Transition conduction types of electrons in cryogenic media

Discussed in the paper are possibilities for description of electron conduction in transitional density range separating electron free and localized states in cryogenic media.

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Date:	2011
Main Authors:	Nazin, S., Shikin, V.
Format:	Article
Language:	English
Published:	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2011
Series:	Физика низких температур
Subjects:	8th International Conference on Cryocrystals and Quantum Crystals
Online Access:	https://nasplib.isofts.kiev.ua/handle/123456789/118560
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Cite this:	Transition conduction types of electrons in cryogenic media / S. Nazin, V. Shikin // Физика низких температур. — 2011. — Т. 37, № 5. — С. 505–508. — Бібліогр.: 33 назв. — англ.

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spelling	nasplib_isofts_kiev_ua-123456789-1185602025-02-09T14:20:53Z Transition conduction types of electrons in cryogenic media Nazin, S. Shikin, V. 8th International Conference on Cryocrystals and Quantum Crystals Discussed in the paper are possibilities for description of electron conduction in transitional density range separating electron free and localized states in cryogenic media. The work was supported by the RFFI grant 09-02-00894a and the Program of the Presidium of Russian academy of sciences ''Quantum physics of condensed matter''. 2011 Article Transition conduction types of electrons in cryogenic media / S. Nazin, V. Shikin // Физика низких температур. — 2011. — Т. 37, № 5. — С. 505–508. — Бібліогр.: 33 назв. — англ. 0132-6414 PACS: 71.10.–w https://nasplib.isofts.kiev.ua/handle/123456789/118560 en Физика низких температур application/pdf Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
topic	8th International Conference on Cryocrystals and Quantum Crystals 8th International Conference on Cryocrystals and Quantum Crystals
spellingShingle	8th International Conference on Cryocrystals and Quantum Crystals 8th International Conference on Cryocrystals and Quantum Crystals Nazin, S. Shikin, V. Transition conduction types of electrons in cryogenic media Физика низких температур
description	Discussed in the paper are possibilities for description of electron conduction in transitional density range separating electron free and localized states in cryogenic media.
format	Article
author	Nazin, S. Shikin, V.
author_facet	Nazin, S. Shikin, V.
author_sort	Nazin, S.
title	Transition conduction types of electrons in cryogenic media
title_short	Transition conduction types of electrons in cryogenic media
title_full	Transition conduction types of electrons in cryogenic media
title_fullStr	Transition conduction types of electrons in cryogenic media
title_full_unstemmed	Transition conduction types of electrons in cryogenic media
title_sort	transition conduction types of electrons in cryogenic media
publisher	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate	2011
topic_facet	8th International Conference on Cryocrystals and Quantum Crystals
url	https://nasplib.isofts.kiev.ua/handle/123456789/118560
citation_txt	Transition conduction types of electrons in cryogenic media / S. Nazin, V. Shikin // Физика низких температур. — 2011. — Т. 37, № 5. — С. 505–508. — Бібліогр.: 33 назв. — англ.
