[Paper Review] Current oscillations in a superlattice under non-quantizing electric and magnetic fields

G. М. Shmelev, É. M. Épshteǐn+1 more|ArXiv.org|May 21, 2009

Theoretical and Computational Physics1 references3 citations

TL;DR

This study investigates current oscillations in a semiconductor superlattice with a parabolic miniband under crossed non-quantizing electric and magnetic fields in Corbino geometry. Using a quasi-classical approach, it derives the current density and shows that the current-voltage curve exhibits oscillations with period proportional to the magnetic field, including regions of negative absolute conductivity and overshoots in Ampere-Gauss characteristics, all of which smear with increasing temperature.

ABSTRACT

We calculate the current density in a semiconductor superlattice with parabolic miniband under crossed non-quantizing electric and magnetic fields. The Corbino disk geometry is considered. The current-voltage curve contains oscillations with period proportional to the magnetic field. The possibility is shown of the negative absolute conductivity. The Ampere-Gauss characteristics also contain overshoots under high enough electric fields. In all cases, the peaks smear with temperature rising.

Motivation & Objective

• To analyze nonlinear magnetotransport in a semiconductor superlattice with a parabolic miniband under crossed non-quantizing electric and magnetic fields.
• To investigate the current-voltage (CVC) and Ampere-Gauss characteristics in Corbino geometry, where the electric field is parallel to the superlattice axis and the magnetic field is perpendicular.
• To determine the conditions under which negative absolute conductivity and current overshoots can emerge in such systems.
• To examine the temperature dependence of oscillatory features in the current response, particularly peak broadening with increasing temperature.

Proposed method

• Formulates the electron energy in the parabolic miniband as a function of in-plane and axial quasi-momenta, with a truncated parabolic dispersion law.
• Applies the equation of motion for electrons under crossed E and B fields, using dimensionless variables to simplify the dynamics.
• Uses the quasi-classical approximation with a constant relaxation time τ and assumes nondegenerate electron gas.
• Applies Chambers' method to compute the current density by integrating over initial momentum distributions with a Maxwell-Boltzmann form.
• Derives analytical expressions for current density at zero temperature using the Heaviside step function and Dirac delta functions to describe periodic current modulations.
• Numerically evaluates the current density at finite temperatures using the equilibrium distribution function with temperature-dependent normalization.

Experimental results

Research questions

• RQ1 How do crossed non-quantizing electric and magnetic fields affect the current-voltage characteristics in a superlattice with a parabolic miniband?
• RQ2 What is the origin and periodicity of current oscillations in the presence of a magnetic field in this system?
• RQ3 Under what conditions does negative absolute conductivity emerge in the current-voltage curve?
• RQ4 How do overshoots in the Ampere-Gauss characteristics arise, and what is their dependence on electric field and magnetic field strength?
• RQ5 How does increasing temperature affect the visibility and structure of current oscillations and peaks?

Key findings

• The current-voltage curve exhibits oscillations with a period of Δ(E) = 2ω in dimensionless units, or Δ(E) = 2πℏ/(ed)ω in dimensional units, proportional to the magnetic field strength.
• Negative absolute conductivity is observed in regions where the current decreases with increasing voltage, particularly at specific magnetic field values and electric field ranges.
• Overshoots appear in the Ampere-Gauss characteristics at electric fields E_N = 2ω(N + 1/2) for N = 0, 1, ..., indicating non-monotonic current response.
• The oscillation peaks smear and diminish with increasing temperature, as shown in numerical simulations at T = 0.1, 0.2, and 0.5 (dimensionless units).
• At T = 1 (dimensionless), corresponding to ~230 K, the peaks are significantly broadened, indicating strong thermal suppression of quantum-like features.
• The analytical solution at zero temperature reveals a multi-N-type current-voltage characteristic with discontinuous jumps and oscillations tied to the sawtooth-like Fourier expansion of the velocity function.