Spectroscopy of discrete energy levels in ultrasmall metallic grains

Delft, Jan von; Ralph, D. C.

doi:10.1016/s0370-1573(00)00099-5

Cited by 437 publications

(636 citation statements)

References 168 publications

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“…The amplitude of oscillations of Tc increases with decreasing R and can reach a value of 6 K for nanopartilces with sizes about 25 nm, in a good agreement with experimental studies of YBa2Cu3O 7−δ nanoparticles. After experiments by Ralph et al 1,2 on the electronic states in nanosize Al particles there has been increasing experimental and theoretical interest in properties of ultrasmall superconducting samples with discrete fermionic energy spectrum (see 3,4 and Refs therein). Incorporation of the nanosize particles as a part of single-electron tunneling transistor schemes allowed for measurements of excitation spectra as a function of the number of electrons in a superconducting particle.…”

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confidence: 99%

Superconductivity in mesoscopic high-Tc superconducting particles

Ivanov

Фомин

Devreese

2003

Solid State Communications

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Based on the Hubbard model in the framework of non-phonon kinematical mechanism and taking into account the discreetness of an electronic energy spectrum, the superconducting critical temperature of a mesoscopic high-Tc sphere is analyzed as a function of doping and as a function of a particle's radius. The critical temperature Tc is found to be an oscillating function of the radius of a particle. The size-dependent doping regime is revealed in high-Tc nanoparticles. Our analysis shows that each oscillation in Tc corresponds to the increase of a number of the energy levels in the sphere by one. The amplitude of oscillations of Tc increases with decreasing R and can reach a value of 6 K for nanopartilces with sizes about 25 nm, in a good agreement with experimental studies of YBa2Cu3O 7−δ nanoparticles.

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mentioning

confidence: 99%

Superconductivity in mesoscopic high-Tc superconducting particles

Ivanov

Фомин

Devreese

2003

Solid State Communications

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“…The opposite limit corresponds to the case of a mesoscopic superconducting nanograin in which the notion of the gap is not well-defined (see Ref. [20] for a review). Therefore, the smallest possible size of the puddle with a well defined gap ∆ 0 is ξ min ∼ v F /∆ 0 , which implies that the dimensionless ratio ξ min /l ∼ (T p τ) −1 .…”

Section: Metallic [If ǫ < (T − T P )/T ] Puddlementioning

confidence: 99%

Mesoscopic gap fluctuations in an unconventional superconductor

Galitski

2008

Phys. Rev. B

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We study mesoscopic disorder fluctuations in an anisotropic gap superconductor, which lead to the spatial variations of the local pairing temperature and formation of superconducting islands above the mean-field transition. We derive the probability distribution function of the pairing temperatures and superconducting gaps. It is shown that above the mean-field transition, a disordered BCS superconductor with an unusual pairing symmetry is described by a network of superconducting islands and metallic regions with a strongly suppressed density of states due to superconducting fluctuations. We argue that the phenomena associated with mesoscopic disorder fluctuations may also be relevant to the high-temperature superconductors, in particular, to recent STM experiments, where gap inhomogeneities have been explicitly observed. It is suggested that the gap fluctuations in the pseudogap phase should be directly related to the corresponding fluctuations of the pairing temperature. PACS numbers: 74.40.+k, 74.81.Bd, 74.20.De Understanding the phase diagram and the properties of the high-temperature and other unconventional superconductors has been among the most complex problems of modern condensed matter physics. Most current theoretical approaches to the problem concentrate on strong correlation physics and usually assume that the effects of disorder are unimportant. However, there exist a number of recent experimental works, in particular STM studies of the high-T c cuprates, 1,2,3,4,5,6,7 which provide a tentative indication that at least in some materials disorder plays an important role in the local formation of the superconducting gap. In particular, Gomes et al. 2 have studied the local development of the gap as a function of temperature in Bi 2 Sr 2 CaCu 2 O 8+δ above the superconducting transition and up to a pseudogap temperature, where the gap inhomogeneities cease to exist. An important result of this experiment is that the real-space gap map observed was static and reproducible. This strongly suggests that the inhomogeneous gap formation is unlikely to be a phase-separation or superconducting fluctuation effect, but is due to some kind of disorder in the system.Motivated by these experiments, we theoretically consider a disordered superconductor with an unusual pairing symmetry (e.g., a d-wave superconductor) and study mesoscopic variations of the local pairing temperature. We point out that the existence of the Griffiths-type 8,9,10 phase in the superconducting phase diagram is specific to an anisotropic gap superconductor and should not occur in the conventional swave systems (due to Anderson theorem), unless they are extremely dirty or time-reversal symmetry is broken. 11,12,13 An important observation is that if the pairing gap is anisotropic, the Anderson theorem breaks down and the superconducting pairing temperature, T p , is suppressed by disorder even if time-reversal symmetry is preserved (here and below we make a distinction between the pairing temperature, T p , and the superconducting trans...

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“…(5) explicitly includes the Coulomb energy which forbids states not having N 0 or N 1 electrons, but this is implicit in Eq. (6). The condition N = N 0 or N 1 has therefore to be assumed explicitly when using Eq.…”

Section: Electrostatic Energymentioning

confidence: 99%

“…The general procedure for completing this type of analysis has been outlined previously, for example in Ref. 4,5,6. Our purpose in this paper is to present the solutions of this model for selected simple cases important for analyzing experiments on non-magnetic islands, and we describe several previously-unappreciated consequences of the model that explain recent observations.…”

Section: Introductionmentioning

confidence: 99%

Solving rate equations for electron tunneling via discrete quantum states

2002

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We consider the form of the current-voltage curves generated when tunneling spectroscopy is used to measure the energies of individual electronic energy levels in nanometer-scale systems. We point out that the voltage positions of the tunneling resonances can undergo temperature-dependent shifts, leading to errors in spectroscopic measurements that are proportional to temperature. We do this by solving the set of rate equations that can be used to describe electron tunneling via discrete quantum states, for a number of cases important for comparison to experiments, including (1) when just one spin-degenerate level is accessible for transport, (2) when 2 spin-degenerate levels are accessible, with no variation in electron-electron interactions between eigenstates, and (3) when 2 spin-degenerate levels are accessible, but with variations in electron-electron interactions. We also comment on the general case with an arbitrary number of accessible levels. In each case we analyze the voltage-positions, amplitudes, and widths of the current steps due to the quantum states.

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Spectroscopy of discrete energy levels in ultrasmall metallic grains

Cited by 437 publications

References 168 publications

Superconductivity in mesoscopic high-Tc superconducting particles

Superconductivity in mesoscopic high-Tc superconducting particles

Mesoscopic gap fluctuations in an unconventional superconductor

Solving rate equations for electron tunneling via discrete quantum states

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