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Register a new userGiant magnetoresistance in the variable range hopping regime
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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.
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We have studied the AC response of a hopping model in the variable range hopping regime by dynamical Monte Carlo simulations. We find that the conductivity as function of frequency follows a universal scaling law. We also compare the numerical results to various theoretical predictions. Finally, we study the form of the conducting network as function of frequency.
Despite the fact that the problem of interference mechanism of magnetoresistance in semiconductors with hopping conductivity was widely discussed, most of existing studies were focused on the model of spinless electrons. This model can be justified only when all electron spins are frozen. However there is always an admixture of free spins in the semiconductor. This study presents the theory of interference contribution to magnetoresistance that explicitly includes effects of both frozen and free electron spins. We consider the cases of small and large number of scatterers in the hopping event. For the case of large number of scatterers the approach is used that takes into account the dispersion of the scatterer energies. We compare our results with existing experimental data.
We present a theory for tunneling spectroscopy in a break-junction semiconductor device for materials in which the electronic conduction mechanism is hopping transport. Starting from the conventional expression for the hopping current we develop an expression for the break-junction tunnel current for the case in which the tunnel resistance is much larger than the effective single-hop resistances. We argue that percolation like methods are inadequate for this case and discuss in detail the interplay of the relevant scales that control the possibility to extract spectroscopic information from the characteristic of the device.
We study many-body localization (MBL) in a one-dimensional system of spinless fermions with a deterministic aperiodic potential in the presence of long-range interactions or long-range hopping. Based on perturbative arguments there is a common belief that MBL can exist only in systems with short-range interactions and short-range hopping. We analyze effects of power-law interactions and power-law hopping, separately, on a system which has all the single particle states localized in the absence of interactions. Since delocalization is driven by proliferation of resonances in the Fock space, we mapped this model to an effective Anderson model on a complex graph in the Fock space, and calculated the probability distribution of the number of resonances up to third order. Though the most-probable value of the number of resonances diverge for the system with long-range hopping ($t(r) sim t_0/r^alpha$ with $alpha < 2$), there is no enhancement of the number of resonances as the range of power-law interactions increases. This indicates that the long-range hopping delocalizes the many-body localized system but in contrast to this, there is no signature of delocalization in the presence of long-range interactions. We further provide support in favor of this analysis based on dynamics of the system after a quench starting from a charge density wave ordered state, level spacing statistics, return probability, participation ratio and Shannon entropy in the Fock space. We demonstrate that MBL persists in the presence of long-range interactions though long-range hopping with $1<alpha <2$ delocalizes the system partially, with all the states extended for $alpha <1$. Even in a system which has single-particle mobility edges in the non-interacting limit, turning on long-range interactions does not cause delocalization.
We develop a theory of magnetoresistance based on variable-range hopping. An exponentially large, low-field and necessarily positive magnetoresistance effect is predicted in the presence of Hubbard interaction and spin-dynamics under certain conditions. The theory was developed with the recently discovered organic magnetoresistance in mind. To account for the experimental observation that the organic magnetoresistance effect can also be negative, we tentatively amend the theory with a mechanism of bipolaron formation.
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