Overbias Light Emission due to Higher-Order Quantum Noise in a Tunnel Junction

Abstract

Understanding tunneling from an atomically sharp tip to a metallic surface requires to account for interactions on a nanoscopic scale. Inelastic tunneling of electrons generates emission of photons, whose energies intuitively should be limited by the applied bias voltage. However, experiments [Phys. Rev. Lett. 102, 057401 (2009)] indicate that more complex processes involving the interaction of electrons with plasmon polaritons lead to photon emission characterized by over-bias energies. We propose a model of this observation in analogy to the dynamical Coulomb blockade, originally developed for treating the electronic environment in mesoscopic circuits. We explain the experimental finding quantitatively by the correlated tunneling of two electrons interacting with an LRC circuit modeling the local plasmon-polariton mode. To explain the over-bias emission, the non-Gaussian statistics of the tunneling dynamics of the electrons is essential.PACS numbers: 73.23. Hk, 73.20.Mf, 68.37.Ef, 72.70.+m Light emission of electrons tunneling from a scanning tunneling microscope (STM) to a metallic surface has already been studied for many years [1]. The basic mechanism leading to light emission has been identified as the interaction of the tunneling electrons with a localized surface plasmon-polariton (SPP) mode [2]. Considering such a mechanism in a simple picture shows that the emitted light spectrum is limited in frequency by the bias voltage according to ω < eV . This is a simple consequence of the presence of Fermi seas in the electronic leads, which prohibits inelastic tunneling transitions with higher energy exchange due to the Pauli principle. The SPP resonance, which is finally responsible for the photon emission, acts as a frequency filter and hence the measured spectrum is essentially the SPP resonance cut off at a frequency eV / . This picture has been confirmed in numerous experimental [3] and theoretical [4] studies. However, a closer look at some experiments [5][6][7] reveals the unexpected feature that, in addition, light with energy ω > eV is emitted that shows a spectrum which is also reminiscent of the SPP modes. Using energy considerations, such a process can be attributed to two simultaneously tunneling electrons providing enough energy to explain the observation of over-bias emission. However, why the electrons tunnel in a correlated manner remains speculative. A possible explanation is a hot electron distribution created by an effective electron-electron interaction [8,9], which however has been not experimentally tested yet.In this Letter, we will develop an alternative approach based on the idea that on a short time scale multielectron coherent processes appear at a tunnel junction. In a coherent two-electron tunneling process where each electron gives contributes an energy eV an excitation of an overbias plasmon resonance via a virtual state can be created. The SPP mode finally leads to the over-bias light in a standard emission process. Essentially in our model the coupled electron-SPP system h...

Spontaneous Hot-Electron Light Emission from Electron-Fed Optical Antennas

“…23,24 A quantitative agreement with the experiment was obtained using the framework of dynamical Coulomb blockade theory for processes implying the coherent interaction of two electrons. 25 Our results departs from a correlated two-electron process as illustrated in Fig. 3 showing the bias evolution of the largest photon energy hν max emitted by the antenna.…”

Dynamical Coulomb blockade theory of plasmon-mediated light emission from a tunnel junction

“…As pointed out in Ref. [30], comparing the absolute orders of magnitude, the non-Gaussian phase fluctuations are smaller than the dominating Gaussian fluctuations due to the small environmental impedance g c z 1. However, the non-Gaussian rate represents the only one contribution to the total rate in the overbias region | | eV at T = 0.…”

“…Such an overbias spectrum appears as reminiscent of the surface plasmon-polariton (SPP) modes which can be also observed via other methods. Using essentially energy considerations, such a process can be attributed to two simultaneously tunneling electrons providing enough energy to explain the overbias emission 30,31 . Similar findings have also been reported in photon emission from Josephson junctions [32][33][34][35][36][37][38] and molecular films [39][40][41][42] with fluorescent emission of photons with energies above the threshold energy.…”

“…In order to understand these diverse systems, a detailed understanding of the electron tunneling processes involved is necessary 43 . In a previous Letter [30], we developed a theoretical framework for the description of the plasmon-mediated light emission by a tunnel contact based on dynamical Coulomb blockade. In qualitative terms, in an elemental tunneling event, an electron gains energy eV at bias voltage V but must pay a charging cost of E c ∼ e 2 /C with C the junction capacitance.…”

“…[30] to include a finite temperature in the general expression for the tunneling rate. First, we confirm that the nonGaussian voltage fluctuations in the tunnel junction explain the light emission with energy above the bias voltage, ω > eV , in the limit of low temperature.…”