Giant magnetoresistance in the variable-range hopping regime

Abstract

We predict the universal power law dependence of localization length on magnetic field in the strongly localized regime. This effect is due to the orbital quantum interference. Physically, this dependence shows up in an anomalously large negative magnetoresistance in the hopping regime. The reason for the universality is that the problem of the electron tunneling in a random media belongs to the same universality class as directed polymer problem even in the case of wave functions of random sign. We present numerical simulations which prove this conjecture. We discuss the existing experiments that show anomalously large magnetoresistance. We also discuss the role of localized spins in real materials and the spin polarizing effect of magnetic field.

Large magnetoresistance of insulating silicon films with superconducting nanoprecipitates

“…Above the critical temperature the positive MR decreases rapidly and falls below 0.2 % at 10 K. Because hopping is still the dominating transport process in this temperature region one can exclude this mechanism as origin of large MR as supposed in Ref. 12.…”

“…thin amorphous or granular metallic films on insulators, [23][24][25][26] fractal Pb films on silicon, 27 Pb-Si hetorojunctions, 28 amorphous metal-metalloid films, [29][30][31][32][33] cuprate superconductors [34][35][36][37][38] and heavily doped semiconductors. [39][40][41][42][43] There has been an academic debate about the nature of this phase transition and the origin of the large negative MR. 12,[44][45][46] Some theories consider a global quantum phase transition 21,33,47,48 or quantum corrections to the classical magnetotransport. 12,24,49,50 Here we report on large negative and positive MR in Ga-rich, p-type Si films and demonstrate that a simple phenomenological model based on local superconductivity and hopping transport can describe the complex temperature and field dependence of the resistance.…”

“…6,7 Another physical mechanism for large MR effects are magnetic field induced metal-insulator transitions in special transition metal oxides and ferromagnetic semiconductors. 8,9 In such materials the negative MR, which is called "colossal", can exceed 100,000 % at 77 K and fields of 6 T. 10 In manganese-substituted zinc oxide the magnetically induced transition from hopping to band conduction leads to a giant negative MR of more than 200 % at 1.4 K and 12 T. 11 Recently, it has been supposed that under hopping conditions even quantum interferences can cause a giant negative MR. 12 Topological semimetals 13,14 and insulators 15 with complex band structure and high mobility carriers demonstrate anomalous, large positive and negative MR, too. Extremely large positive MRs up to 750,000 % have been obtained in semiconductor structures with extrinsic 16 or intrinsic inhomogeneities.…”

Negative Magneto- and Electroresistance of Silicon Films with Superconducting Nanoprecipitates: The Role of Inelastic Cotunneling

“…There has been a debate whether Cooper pairs survive (bosonic model) or break (fermionic model) in the insulating state [27,28]. Even the origin of the giant negative magnetoresistance observed at low temperatures in such systems is under discussion [9,[31][32][33][34].…”

“…This effect is known as weak localization [7,8]. Recently, it has been supposed that in the hopping transport regime quantum interferences can also lead to strong localization and, therefore, to giant negative magnetoresistance [9]. In addition to interference effects further quantum corrections of the Drude conductivity have to be considered for electronic transport in disordered materials [1,2,10,11].…”