series	Физика низких температур
work_keys_str_mv	AT nazins transitionconductiontypesofelectronsincryogenicmedia AT shikinv transitionconductiontypesofelectronsincryogenicmedia
first_indexed	2025-11-26T19:05:18Z
last_indexed	2025-11-26T19:05:18Z
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fulltext	© S. Nazin and V. Shikin, 2011 Fizika Nizkikh Temperatur, 2011, v. 37, No. 5, p. 505–508 Transition conduction types of electrons in cryogenic media S. Nazin and V. Shikin Institute of Solid State Physics of Russian Academy of Sciences Chernogolovka 142432, Moscow dist., Russia E-mail: shikinv@yandex.ru Received December 1, 2010 Discussed in the paper are possibilities for description of electron conduction in transitional density range se- parating electron free and localized states in cryogenic media. PACS: 71.10.–w Theories and models of many-electron systems. Keywords: mobility, charges, inert gases. 1. One of the most interesting and important problems in condensed matter physics remains the study of electron- related clusters and techniques of their detection. Experi- mentally, the main source of information on these clusters is the effective conductivity effσ of the medium contain- ing artificially injected charged particles. When considering the conduction phenomena, it is con- venient to identify two different domains of external para- meters. In the first one, where rather complex quasipar- ticles (bubbles or charged clusters) have already been formed, their ohmic mobility (and, hence, conductivity) can be calculated with standard methods. However, there exist (and seem to be most interesting) some transition domains where the bare charge energy is substantially changed due to autolocalization or reverse process. In par- ticular, the involved phenomena include: A. Sharp change in electron conductivity of the media with positive scattering length as the gas density gn is varied in the vicinity of the point where electron bubbles start to appear. B. Sharp nonmonotonous variations of this conductivity in media with negative scattering length as the density is changed near the point of electron localization-deloca- lization transition. C. 2D electron transition from free to 2D bubble state as the vapor density gn above the cryogenic liquid surface is changed. D. 2D electron transition from free to 2D dimple state as the magnetic field normal to the surface is monotonous- ly raised. Almost in all the above cases a number of concepts have been developed which provide to some extent description of the observed details in the eff ( )gnσ behavior. For the prob- lems of type A, this means a variety of the general formal- ism of description of electron conduction in systems with spatial disorder (e.g., see Refs. 1–4). Special attention was paid to problem B where the existing analysis, mainly for electrons in argon, was focused on finding out whether the electron mobility is governed by their single-particle colli- sions with gas atoms [5–8] or by collective electron interac- tion with gas density fluctuations [9–13]. The latter view- point proved to be dominating in later studies. Sections C and D consider kinetics of formation of 2D electron bubbles [14,15] and formally very similar problem of 2D electron transition from free to dimple state [16]. The characteristic feature of all indicated studies are manipulations with electron mobility. Their autolocaliza- tion (in our opinion, the most important factor affecting transition domain kinetics) proves to be almost hidden and lacking the status it deserves in transition kinetics. That is one of the reason (the other one is the availability of new results [17] on the mechanism of electron localization in media with negative scattering length) why we have de- cided to address once again the transition phenomena in electron conduction in cryogenic media (judging by avail- able references, the problem first considered in 1970s). The present paper provides a uniform description of transi- tion kinetics where the idea of dominating role played by electron localization in the transition conductivity eff ( )nσ is employed from the outset. Within this approach, eff loc loc free free( ) =gn n nσ μ + μ , (1) loc free = ,en n n+ (2) where en is the total electron density, loc ,μ freeμ are mo- bilities corresponding to localized and free electrons, and S. Nazin and V. Shikin 506 Fizika Nizkikh Temperatur, 2011, v. 37, No. 5 the relative fractions of localized locn and free freen elec- trons are found from the law of mass action [18] which explicitly takes into account the energy difference of free and bound electron states. It should be noted that almost evident equations (1) and (2) have already been mentioned in the literature [19,20]. The only problem is how to relate the fractions locn and freen to energy parameters of the system. The appropriate analysis has not yet been per- formed. 