Electron-electron interactions and the electrical resistivity of lithium at low temperatures

Awasthi, O. N.; Pundhir, V. K.

doi:10.1007/s12043-007-0007-7

Cited by 5 publications

(5 citation statements)

References 21 publications

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“…It has been believed that the experimental parameter Aexp would be the same for all samples of the same metal, but the values Aexp are different about ten times. For lithium, it has been expected that values Aexp would be similar to K, but the observed values are more than an order larger [24,35,36].…”

Section: The Study Of the Electrical Resistivity Law At 2 Of Metals A...mentioning

confidence: 99%

New Insight into Electric Force in Metal and the Quadratic Electrical Resistivity Law of Metals at Low Temperatures

Palenskis

2024

Preprint

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: Considering that Einstein's relation between the diffusion coefficient and the drift mobility of the free randomly moving charge carriers in homogeneous materials including metals is always valid, it is shown that the effective electric force acting on free electrons in metal depends on the ratio between the kinetic free electron energy at the Fermi surface to the classical particle energy 3kT/2. The electrical resistivity of elemental metals dependence on very low temperatures has the quadratic term, which has been explained by electron-electron scattering. In this paper, it is shown that the quadratic term of the electrical resistivity at low temperatures is caused by scattering of the free RM electrons by electronic defects due to linear effective free electron scattering cross-section dependence on temperature, but not by electron-electron scattering.

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Section: The Study Of the Electrical Resistivity Law At 2 Of Metals A...mentioning

confidence: 99%

New Insight into Electric Force in Metal and the Quadratic Electrical Resistivity Law of Metals at Low Temperatures

Palenskis

2024

Preprint

View full text Add to dashboard Cite

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“…It has been believed that the experimental parameter A exp would be the same for all samples of the same metal, but the values A exp are different by about 10-fold. For lithium, it was expected that values A exp would be similar to K, but the observed values are more than an order larger [24,35,36].…”

Section: Study Of the Electrical Resistivity Law At 2 Of Metals At Ve...mentioning

confidence: 99%

New Insight into Electric Force in Metal and the Quadratic Electrical Resistivity Law of Metals at Low Temperatures

Palenskis

2024

Metals

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Considering that Einstein’s relation between the diffusion coefficient and the drift mobility of free randomly moving charge carriers in homogeneous materials including metals is always valid, it is shown that the effective electric force acting on free electrons in metal depends on the ratio between the kinetic free electron energy at the Fermi surface to the classical particle energy 3 kT/2. The electrical resistivity of elemental metals dependence on very low temperatures has the quadratic term, which has been explained by electron–electron scattering. In this paper, it is shown that the quadratic term of the electrical resistivity at low temperatures is caused by scattering of the free randomly moving electrons by electronic defects due to linear effective free electron scattering cross-section dependence on temperature, but not by electron–electron scattering.

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“…[16,17,15,18] did not expose why and/or how the physical constant A can or cannot be a numerical constant (independent of any physical mechanisms or processes) unambiguously. Subsequently, Awasthi and Pundhir [19] made use of the procedure given by Ziman [20] to calculate the low temperature resistivity of Li metals with a guessed parameter, known as the the overlap integral, G and after invoking the electron-electron Umklapp scattering. In the calculation made in Ref.…”

Section: Collision Probability and Scattering Rate Formulamentioning

confidence: 99%

“…In the calculation made in Ref. [19], the scattering rate constant, A is due to both normal electron-electron and Umklapp electron-electron scattering processes and these two processes are implicitly assumed to have identical temperature dependence, namely, T 2 . Note this and note this carefully, if A is dependent on any physical processes or physical mechanisms as claimed in Refs.…”

Section: Collision Probability and Scattering Rate Formulamentioning

confidence: 99%

“…Note this and note this carefully, if A is dependent on any physical processes or physical mechanisms as claimed in Refs. [16,17,18,19,20], then writting ρ ∝ AT 2 is physically meaningless because A has got to be T -dependent as well, unless of course, the physical processes or mechanisms themselves (that are responsible for A) are T -independent, which is never the case in T -dependent electrical resistivity.…”

Section: Collision Probability and Scattering Rate Formulamentioning

confidence: 99%

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Low-temperature small-angle electron-electron scattering rate in Fermi metals

Arulsamy

2023

Zeitschrift Für Naturforschung A

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Low-temperature elementary conductivity formula in Fermi metals is reviewed starting from Ohm’s law. This provides the background needed to understand why and how the equations exploited are complicated due to effective mass effect and complex scattering rate even in the presence of small-angle electron-electron scattering at low temperatures. Using the mathematical conditions and physical arguments exploited to derive the Drude conductivity formula, we arrive at our main result—the analytic scattering rate formula at low temperatures that gives rise to the famous T 2 dependence without any ad hoc constants. Our derivation formally proves that the formula, 1 / τ = ( A / ℏ ) ( k B T ) 2 / E F $1/\tau =(A/\hslash ){({k}_{\text{B}}T)}^{2}/{E}_{\text{F}}$ first guessed by Ashcroft and Mermin to be correct where A = N impurity/4π 2 and N impurity is the number of impurities (or scattering centers) present in a given sample. We also highlight the discovery of a new fundamental physical constant, λ Arulsamy = 3 ℏ 2 ( 4 π ϵ 0 ) 2 / m el e 4 ${\lambda }_{\text{Arulsamy}}=\left[3{\hslash }^{2}{(4\pi {{\epsilon}}_{0})}^{2}\right]/\left[{m}_{\text{el}}{e}^{4}\right]$ that associates quantum mechanical energy with that of thermal energy, and is also related to Rydberg constant.

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Electron-electron interactions and the electrical resistivity of lithium at low temperatures

Cited by 5 publications

References 21 publications

New Insight into Electric Force in Metal and the Quadratic Electrical Resistivity Law of Metals at Low Temperatures

New Insight into Electric Force in Metal and the Quadratic Electrical Resistivity Law of Metals at Low Temperatures

New Insight into Electric Force in Metal and the Quadratic Electrical Resistivity Law of Metals at Low Temperatures

Low-temperature small-angle electron-electron scattering rate in Fermi metals

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