Variable-range hopping conductivity in thin film of the ladder compound [Ca1+δCu2O3]4

Abstract

Low-temperature charge transport in [Ca1+δCu2O3]4 films with δ=0 and 0.08 is investigated at T=1.4–290 K in magnetic fields of B=0–30 T. Between Tv≈20 and 40 K, depending on δ, and Tv′≈2–3 K three-dimensional (3D) Mott variable-range hopping (VRH) conductivity is observed. Deviations from 3D Mott VRH conductivity below Tv′ can be attributed to the onset of the Shklovskii–Efros VRH regime, accompanied by violation of the 3D hopping condition, Rh≪d (where Rh is the mean hopping length and d is the thickness of the film). The density of the localized states (DOS) at the Fermi level, g3(μ)≈4.4×1020 eV−1 cm−3, the values of the localization radius, α≈46 and 34 Å, the concentration of sites involved in hopping charge transfer, N≈9.9×1018 and 9.0×1018 cm−3, the width of the band of localized electron states, 2W≈22 and 20 meV, and the width of the Coulomb gap in the DOS spectrum, 2Δ≈1 and 1.6 meV are obtained for films with δ=0 and 0.08, respectively. These values characterize the films as being near the 3D metal–insulator transition given by the critical concentration NC≈1.3×1019 cm−3.

Mechanisms of charge transfer and electronic properties of Cu2ZnGeS4 from investigations of the high-field magnetotransport

“…Here, a 2 ( T ) ∝ T −1 , a 1 ( T ) ∝ T −3/4 andwhere Δ =  k B ( T 3 T 0 ) 1/4 , B q ≈ 2 2/3 πħ( E A k B T ) 1/2 /( eJ 0 a 2 ) × ( T / T 0 ) 1/4 and J 0 is the prefactor of the overlap integral 68 . Finally, at B  >  B c ′, where B c ′ is defined by the condition of λ 2 ( B c ′) ≈ R h a and R h ≈ γ 4 a ( T 0 / T ) 1/4 is the mean hopping length (where γ 4 ≈ 0.357 is a constant 72 ), the nMR law of Δρ/ρ ∝ B 1/2 has been predicted 69 .…”

Strongly Correlated Properties and Enhanced Thermoelectric Response in Ca3Co4−xMxO9 (M = Fe, Mn, and Cu)

“…Generally, the variation of state density at the Fermi surface with carrier concentration is not strong. Then assuming the density of localized states N (ε F ) to possess a reasonable value of 10 20 cm −3 eV −1 , the plane density of states at the Fermi level (in the CoO 2 layer) can be deduced to be ∼10 13 cm −2 eV −1 . , (The detailed estimation process can be found in refs and , Chapters 1 and 2.) Subsequently, one can estimate the localization length l v ∼ 22 nm and ∼ 29 nm for Fe 0.1 and Mn 0.1, respectively.…”

Electronic structure and transport measurements of amorphous transition-metal oxides: observation of Fermi glass behavior

“…for the range of the localization wave decay lengths, estimated in the literature to be 0.2 nm −1 < α < 1 nm −1 [29,31,[36][37][38]. Consequently, the optimum hopping length, l 0 , and energy, W , can be calculated [29,36,37]:…”