Momentum conservation in tunneling processes between barrier-separated 2D-electron-gas systems

Abstract

We directly determine the momentum conservation rules for tunneling processes between two independently contacted two-dimensional-electron-gas systems on GaAs-GaAlAs heterostructures. In transverse magnetic fields, the conservation of the canonical momentum results in a new and giant broadening of the subband resonances. As a consequence, the mean values of the wave functions, even for nonoccupied subbands, can be determined directly.PACS numbers: 72.20. My, 73.20.Dx, 73.40.Gk Tunneling processes in transverse magnetic fields became a topic of increased interest in the last few years. In double-barrier heterostructures, it was found that the position of the negative differential resistance is shifted if a magnetic field is applied parallel to the plane of the barriers. 1 Further, the tunneling current is reduced by an increased effective barrier height. 2,3 Magnetoquantized interface states, corresponding to classical skipping orbits, were investigated on both InP-InGaAs (Refs. 4 and 5) and GaAs-AlGaAs (Ref. 6) single-barrier heterostructures. Resonant tunneling into so-called cycloidal interface states is also evident at high magnetic fields. 7 ' 8 At extremely high fields, an anticrossing of the energy levels on both sides of a tunneling barrier occurs, which is apparent as a new series of resonances in the tunneling current. 9 " 11 As an additional feature, the negative differential conductivity region in the current-voltage characteristics of double-barrier structures is washed out. 12 Basic calculations about tunneling in transverse magnetic fields 13 " 16 and hybrid magnetoelectric quantized states 17 ' 18 were also performed, since in narrow-gap semiconductors these states offer interesting possibilities for tunable light sources and far-infrared detectors.In order to investigate the momentum conservation rules, we have studied the tunneling processes between two independently contacted two-dimensional-electrongas systems, separated by a barrier of 200 A. Applying a bias voltage V^ across the barrier, the quantized states on both sides of the barrier are shifted energetically by eVb with respect to each other. All transitions between quantized states are reflected in the tunneling current directly. 19 In transverse magnetic fields, we observe a tremendous splitting of the subband resonances, being more than 1 order of magnitude larger than the cyclotron energy h(o c . This confirms that Landau levels are not involved in this effect.

Mesoscopic effects in tunneling between parallel quantum wires

“…Since the experimental study of tunneling between two separately contacted, parallel, vertically separated two-dimensional (2D) electron systems became possible, 2 electronic structure and interaction effects in low dimensions have been the subject of careful investigation. In the ideal case, conservation of canonical momentum in the plane of the 2D electron systems leads to sharp tunneling resonances; allowing for exploration of electronic subband energies, 3 mapping of the 2D Fermi surface, 4 and life-time measurements of 2D Fermiliquid quasiparticles. 5 Modification of one of the 2D layers into a superlattice of one-dimensional (1D) quantum wires has been employed to measure vertical tunneling between 1D and 2D electron systems.…”

Inhomogeneous broadening of tunneling conductance in double quantum wells

“…New developments came through from studies of interlayer tunneling spectroscopy between parallel two-dimensional electron systems (2DES) using the technique of independent contacts to closely located 2DES. [3,4]. The 2DES are formed in two GaAs quantum wells (QW) separated by a Al x Ga 1−x As barrier.…”

Subband structure of two-dimensional electron gases in SrTiO3

“…[35][36][37] The energy minima of the subbands can be obtained directly, as resonant tunneling requires conservation of the in-plane momentum. 38 SrTiO 3 /GdTiO 3 /SrTiO 3 structures are suitable for such 2D-to-2D tunneling experiments, because a high-density 2DEG with the theoretically expected charge density of 3 Â 10 14 cm À2 forms at each SrTiO 3 /GdTiO 3 interface, 12 and the GdTiO 3 can serve as the tunnel barrier (see Fig. 1).…”

“…Theory also predicts higherlying subbands with d xz,yz character. In 2D resonant tunneling, the energy and in-plane (parallel to the barrier) momentum of the electrons is conserved, 38 Thus, only d xy -to-d xy tunneling should be observed, as the first subband (d xy ) lines up with other subbands with increasing bias. We therefore conclude that at least four of the higher-lying subbands have sufficient d xy character for resonant tunneling to be allowed.…”