Partially coherent electron transport in terahertz quantum cascade lasers based on a Markovian master equation for the density matrix
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We derive a Markovian master equation for the single-electron density matrix, applicable to quantum cascade lasers (QCLs). The equation conserves the positivity of the density matrix, includes off-diagonal elements (coherences) as well as in-plane dynamics, and accounts for electron scattering with phonons and impurities. We use the model to simulate a terahertz-frequency QCL, and compare the results with both experiment and simulation via nonequilibrium Green’s functions (NEGF). We obtain very good agreement with both experiment and NEGF when the QCL is biased for optimal lasing. For the considered device, we show that the magnitude of coherences can be a significant fraction of the diagonal matrix elements, which demonstrates their importance when describing THz QCLs. We show that the in-plane energy distribution can deviate far from a heated Maxwellian distribution, which suggests that the assumption of thermalized subbands in simplified density-matrix models is inadequate. We also show that the current density and subband occupations relax toward their steady-state values on very different time scales.
KeywordsQCL Superlattice Quantum transport Dissipation Density matrix Phonons Terahertz
The authors gratefully acknowledge the support provided by the U.S. Department of Energy, Basic Energy Sciences, Division of Materials Sciences and Engineering, Physical Behavior of Materials Program, Award No. DE-SC0008712. The work was performed using the resources of the UW-Madison Center for High Throughput Computing (CHTC).
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