Classical and quantum dynamics in a random magnetic field

Izyumov, A. V.; Simons, Benjamin D.

doi:10.1088/0305-4470/32/30/304

Cited by 3 publications

(1 citation statement)

References 32 publications

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“…(4), this applies in the limit of κ → 0), one needs to employ a cutoff at large momentum k (short distance). The need for an ultra-violet regularization is well-known [52][53][54] in the context of the ballistic σ-model and originates from the fact that the gradient (Liouvillean) operator in the logarithm of the initial Lagrangian, Eq. (10), is singular in two dimensions.…”

Section: B Fluctuationsmentioning

confidence: 99%

Influence of long-range disorder on electron motion in two dimensions

Taras-Semchuk

Efetov

2001

Phys. Rev. B

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We consider a two-dimensional electron gas with long range disorder. Assuming that time reversal symmetry is broken either by an external magnetic field or, as in the case of a delta-correlated random magnetic field, by the disorder itself, we derive a supermatrix σ-model. As an intermediate step, we provide a microscopic derivation of the ballistic σ-model, and find that certain corrections to its usual form may become important. We then integrate out degrees of freedom corresponding to short length scales to derive a low-energy supermatrix σ-model. We find an extra term in the free energy that couples to the correlator of local currents. Use of a proper ultraviolet regularisation procedure that preserves gauge invariance indicates that the contribution of the extra term seems finally to become irrelevant. Within the scope of our analyis, we therefore do not find any deviation of the scaling behaviour of the delta-correlated random magnetic field model from that of the conventional unitary ensemble. We then generalize the discussion to include models of even longer-ranged disorder, plus short-range disorder. When the disorder is sufficiently long-ranged that the local currents become delta-correlated, a new term appears in the free energy that does give rise to logarithmic corrections to the conductivity. A renormalisation group analysis of the free energy yields a scaling form for the diffusion coefficient which contains both a positive correction, that represents classical superdiffusion, and a negative correction, which is the usual weak localization correction. The fact that both corrections are of the same order and opposite sign leads to the interesting possibility of a quantum phase transition at weak disorder in two dimensions, tuned by the relative strengths of the short and long range disorder.PACS numbers: 72.15. Rn,73.20Fz, Typeset using REVT E X 1

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Section: B Fluctuationsmentioning

confidence: 99%

Influence of long-range disorder on electron motion in two dimensions

Taras-Semchuk

Efetov

2001

Phys. Rev. B

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Interaction effects in a two-dimensional electron gas in a random magnetic field: Implications for composite fermions and the quantum critical point

Sedrakyan

Raǐkh

2008

Phys. Rev. B

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We consider a clean two-dimensional interacting electron gas subject to a random perpendicular magnetic field, h(r). The field is nonquantizing, in the sense, that N h -a typical flux into the area λ 2 F in the units of the flux quantum (λF is the de Broglie wavelength) is small, N h ≪ 1. If the spacial scale, ξ, of change of h(r) is much larger than λF, the electrons move along semiclassical trajectories. We demonstrate that a weak field-induced curving of the trajectories affects the interaction-induced electron lifetime in a singular fashion: it gives rise to the correction to the lifetime with a very sharp energy dependence. The correction persists within the interval ω ∼ ω0 = EFN 2/3 h much smaller than the Fermi energy, EF. It emerges in the third order in the interaction strength; the underlying physics is that a small phase volume ∼ (ω/EF) 1/2 for scattering processes, involving two electron-hole pairs, is suppressed by curving. Even more surprising effect that we find is that disorder-averaged interaction correction to the density of states, δν(ω), exhibits oscillatory behavior, periodic in`ω/ω0´3 /2 . In our calculations of interaction corrections random field is incorporated via the phases of the Green functions in the coordinate space. We discuss the relevance of the new low-energy scale for realizations of a smooth random field in composite fermions and in disordered phase of spin-fermion model of ferromagnetic quantum criticality.

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Phase diagram of the weak-magnetic-field quantum Hall transition quantified from classical percolation

et al. 2011

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We consider magnetotransport in high-mobility 2D electron gas, σxx ≫ 1, in a non-quantizing magnetic field. We employ a weakly chiral network model to test numerically the prediction of the scaling theory that the transition from an Anderson to a quantum Hall insulator takes place when the Drude value of the non-diagonal conductivity, σxy, is equal to 1/2 (in the units of e 2 /h). The weaker is the magnetic field the harder it is to locate a delocalization transition using quantum simulations. The main idea of the present study is that the position of the transition does not change when a strong local inhomogeneity is introduced. Since the strong inhomogeneity suppresses interference, transport reduces to classical percolation. We show that the corresponding percolation problem is bond percolation over two sublattices coupled to each other by random bonds. Simulation of this percolation allows to access the domain of very weak magnetic fields. Simulation results confirm the criterion σxy = 1/2 for values σxx ∼ 10, where they agree with earlier quantum simulation results. However for larger σxx we find that the transition boundary is described by σxy ∼ σ κ xx with κ ≈ 0.5, i.e., the transition takes place at higher magnetic fields. The strong inhomogeneity limit of magnetotransport in the presence of a random magnetic field, pertinent to composite fermions, corresponds to a different percolation problem. In this limit we find for the delocalization transition boundary σxy ∼ σ 0.6 xx .

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Classical and quantum dynamics in a random magnetic field

Cited by 3 publications

References 32 publications

Influence of long-range disorder on electron motion in two dimensions

Influence of long-range disorder on electron motion in two dimensions

Interaction effects in a two-dimensional electron gas in a random magnetic field: Implications for composite fermions and the quantum critical point

Phase diagram of the weak-magnetic-field quantum Hall transition quantified from classical percolation

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