Gennes-Saint-James resonant transport in Nb/GaAs/AlGaAs heterostructures

Resonant transport is demonstrated in a hybrid superconductorsemiconductor heterostructure junction grown by molecular beam epitaxy on GaAs. This heterostructure realizes the model system introduced by de Gennes and Saint-James in 1963 [P. G. de Gennes and D. Saint-James, Phys. Lett. 4, 151 (1963)]. At low temperatures a single marked resonance peak is shown superimposed to the characteristic Andreev-dominated subgap conductance. The observed magnetotransport properties are successfully analyzed within the random matrix theory of quantum transport, and ballistic effects are included by directly solving the Bogoliubov-de Gennes equations. Typeset using REVTEX a)Electronic mail: [email protected] b)Also with Dipartimento di Fisica, Università di Trieste, I-34127 Trieste, Italy 1 Transport dynamics in mesoscopic devices comprising superconducting electrodes is a subject of increasing interest and rapid development thanks to the progress in nanofabrication techniques and materials science [1]. Transmission of quasi-particles through superconductor-normal metal (SN) interfaces requires conversion between dissipative currents and dissipationless supercurrents and is made possible by a two-particle process known as Andreev reflection (AR) [2]. An electron injected from the normal metal with energy lower than the superconductor gap is reflected as a phase-matched hole, while a Cooper pair is transmitted in the superconductor. Due to its two-particle nature, AR is strongly affected by the transmissivity at the SN interface and much effort has to be devoted to the optimization of this parameter [3–7]. In the presence of scattering centers in the normal region, the phase relationship between incoming and retroreflected particles can give rise to marked coherent-transport phenomena such as reflectionless tunneling [8–11]. One particularly interesting case is that of a single scatterer represented by an insulating barrier (I) inserted in the structure during growth in the normal region. This configuration can give rise to controlled interference effects. Among these, one of the most intriguing is represented by de Gennes-Saint-James resonances [12] in SNIN systems where the N interlayer is characterized by a constant pair potential. The case of a null pair potential is especially relevant to the present case. Multiple reflections off the superconductive gap (i.e. Andreev reflections) and off the insulating barrier (i.e. normal reflections) may give rise to quasi-bound states [12,13] that manifest themselves as conductance resonances. Transport resonances linked to similar multilayer configuration were observed experimentally in all-metal structures [14–16] and provided elegant evidence of quasi-particle coherent dynamics in SN systems. In this Letter we report the experimental observation of de Gennes-Saint-James (dGSJ)type resonances in a microstructure consisting of a Nb/GaAs/AlGaAs/GaAs hybrid heterojunction. This result was made possible by the exploitation of semiconductor epitaxial growth to tailor electronic states according to the original dGSJ model system. We analyzed the data within the random matrix theory of quantum transport and included ballistic effects by directly solving the Bogoliubov-de Gennes equations in a model potential profile. 2 Our description of the system is confirmed by the observed temperature and magnetic-field dependence. A sketch of the Nb/GaAs/AlGaAs structure is shown in Fig. 1(a). The semiconductor portion consists of a 1 μm thick n-GaAs(001) buffer layer Si-doped nominally at n = 2×10 cm grown by molecular beam epitaxy (MBE) on a n-GaAs(001) substrate, followed by a 4 nm thick Al0.3Ga0.7As barrier. This was followed by the growth of a 12 nm thick GaAs(001) epilayer Si-doped at n = 2 × 10 cm and by 14 nm of GaAs doped by a sequence of six Si δ-doped layers spaced by 2 nm. A 1-μm-thick amorphous As cap layer was deposited in the MBE growth chamber to protect the surface during transfer in air to an UHV sputter-deposition/surface analysis system. After thermal desorption of the As protective cap layer, a 100-nm-thick Nb film was then deposited in situ by DC-magnetron sputtering. The thickness of the GaAs epilayer sandwiched between the superconductor and the AlGaAs barrier was selected in order to have an experimentally-accessible single quasi-bound state below the superconductive gap, and the Si δ-doped layers at the Nb/GaAs interface were employed to achieve the required transmissivity. More detail on the contact fabrication procedure is reported elsewhere [11] where the reference SN junctions are also described. The latter consisted of a Nb/δ-doped-GaAs junction without the AlGaAs insulating barrier. A qualitative sketch of the energy-band diagram of our SNIN structure is depicted in Fig. 1(b). 100×160μm junctions were defined by standard photolithographic techniques and reactive ion etching. 4-wire measurements were performed with two leads on the junction under study and the other two connected to the sample back contact. Figure 2 shows the measured differential conductance vs bias (G(V )) for the resonant structure (SNIN structure, panel (a)) and for the reference junction (SN structure, panel (b)) at T = 0.34 K. Comparison of the two characteristics clearly shows the presence of a marked subgap conductance peak in the SNIN, resonant device. As we shall argue this is the first demonstration of dGSJ resonant transport in a hybrid superconductor-semiconductor system. The resonance is superimposed to the typical Andreev-dominated subgap conduc3 tance. The symmetry of conductance and the zero-bias conductance peak (ZBCP) peculiar to reflectionless tunneling (RT) further demonstrate the effectiveness of the fabrication protocol. Quantitative determination of the resonant transport properties in such a system is not trivial as it can be inferred by inspecting Fig. 1(b) and considering the diffusive nature of the normal regions. dGSJ-enhancement, however, is an intrinsically ballistic phenomenon so that its essential features can be captured with relative ease. One study particularly relevant for our system was performed in Ref. [13]. In the context of ballistic transport a one-dimensional SNIN structure was studied as a function of the N interlayer thickness d and it was demonstrated that resonances can occur in the subgap conductance spectrum for suitable geometric conditions. The insulating barrier was simulated by a δ-like potential V(x) = VIδ(x − d). Customarily the barrier strength is described by the dimensionless coefficient Z = VI/h̄vF , where vF is the electron Fermi velocity [17], and in the following we shall make use of it to characterize our system. The key-results of the analysis are: (a) the number of resonances increases for larger thickness d of the metallic interlayer and is virtually independent of Z; (b) the energy-width of such resonances decreases for increasing Z. The one-dimensional differential conductance G(V ) at temperature T can be expressed as [17]