Strong Magnetoresistance Induced by Long-Range Disorder

Abstract

We calculate the semiclassical magnetoresistivity r xx ͑B͒ of noninteracting fermions in two dimensions moving in a weak and smoothly varying random potential or random magnetic field. We demonstrate that in a broad range of magnetic fields the non-Markovian character of the transport leads to a strong positive magnetoresistance. The effect is especially pronounced in the case of a random magnetic field where r xx ͑B͒ becomes parametrically much larger than its B 0 value. 73.50.Jt The magnetoresistance (MR) is one of the most frequently studied characteristics of the two-dimensional electron gas (2DEG). When the effect of disorder is described by a collision integral within the semiclassical Boltzmann equation approach, the resistivity tensorr͑B͒ for an isotropic system has the Drude formwhere n is the carrier density, m the effective mass, v c eB͞mc the cyclotron frequency, and t the transport scattering time. In particular, the longitudinal resistivity r xx is independent of the magnetic field B, r xx ͑B͒ r 0 ϵ m͞e 2 nt, irrespective of the form of the impurity collision integral. This result is solely determined by the Markovian character of the transport assumed in the Boltzmann equation description. Deviations from the constant r xx ͑B͒ are conventionally termed a positive͞negative MR, depending on the sign of the deviation. The negative MR [1] induced by the suppression of the quantum interference correction by the magnetic field is a famous manifestation of weak localization. Another source of negative MR is the Altshuler-Aronov correction to the conductivity due to enhancement of the electron-electron interaction by the diffusive motion of particles [1]. Both these effects are of quantum nature and lead to a correction of order e 2 ͞h to the conductivity s xx , and thus to a small correction to r xx .However, as we will show, already at the classical level there exists a nontrivial MR which can be much stronger than the quantum one, if the correlation length d of disorder is sufficiently large, k F d ¿ 1 (where k F is the Fermi wave vector). This is due to memory effects which are neglected in the collision integral description of disorder.Transport properties of the 2DEG in a smooth random potential (RP) V ͑r͒ are of particular interest, since in currently fabricated high-mobility semiconductor heterostructures the disorder has long-range character. The high mobility of these samples is achieved by placing the charged donor ions in a layer separated by a large distance d (k F d ϳ 10) from the 2DEG plane. Assuming the positions of these impurities to be statistically distributed with a sheet density n i , the correlation function W V ͑r 2 r 0 ͒ ͗V ͑r͒V ͑r 0 ͒͘ is given in momentum space bỹ W V ͑q͒ ͑ph 2 ͞m͒ 2 n i e 22qd .(2)A new type of transport problem occurs in these systems when a large magnetic field B Ӎ B 1͞2 2͑hc͞e͒n is applied such that the lowest Landau level is approximately half filled. The metallic state then observed has been described [2] in terms of composite fermions (CF's) moving in ...

Memory effects in backscattering of two-dimensional electrons in corrugated systems

“…The classical low-field magnetoresistance (MR) in metals and semiconductors has been recently revised, since it was recognized that the conventional Boltzmann-Drude approach fails to describe the electron dynamics in disordered systems [1][2][3]. According to the Boltzmann-Drude model, magnetoresistance must yield no change, in the presence of short range electrostatic potential, which is in disagreement with the facts observed in experiments [4][5][6].…”

2D Electron Gas in Non-Uniform Magnetic Fields

“…For large amplitude random magnetic fields with correlation lengths which are small compared to the electron mean free path (due to electrostatic disorder) the situation is much more interesting. The semiclassical trajectories are "snake orbits" which are guided along lines of zero magnetic field and drifting cyclotron-like or- bits which are guided along contours of constant Bz [3]. These are similar to the trajectories for the periodic case.…”

“…These are similar to the trajectories for the periodic case. The key difference is that these contours are generically closed and the conductance arises from scattering [3].…”

“…The transport properties of a two-dimensional electron gas (2DEG) in the presence of a spatially random magnetic field has attracted great theoretical interest recently [3,28,29], largely due to its relevance for the study of composite fermions [3,28]. When the resistivity is dominated by the disordered electrostatic potential, the random magnetic field can be considered as a perturbation [29][30][31].…”

“…The theory of 2D electrons in non-uniform magnetic fields has an extensive research literature in which a range of new semiclassical and quantum effects are predicted [1][2][3]. Until recently there have been very few experimental studies however.…”