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تسجيل مستخدم جديدSmearing of the 2D Kohn anomaly in a nonquantizing magnetic field: Implications for the interaction effects
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Thermodynamic and transport characteristics of a clean two-dimensional interacting electron gas are shown to be sensitive to the weak perpendicular magnetic field even at temperatures much higher than the cyclotron energy, when the quantum oscillations are completely washed out. We demonstrate this sensitivity for two interaction-related characteristics: electron lifetime and the tunnel density of states. The origin of the sensitivity is traced to the field-induced smearing of the Kohn anomaly; this smearing is the result of curving of the semiclassical electron trajectories in magnetic field.
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We consider a clean two-dimensional interacting electron gas subject to a random perpendicular magnetic field, h({bf r}). The field is nonquantizing, in the sense, that {cal N}_h-a typical flux into the area lambda_{text{tiny F}}^2 in the units of th
e flux quantum (lambda_{text{tiny F}} is the de Broglie wavelength) is small, {cal N}_hll 1. If the spacial scale, xi, of change of h({bf r}) is much larger than lambda_{text{tiny F}}, 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 omega sim omega_0= E_{text{tiny F}}{cal N}_h^{2/3} much smaller than the Fermi energy, E_{text{tiny F}}. It emerges in the third order in the interaction strength; the underlying physics is that a small phase volume sim (omega/E_{text{tiny F}})^{1/2} for scattering processes, involving {em two} electron-hole pairs, is suppressed by curving. Even more surprising effect that we find is that {em disorder-averaged} interaction correction to the density of states, delta u(omega), exhibits {em oscillatory} behavior, periodic in bigl(omega/omega_0bigr)^{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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