Quantum size phenomena in single-crystalline bismuth nanostructures

Abstract

Size-dependent quantization of energy spectrum of conducting electrons in solids leads to oscillating dependence of electronic properties on corresponding dimension(s). In conventional metals with typical energy Fermi E F~1 eV and the charge carrier's effective masses m* of the order of free electron mass m 0 , the quantum size phenomena provide noticeable impact only at nanometer scales. Here we experimentally demonstrate that in single-crystalline semimetal bismuth nanostructures the electronic conductivity non-monotonously decreases with reduction of the effective diameter. In samples grown along the particular crystallographic orientation the electronic conductivity abruptly increases at scales of about 50 nm due to metal-to-insulator transition mediated by the quantum confinement effect. The experimental findings are in reasonable agreement with theory predictions. The quantum-size phenomena should be taken into consideration to optimize operation of the next generation of ultra-small quantum nanoelectronic circuits.npj Quantum Materials (2017) 2:18 ; doi:10.1038/s41535-017-0017-8 INTRODUCTIONWith reduction of dimension(s) classic physics gradually degenerates into quantum. For example, energy separation between the n-th and the (n+1)-th energy levels of a particle with mass m confined to a space of characteristic dimension a is ΔE(n)~n/ma

Shape resonances and the T c dependence on film thickness of Ni/Bi systems

“…Interestingly, oscillations in the normal state of Bi have been reported in the literature [39,45,[47][48][49]. They were observed in the resistivity and in the magnetoresistance as a function of thickness at low temperature [45,47,49]. They all point to λ F ≈ 40 nm.…”

“…Bi is not a BCS superconductor since the Fermi energy is quite low [17,45], E F ≈ 25.0 meV, yet not the Debye energy [17,46], ℏω D ≈ 12 meV ≈ 140 K. Therefore the ratio between these two energies, ℏω D /E F , is approximately 0.5 while for a BCS superconductor it must hold that ℏω D /E F ≪ 1. Interestingly, oscillations in the normal state of Bi have been reported in the literature [39,45,[47][48][49]. They were observed in the resistivity and in the magnetoresistance as a function of thickness at low temperature [45,47,49].…”

“…For instance for L = 600 nm there are only L/λ F ≈ 15 discrete levels below the Fermi surface. Bi has a low carrier density [45,47,49], that in a thin film is approximately described by n(L) = (0.25 + 27.5/L) × 10 −3 nm −3 , where L (nm) is the thickness of the film [48,51,52]. The most striking feature of Bi is its extremely long mean free path (l) that renders the CSL easily fulfilled in Bi films.…”