2. The problem with positive scattering length. The formalism on which the scheme (1), (2) should be imple- mented looks rather impressive. For example, following Ref. 1, the theory starts with the general expression for mobility μ in terms of Kubo formula with the Hamiltonian including a δ -shaped repulsion with scattering length 0 > 0a for the interaction between the gas atom and elec- tron. In this formulation, the problem of electron mobility in dense cryogenic medium is finally reduced to the prob- lem of metal–dielectric transition occurring in all studies of mobility in inhomogeneous media. Within the general analysis, it is only possible to prove the existence of this transition. It is this transition that can be associated with the observed rapid variations in ( )gnμ . As to the details, one can only resort to numerical calculations or employ expansion in powers of the gas parameter 3 0 < 1gn a . In the latter case it is possible to show that mobility threshold c gn is shifted with temperature as [2,3] 3/4 .c gn T∝ (3) Authors of Refs. 1–3 also note that the formalism they em- ploy does not involve electron localization. The same problem considered with the autolocalization phenomena taken into account looks much more physically transparent. Starting with the experimentally confirmed [21] statement on the existence of electron injection energy 2 0 0 0 2 = , > 0g a V n a m π (4) where gn is the gas density, m is the free electron mass, 0a is the electron scattering length on the gas atom pos- sessing polarizability ,α the autolocalization scenario re- veals that starting from certain critical density ,c gn it s more favorable for the electron to break the medium conti- nuity and reside in created cavity of radius 0R a which is practically free from gas atoms (this cavity is maintained by electron pressure from inside). The critical point posi- tion estimated (without any adjustable parameters, if the scale of 0a is found from independent experiments, e.g., see Ref. 21) coincides with observed critical drop in the telectron conductivity [22]. This point predictably moves with the temperature [23], 2/3.c gn T∝ (5) The expression for 0V (4) which is linear in gas density is consistent with more refined theory [24,25]. Turning back to Eqs. (1) and (2), we now specify ex- pressions for ocln and reefn . According to the law of mass action [18], loc 0 loc free free ln = , = ( ) > 0, = ,e n T V W n n n n ⎛ ⎞ Δ Δ − +⎜ ⎟ ⎝ ⎠ (6) where W is the autolocalized electron energy. The differ- ence 0( ) > 0V W− is calculated according to [22] or [26,27]. Results of such calculations preformed with spher- ical potential well model are given in Fig. 1. For TΔ one naturally has loc free .n n For electron mobility freeμ the classical Langevin re- sult on electron mobility in gases reads free 1/2 4= . 3 (2 )g e n mT μ σ π (7) Here σ is the electron scattering cross-section at a single atom. When dealing with electron scattering at the fluctua- tions Vδ of the potential (4) 2 02 = ,g a V n m π δ δ (8) one can note that its structure is similar to that of electron- phonon interaction in semiconductors. This analogy yields Fig. 1. Energies: V0 is the energy of free electron in a cryogenic media obtained within the optical approximation [4] with nega- tive scattering length a0 > 0 for helium; W is the energy of auto- localized electron calculated for a spherically symmetric potential well with the following dimensionless parameters: = / ,gn n n max/ ,R R R= 2 0 max= / (16 ),n a Rπ 3 max 0= 6 / .eR a m T Intersec- tion of the curves V0(n) and ( )W n at the point = 23cn cor- responds to usual dimensional density of 21= 2.7 10c gn ⋅ cm–3. W V , 0 80 60 40 20 0 5 10 15 20 25 30 n W V0 Transition conduction types of electrons in cryogenic media Fizika Nizkikh Temperatur, 2011, v. 37, No. 5 507 free 2 1/2 0 = , 8 ( ) p v g c e c n a mT ⎛ ⎞ μ ⎜ ⎟⎜ ⎟ π⎝ ⎠ (9) where /p vc c is the heat capacities ratio. Equations (7) and (9) possess similar structures, and that is why in the prob- lem with positive scattering length transition from one density limit to the other at the critical level is not very prominent. As to the mobility loc ,μ it can be approximated by the simplest Stokes-type formula loc ,eC R μ η (10) where R is the effective cluster radius, η is the cryogenic media density, and C is the a numerical factor which equals 1/ 6π for a solid sphere or 1/ 4π for a bubble of different liquid. Equations (1), (2), (6), (9), and (10) together with the data of Fig. 1 allows to calculate the curve eff ( )gnσ in the transition domain within the framework of the autolocali- zation scenario. This approach to the critical domain is at least not inferior to the metal–dielectric scenario [1–3] in its qualitative content. Actually, it seems to be preferable in the sense of comparing predictions (3), (5) with the ex- periment and it certainly contains the correct (Stokes-type) asymptotic behavior of the conductivity eff ( )gnσ for large helium (neon) densities (the metal–dielectric scenario does not possess these properties). 