Tunneling current bistability of correlated 2D electron±hole layers

We study the low-temperature vertical tunneling current (TC) of a system of coupled 2D electron and hole gases (2DEG, 2DHG) of equal density realized in a single-barrier GaAs/AlAs/GaAs p±i±n heterostructure under conditions of forward bias. The density can be tuned by external voltage and the in-plane inter-particle distance can be made comparable to the layer separation (25 nm), the GaAs Bohr radius (12 nm), and the magnetic length for a perpendicular magnetic ®eld Bˆ 10 T. We observe a discontinuous bistability in the I±V characteristic at T 6 300 mK, which has been never observed in n-type structures, and which is strongly enhanced for Bˆ 10 T. Out of the bistability, the current at ®xed external voltage is observed to be exactly periodic in the inverse magnetic ®eld for the high current states (HCS), while the 1/B oscillations of the low current states (LCS) are clearly phase shifted. The transition is found to be discontinuous both in the phase and in the period (i.e. density) in the region of bistability. We interpret the bistability as a phase transition between states of inter-layer correlated exciton-like states (LCS) and the two uncoupled free-carrier 2DEG and 2DHG (HCS) in our bilayer system. Ó 1998 Elsevier Science B.V. All rights reserved. Keywords: Electron±hole correlations; Bistability; Single barrier; Tunneling The interaction between two dimensional (2D) electron±hole layers [1±4] has recently attracted a lot of attention, as a natural extension of the investigation of the 2D electron gas (2DEG). Those systems have the additional degree of freedom of the inter-layer distance which de®nes another length scale leading to many new and still largely unexplored physical phenomena. We realize such a system in a 12 nm thick single barrier p±i±n GaAs/AlAs/GaAs heterostructure under forward bias, in which the vertical current is mainly due to electron tunneling. The sample [1,2] was grown by molecular beam epitaxy on a [3 1 1] substrate and Si was used both as donor and as acceptor in the doping regions, both separated from the barrier by 100 nm thick layers of intrinsic GaAs. It was processed into circular mesas of 50±100 lm diameter to ensure homogeneity and optical access. The results shown here are from a 50 lm measurement, but they were reproduced on the other ones. Under an external voltage V, the potential drop across the structure forces electrons and holes to accumulate at opposite sides of the barrier to form Physica B 256±258 (1998) 531±534 * Corresponding author. Tel.: 31 24 3653052; fax: 31 24 3652440; e-mail: [email protected] 0921-4526/98/$ ± see front matter Ó 1998 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 4 5 2 6 ( 9 8 ) 0 0 4 9 9 2 two 2D gases of equal density, the relative distance of which (de±h) can be estimated by the Fang±Howard approach to be around 25 nm. This length is comparable to the GaAs Bohr radius of 12 nm (the exciton length scale) and the magnetic length lB ˆ 25:66 nm=  B p (where B is the magnetic ®eld in Teslas). The in-plane inter-particle distance de±e ( 1=  n p , where n is the density, determined experimentally as shown below), can be tuned by external bias and made comparable to de±h for n 10 cmÿ2. In this regime, only the ®rst heavy hole subband is populated. The I±V characteristics at Tˆ 70 mK show a discontinuous bistability at voltages corresponding to n  2:5 10 cmÿ2 (Fig. 1(a)). Such a behavior has never been observed in similar devices without a hole layer, suggesting that it is an intrinsic property of our double layer system. The size of the bistability shows an overall increase of one order of magnitude in a quantizing magnetic ®eld, as shown in Fig. 3(b) for Bˆ 10 T, but is also observed to depend strongly on ®lling factor (number of ®lled Landau levels, where we resolve spin-splitting). In particular, the width has a pronounced minimum around integer ®lling factor. In Fig. 1, we can distinguish two types of states corresponding to the two branches of the bistability: the `low current states' (LCS), and the `high current states' (HCS). We further characterize those states by measuring the dependence of the tunneling current (TC) as the magnetic ®eld is swept at ®xed external voltage. This technique, in fact, is commonly used to determine the density in similar single barrier devices [5,6]. In a simpli®ed picture, the TC oscillates periodically in 1/B because of the quantization of the 2D density of states into Landau levels (LLs). The minima occur at integer ®lling factor m, at ®elds given by Bm ˆ nh em ˆ B1 m ; …1† when the Fermi energy EF (the energy of the highest occupied electron states with respect to the quantized level) lies mid-way between LLs [7]. We see in Fig. 2 that also under these conditions a bistability appears in the TC between LCS and HCS when B is swept in both directions. Plotting both curves together we observe part of the oscillatory behavior in the two regimes and we notice that at the same applied voltage, the minimum in the magneto-oscillations is realized at lower ®elds for the LCS (10.5 ‹ 0.1 T) than for the HCS (11.5 ‹ 0.5 T). We assign this change to a discontinuity of periodicity (i.e. density) and phase. As shown in Fig. 3(b), out of the bistability the oscillations of the HCS (Vˆ)1.660 V) are periodic in 1/B (mBm=B1 ˆ 1 within our accuracy, as in Eq. (1)), while the ones of the LCS (Vˆ)1.642 V) satisfy Eq. (1) only when m! mÿ 0:25 (1/B periodicity, with a phase shift of 0.25 ́ 360°ˆ 90° ‹ 15°). This behavior is not particular of the chosen voltage, but rather a general property of the LCS. Fig. 1. Bistability of the Tˆ 70 mK tunneling current at Bˆ 0 (a) and Bˆ 10 T (b). The measured points are represented by ®lled and open circles for the sweep up (decreasing voltage) and sweep down, respectively. The states involved are named high current states (HCS) for the upper branch and low current states (LCS) for the lower one. The width of the loop can be estimated to correspond to 30 leV and 0:7 meV of electron energies, respectively (see text). 532 A. Parlangeli et al. / Physica B 256±258 (1998) 531±534