound electron–hole pairs and the photon field. Recently, a non-equilibrium BEC and superfluidity have been demonstrated in such structures."
"Here we demonstrate non-equilibrium BEC of exciton–polaritons in a polymer-filled microcavity at room temperature. We observe thermalization of polaritons and, above a critical excitation density, clear evidence of condensation at zero in-plane momentum, namely nonlinear behaviour, blueshifted emission and long-range coherence."
by T. H.
さて、真空偏極（とついでにZitterbewegung）、電子－格子相互作用、電磁場－－電子相互作用と話しをしてきたが、
- 電子は真空中においては真空偏極にシールドされ、
- 動けばそのスピンも真空から影響を受け、
- 物質中では原子核とのクーロン相互作用にシールドされる。
- クーロン相互作用自体が電磁場を介した相互作用だが、電磁場と電子の相互作用は室温BE凝縮が報告されて多少注目を浴びた。