3. The problem of electron mobility in media with nega- tive scattering length (cryogenic gases starting with argon, and heavier atoms with rising polarizability) was addressed in a large number of papers (e.g., see Refs. 5–13) initially within the approach different from that outlined in the pre- ceding section. Possible role of electron localization (autolo- calization) processes in the transition conductivity in these studies was not considered. The analysis was focused on finding out whether the electron mobility is governed by their single-particle collisions with gas atoms [5–8] or by collective electron interaction with gas density fluctuations [9–13]. That was partly due to the data of Refs. 5 and 9–13 revealing that electron mobility in such media is sufficiently high, at least in typical systematically observed peaks, and only later [28–30] it has became clear that electron autoloca- lization involving formation of density enhancement clusters is unavoidable in media with 0V from (4) and 0 < 0.a The corresponding density singularity develops just in the range of enhanced electron mobility (in the rest of the paper we shall denote the energy defined by Eq. (4) as V− ). This point makes the concept of free electrons in heavy cryogenic media with linear interaction (4) completely unjustifiable. Neverthe- less, the approach of Refs. 5–13 is still sometimes used in the literature (see Ref. 29). The paradox with mobility is resolved simultaneously with the problem of divergency in the self-energy of elec- tron cluster in the case of negative 0a . The situation was found to be mainly controlled by the density range in the vicinity of the point \| = min ( ) / = 0 ,g n nV n n−∂ ∂ (11) and this non-linearity was indeed observed in the behavior of ( )gW n (photoinjection of electrons from metal into cryogenic medium [31–33]). Actually, to develop a non- linear theory of electron clusters we used the simplest ap- proximation of the type 2 202 ( ) = (1 ).g g g a V n n An Bn m− π + + (12) Here the parameters A and B are chosen to correctly re- produce for each gas the minimum minV− position on the density scale gn (i.e., at min=gn n ) and its depth min .V− For electron energy described by Eq. (12) the minimal cluster free energy minFδ is no longer a monotonous func- tion of gn (in contrast to the problem for 0V and W in the case of positive scattering length 0 > 0a , see Fig. 1). Results of calculations of minFδ performed, e.g., for Xe [17] are shown in Fig. 2. In addition to finite values of minFδ in a wide density range (which means that the sin- gularities have been successfully eliminated), one can clearly see a gap where electrons prove to be free. This result dots the i's and crosses the t's in the interpretation of extremely high electron mobility. Thus, the acceptable scenario for calculations of elec- tron conductivity eff ( )gnσ in the media with negative scattering length within the critical density range should necessarily have the structure (1), (2) with the components locn and freen following from Eq. (6) and data of Fig. 2 for minFδ and mobilities locμ (10), freeμ (7). The result (7) should of course be corrected by using Lekner ideas [6–8]. However, in the present case there is no analogy between (7) and (9) since the mobility (9) based on Eq. (8) could hardly be correctly defined in the density range (11). 400 200 0 –200 –400 –600 –800 –1000 � F m in , K n g , 10 cm 21 –3 0 2 4 6 8 10 12 14 16 18 20 Fig. 2. Gain in free energy due to electron localization in Xe as a function of gas atom density for three different temperatures T, K: 150 (---), 200 (⋅⋅⋅), 250 (—). S. Nazin and V. Shikin 508 Fizika Nizkikh Temperatur, 2011, v. 37, No. 5 Resume. Qualitative analysis of the critical conductivity of electron gas in cryogenic media allows to conclude that substantial part of the observed kinetics is governed by formation of autolocalized charged clusters in these do- mains (in the liquid phase these clusters are called cryo- genic ions). This circumstance allows to describe the tran- sition kinetics with Eqs. (1), (2), (6)–(9) using the equilibrium densities of autolocalized and free electrons with their effective mobilities. This approach proves to be useful not only in the cases A and B considered above but also in scenarios C and D which were only briefly men- tioned earlier. The work was supported by the RFFI grant 09-02- 00894a and the Program of the Presidium of Russian acad- emy of sciences ''Quantum physics of condensed matter''. 1. H. Neustadter and M. Coopersmith, Phys. Rev. Lett. 23, 585 (1969). 2. T. Eggarter and M. Cohen, Phys. Rev. Lett. 25, 807 (1970); T. Eggarter and M. Cohen, ibid. 27, 129 (1971). 3. T. Eggarter, Phys. Rev. A5, 2496 (1972). 4. M. Cohen, Can. J. Chem. 55, 1906 (1977). 5. H. Schnyders, S. Rice, and L. Meyer, Phys. Rev. Lett. 15, 187 (1965); H. Schnyders, S. Rice, and L. Meyer, Phys. Rev. 150, 127 (1966). 6. J. Lekner, Phys. Rev. 158, 130 (1967). 7. M. Cohen and J. Lekner, Phys. Rev. 158, 305 (1967). 8. J. Lekner, Phys. Lett. A27, 341 (1968); J. Lekner, Philos. Mag. 18, 1281 (1968). 9. J. Jahnke, L. Meyer, and S. Rice, Phys. Rev. A3, 734 (1971). 10. J. Jahnke, N. 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Transition conduction types of electrons in cryogenic media

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