We use an electron thermometer to measure the temperature rise of approximately 2 x 10(5) electrons in a two-dimensional box, due to heat flow into the box through a ballistic one-dimensional (1D) constriction. Using a simple model we deduce the thermal conductance kappa(Vg) of the 1D constriction, which we compare to its electrical conductance characteristics; for the first four 1D subbands the heat carried by the electrons passing through the wire is proportional to its electrical conductance G(Vg). In the vicinity of the 0.7 structure this proportionality breaks down, and a plateau at the quantum of thermal conductance pi(2)k(2/B)T/3h is observed.

On a high-mobility 2D electron gas we have observed, in strong magnetic fields (ωcτ > 1), a parabolic negative magnetoresistance caused by electron-electron interactions in the regime of kBT τ / ∼ 1, which is the transition from the diffusive to the ballistic regime. From the temperature dependence of this magnetoresistance the interaction correction to the conductivity δσ Electron-electron interaction (EEI) corrections to the Drude conductivity σ 0 of 2D systems have been intensively studied over two decades. These studies were based on the theory of interactions in the diffusive regime,. Physically this condition implies that the effective interaction time, /k B T , is larger than the momentum relaxation time τ and therefore the two interacting electrons experience scattering by many impurities. In the ballistic regime, k B T τ / > 1, electrons interact when scattered by a single impurity. A theory of the interaction correction for such a case was only recently developed [2], and there have already been several experimental attempts to apply it to the conductance of high-mobility (large τ ) semiconductor structures [3,4,5,6,7,8]. An essential feature of this theory is that the impurities are treated as point-like scatterersthe condition which is not satisfied in structures where the impurities are separated from the 2D channel by an undoped spacer (unless the spacer is thick enough for the background impurities to dominate the scattering). There is then a question of how the interaction correction in the ballistic regime manifests itself in a smooth fluctuation potential.Introducing a long-range scattering potential is expected to suppress the interaction correction in the ballistic regime considered in [2]. This correction is caused by electron back-scattering, but in the case of a smooth potential the backscattering is significantly reduced. However, as shown in [9,10], applying a strong magnetic field increases the probability of an electron to return back and restores the interaction correction.

On a high mobility two-dimensional hole gas (2DHG) in a GaAs/GaAlAs heterostructure we study the interaction correction to the Drude conductivity in the ballistic regime, kBT τ /h > 1. It is shown that the 'metallic' behaviour of the resistivity (dρ/dT > 0) of the low-density 2DHG is caused by hole-hole interaction effect in this regime. We find that the temperature dependence of the conductivity and the parallelfield magnetoresistance are in agreement with this description, and determine the Fermi-liquid interaction constant F σ 0 which controls the sign of dρ/dT .It is well known that electron-electron interaction gives rise to a quantum correction to the classical (Drude) conductivity caused by impurity scattering [1]. Its manifestation can be quite different in the two regimes which relate the quasi-particle interaction time,h/k B T , to momentum relaxation time, τ : diffusive (k B T τ /h < 1), and ballistic (k B T τ /h > 1). So far the interaction correction to the conductivity of two-dimensional (2D) systems has been studied, both theoretically and experimentally, only in the diffusive regime, which is applicable to lowmobility (small τ ) systems [1]. Experimentally, the interaction correction was seen to be negative and produce a logarithmic decrease of the resistivity with increasing temperature, similar to the interference correction due to weak localisation (WL). Theory, however, suggests that the sign of the interaction effect in the diffusive regime can be different, dependent on the value of the interaction constant F σ 0 . Thus the correction can become positive and give rise to a 'metallic' temperature dependenceThe role of interactions in the conductance of 2D systems has now been intensely discussed, after the observation of the'metallic' behaviour in some low-density, highmobility 2D systems [3]. If one attempts to apply the conventional interaction theory, it can be seen that in high mobility structures the diffusion approximation becomes invalid even at low T . Recently, a theory of the interaction correction in the ballistic and intermediate regimes has been developed [4]. Stimulated by this theory, in this work we examine the role of the hole-hole interaction effects in a 2D hole gas (2DHG) which shows a 'metallic' ρ(T ). We analyse the temperature dependence of the conductivity and positive magnetoresistance in parallel field, and show that these two main features of the 'metallic' state can be explained by the interaction effect. It has the same origin as the logarithmic correction studied earlier [1], but now manifests itself in the ballistic regime.The interaction theory [4] considers elastic (coherent) electron scattering on the modulated density of other electrons (Friedel oscillation) caused by an impurity with a short-range potential. The phase of the Friedel oscillation, ∆p ∝ exp(i2k F r), is such that the wave scattered from the impurity interferes constructively with the wave scattered from the oscillation, Fig. 1 (a), leading to the quantum correction to the Drude conductivity σ...

