Exciton effective mass enhancement in coupled quantum wells in electric and magnetic fields
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| License | CC Attribution 3.0 Unported: You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. | |
| Identifiers | 10.5446/38806 (DOI) | |
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51
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Transcript: English(auto-generated)
00:03
In this paper, we present a calculation of exiton states in semiconductor coupled quantum wells in the presence of electric and magnetic fields applied perpendicular to the quantum well plane. We focus on a particular example of gallium arsenide coupled quantum wells under external bias as shown here.
00:21
Optically excited electron and hole states are confined to the quantum wells. Here we show the wave functions of the first two electron and hole states neglecting any Coulomb interaction. When the Coulomb interaction is introduced, one can find direct exiton states composed of an electron and a hole in the same quantum well.
00:40
There are also indirect exiton states formed from an electron and a hole in adjacent quantum wells. These are the ground state of the system in the presence of the perpendicular electric field. Indirect exitons acquire a static dipole moment and have a lifetime that is orders of magnitude longer than that of direct exitons. They are studied both for the pursuit of fundamental physics and the development of device applications.
01:05
To make a theoretical treatment, we begin with this two-body Hamiltonian. The first two terms are the single particle Hamiltonians of the electron and hole in the heterostructure in both electric and magnetic fields. The third is the Coulomb potential and last is the semiconductor band gap.
01:24
The electron and hole Hamiltonians contain kinetic and potential terms. The potential term includes the quantum well confinement and the potential due to the external electric field. The electron and hole momentum operators each contain the magnetic vector potential A, given here in the symmetric gauge for magnetic field B.
01:44
In the paper we describe a precise numerical solution of the exiton Schrodinger equation by expanding the wave function into the basis of Coulomb uncorrelated electron hole pair states. We model the exiton's internal structure and its dependence on electric and magnetic fields.
02:00
We calculate the transition energy of each state, shown here as a function of electric field with a magnetic field of 10 Tesla. The circle areas are proportional to the oscillator strength or brightness of each state. We find bright direct and dark indirect exiton lines. We also map the electric and magnetic field dependence of the exiton absorption spectrum where we see the Landau fans of direct and indirect exitons.
02:27
For the exiton ground state we calculate a number of properties such as the Bohr radius, dipole moment, radiative lifetime, and binding energy. These are shown here as a function of magnetic field at different electric fields.
02:42
Of particular interest is the crossover of the ground state from an indirect to a direct exiton with increasing magnetic field, and this is characterized by the drop in dipole length. Our main result is the calculation of the exiton effective mass renormalization due to the magnetic field.
03:01
To calculate this effect we introduce the exiton in-plane center of mass momentum, P, as a small parameter. We first solve the Schrodinger equation for P equals zero, the results for which were shown on the previous slides. We then use perturbation theory up to second order to find the correction to the exiton energy for non-zero P.
03:23
The change in energy is proportional to P squared, allowing us to determine the effective mass enhancement due to the magnetic field. This is plotted here for different electric fields. The effective mass has a non-trivial dependence on magnetic field. In the paper we explain this dependence using a simple classical analogy of two
03:43
masses connected by a linear spring that approximates the Coulomb force between the charges. When balancing the Lorentz force and the restoring force, one arrives at a classical approximation of the mass enhancement. This is shown in the inset and closely resembles the full calculation.
04:01
This analogy helps us to describe the non-monotonous dependence of exiton effective mass on magnetic field in terms of the magnetic field induced crossover from an indirect to a direct exiton. This concludes the summary of our findings. Thank you for your interest.
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