Optical observation of superconducting density of states in luminescence spectra of InAs quantum dots

We study luminescence spectra observed from InAs quantum dots (QDs) embedded in an $n$-type InGaAs-based heterostructure, where electron Cooper pairs penetrate from an adjacent niobium (Nb) superconductor with the proximity effect. Below the superconducting (SC) critical temperature of Nb, we observe substantial luminescence intensity enhancement and a sharp edge in luminescence spectra of InAs QDs. We explain the observed sharp edge in the luminescence spectra with the proximity effect, that is, with the consideration of opening of SC gap and modification of density of states (DOS) near the electron Fermi level in the $n$-type semiconductor heterostructure. We demonstrate that the sharp edge luminescence spectra are well reproduced by the SC DOS, with quasiparticle lifetime broadening and a Gaussian distribution of lowest QD state emission lines. We discuss the reason why it has been difficult to observe the sharp edge luminescence spectra in the previous quantum well-based SC light emitting diodes.

Figure 1

(a) Schematic of InAs QD-based heterostructure sample. (b) Schematic band structure after the Nb deposition on the sample surface. The layers (1)–(4) correspond to those shown in (a). Below $T_{\mathrm{C}}$, the SC gap $2\mathrm{\Delta }$ opens in the Nb superconductor, and Cooper pairs penetrate into InAs QDs through the semiconductor heterostructure with the proximity effect. Minority holes are generated with the external He-Ne laser irradiation and transported to InAs QDs. A Cooper pair recombines with a pair of holes and generates a pair of photons.

Figure 2

(a) Temperature dependence of differential resistance measured on the deposited Nb layer. (b) Temperature dependence of InAs-QD luminescence spectra. (c) Temperature dependence of QD luminescence peak intensity. To confirm the relation to $T_{\mathrm{C}}=9.07\mathrm{K}$ of Nb, measured data for the temperature rising and falling sequences are shown.

Figure 3

Luminescence spectra observed at 4 and 10 K with $600\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$ excitation power from another pillar with the diameter of $1.5\mu \mathrm{m}$. Only the measured photon counts are plotted without connecting lines. The alternate long and short dashed line is the guide to the eye, indicating the luminescence intensity sharp edge.

Figure 4

Measured excitation power dependence of QD luminescence spectra. The measured photon counts are connected with neighboring counts with thin lines: (a) 75, 300, and $600\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$; (b) 30 and $150\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$. The solid lines are fitting with the parameters of $E_{\mathrm{F}}=791.0\mathrm{meV}$ and $\mathrm{\Delta }=1.42\mathrm{meV}$.

Figure 5

Broadened SC DOS with $\mathrm{\Gamma }=0.6\mathrm{meV}$ and Gaussian distribution of QD energy states employed for the fitting in Fig. 4 are shown. The Gaussian peak is given by $E_0=E_{\mathrm{F}}+\delta$, where $E_{\mathrm{F}}$ is the Fermi energy and the energy separation $\delta$ from $E_{\mathrm{F}}$ is given as 0.5 meV for the case of $600\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$ photoexcitation. SC DOS without broadening $(\mathrm{\Gamma }=0\mathrm{meV})$ is also shown. $2\mathrm{\Delta }$ is the SC gap.

Figure 6

Excitation power dependence of the Gaussian-function parameters used for fitting the spectra, shown in Fig. 4. (a) The QD PL peak intensity. (b) The QD PL peak energy relative to the electron Fermi energy (given by the energy separation $\delta$) and Gaussian half energy width.

Figure 7

Schematic band diagram of a doped QW. $E_{\mathrm{C}1}$ and $E_{\mathrm{V}1}$ are the lowest subband energies in the conduction and valence band, respectively. ${\mathit{k}}_{\mathrm{t}}$ is the wave vector in the QW plane. The arrow in the downward direction indicates the photon emission with the photon energy of $\hslash \omega$ from the Fermi level to the valence band QW state.

Figure 8

Lifetime-broadening dependence of the fitted luminescence spectra for the one observed with the excitation power of $600\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$.