In this paper we examine electron-electron interactions in the intermediate regime T τ ∼ 1. It corresponds to the transition between the conventionally studied diffusive regime 1) and the ballistic regime recently developed in two theories.2, 3) In particular, we study the role of interactions in the 'metallic' behaviour of highmobility 2D systems with dρ/dT > 0: a 2DHG in GaAs/AlGaAs 4) and a 2DEG in vicinal Si. 5) We also investigate the manifestation of electron interactions in a 2DEG in GaAs/AlGaAs, in the conditions of a longrange fluctuational potential. 6)The interaction theory 2) considers coherent electron scattering from the Friedel oscillation caused by an impurity with a short-range potential and gives several predictions. Firstly, the logarithmic correction becomes a linear temperature dependence at k B T τ / > 1:where F σ 0 is the Fermi liquid interaction parameter in the triplet channel. Secondly, parallel magnetic field changes the sign of dρ/dT (the effect seen in recent experiments) by suppressing the correction in the triplet channel. The result is a universal correction δσ = σis the field of the full spin polarisation.The first experiments have been performed on a (311)A GaAs/AlGaAs heterostructure with a peak mobility of 6.5 × 10 5 cm 2 V -1 s -1 , which shows the crossover from 'metal' to 'insulator' at p ∼ 1.5 × 10 10 cm −2 . The hole density p in the 'metallic' region is varied in the range (2.09 − 9.4) × 10 10 cm −2 (the interaction parameter r s = 10 − 17). Fig.1(a) represents the temperature dependence of the resistivity, with the 'metallic' region obtained after subtracting the contribution of phonon scattering (significant only at higher densities). Linear fit of ∆σ(T ) in the region k B T τ / ≥ 1, Fig.1(b), gives the parameter F σ 0 shown in Fig.1(c). Experiments at field B ≥ B S show that the temperature dependence is linear, δσ = ασ B 0 T TF , with the slope α = 0.92 at lower densities close to the expected α = 1. We have also analysed the parallel magnetoresistance in small field in terms of theory 7) which predicts a parabolic positive magneroresistance in the bal- * A.K.Savchenko@ex.ac.ukThe comparison with experiment gives an independently determined value of F σ 0 shown in Fig.1(c). It is essential in theory 2) that the scatterers are pointlike. The fact that impurity scattering in our structure with a spacer of 500Å is dominated by a short-range potential, agrees with earlier findings that in high-mobility structures with large spacers it is the background impurities which determine the mobility. 8)We have also analysed the linear temperature dependence with dρ/dT > 0 observed in 2DEG in vicinal Si MOSFET.5) Fig. 2 shows an example of linear fit of σ(T ) and the value of parameter F σ 0 determined using the relation δσ(T ) = σ 0 1 + 9)The condition of short-range scattering cannot be satisfied in structures where the impurities are separated from the 2D channel by a thin spacer. In this case, a long-range scattering potential will suppress the interaction correction in the ...

We examine the validity of the Fermi-liquid description of the dilute 2D hole gas in the crossover from 'metallic'-to-'insulating' behaviour of ρ(T ). It has been established that, at rs as large as 29, negative magnetoresistance does exist and is well described by weak localisation. The dephasing time extracted from the magnetoresistance is dominated by the T 2 -term due to Landau scattering in the clean limit. The effect of hole-hole interactions, however, is suppressed when compared with the theory for small rs.