Interacting Electrons in a Two-Dimensional Disordered Environment: Effect of a Zeeman Magnetic Field

Abstract

The effect of a Zeeman magnetic field coupled to the spin of the electrons on the conducting properties of the disordered Hubbard model is studied. Using the Determinant Quantum Monte Carlo method, the temperature-and magnetic-fielddependent conductivity is calculated, as well as the degree of spin polarization. We find that the Zeeman magnetic field suppresses the metallic behavior present for certain values of interaction-and disorder-strength, and is able to induce a metal-insulator transition at a critical field strength. It is argued that the qualitative features of magnetoconductance in this microscopic model containing both repulsive interactions and disorder are in agreement with experimental findings in two-dimensional electron-and hole-gases in semiconductor structures.A hundred years after the Nobel prize was awarded in 1902 for the discovery of the Zeeman effect and the subsequent explanation by Lorentz, applying a magnetic field continues to be a powerful means to elucidate puzzling phenomena in nature. One of the most recent examples is the interplay of interactions and disorder in electronic systems. This field has witnessed a revival of scientific activity after pioneering experiments in low-density silicon metal-oxide-semiconductor field-effect transistors (MOSFETs) found clear indications of a metal-insulator transition (MIT) in effectively two-dimensional (2D) systems [1]. Until then, electrons in a 2D disordered environment were thought to always form an insulating phase; this mind-set was based on the scaling theory of localization for non-interacting electrons, supplemented by perturbative treatments of weak interactions, as well as studies of the limiting case of very strong interactions. The surprising phenomena were soon confirmed in other semiconductor heterostructures, although the interpretation in terms of a quantum phase transition remains controversial, and a wide variety of experimental and theoretical approaches were unleashed at the problem [2].Among these approaches is the application of magnetic fields. Contrary to the well-known effect of a magnetic field in weak-localization theory to disturb interference phenomena and hence undo localization and insulating behavior, the negative magnetoresistance effect [3], in the Si MOSFETs and similar heterostructures, the magnetic field is found to suppress the metallic behavior and therefore promote insulating behavior [4][5][6]. The effect is present for all orientations of the magnetic field relative to the 2D plane of the electrons. In particular, a Zeeman magnetic field, applied parallel to the 2D plane of electrons and therefore coupling only to the spin, and not the orbital motion of the electrons, has been used extensively. This puts into focus the important role played by the spin degree of freedom of the electron, and its polarization [7][8][9][10].In this Letter, we present a numerical study of a microscopic model for interacting electrons in a disordered environment including the effect of a Zeeman magnetic field. The presen...

Static screening and delocalization effects in the Hubbard-Anderson model

“…This is because for strong interactions, the Mott-Hubbard physics of interaction-suppressed hopping dominates, leading to the formation of two disorder broadened Hubbard bands with a reduced average density of states at the Fermi level and, as a consequence, increasing effectively the disorder strength. In spite of the simplicity of the approach, the results are in good agreement with recent numerical studies, 5,[7][8][9][10]13,14 in the appropriate range of parameters.…”

Determinant quantum Monte Carlo study of the screening of the one-body potential near a metal-insulator transition

“…10 The commonly cited qualitative picture of the appearance of a metallic phase out of a disordered one is that the interactions act to screen the one-body potential. While several quantum Monte Carlo studies of disordered interacting fermions exist, [11][12][13] which demonstrate the possibility of a metallic phase, none have looked quantitatively at this screening in the Hubbard Hamiltonian.…”

Strong-coupling perturbative study of the disordered Hubbard model on the honeycomb lattice

“…But owing to numerical restrictions, the Anderson insulator to metal transition in thermodynamic limit was not concluded as the maximum lattice size of 6 × 8 was not conclusive to establish a metallic state in the thermodynamic limit. Possible metallic phase in between Anderson insulator and Mott insulator has been claimed by other studies based on QMC studies 24,25 in two dimension as well as the results obtained from DMFT in infinite dimension 43 at half-filling. Additionally, the dual-fermion approach in three dimension 44 showed the existence of the metallic phase in weak interaction strengths.…”