Quantum coherence of a narrow-band particle interacting with phonons and static disorder

Qian Niu

Abstract : This work deals with the quantum dynamics of a narrow band particle interacting with phonons and static disorder. The present theory is exact in the limit of small band width compared with the Debye energy, and covers various regimes in the parameter space of temperature and disorder strength. Therefore, the theory provides a unified framework for studying when and how the particle motion changes from coherent band like behavior to incoherent hopping, as the temperature and/or disorder strength are increased. The theory also includes the double well problem as a special case, where rather complete description of the particle motion is obtained.

Kazutaka G. Nakamura, Itsuki Takagi

Yuri I. Dakhnovskii

Yu‐Chen Wang, Yi Zhao

A new diagrammatic quantum Monte Carlo approach is proposed to deal with the imaginary time propagator involving both dynamic disorder (i.e., electron-phonon interactions) and static disorder of local or nonlocal nature in a unified and numerically exact way. The establishment of the whole framework relies on a general reciprocal-space expression and a generalized Wick's theorem for the static disorder. Since the numerical cost is independent of the system size, various physical quantities, such as the thermally averaged coherence, Matsubara one-particle Green's function, and current autocorrelation function, can be efficiently evaluated in the thermodynamic limit (infinite in the system size). The validity and performance of the proposed approach are systematically examined in a broad parameter regime. This approach, combined with proper numerical analytic continuation methods and first-principles calculations, is expected to be a versatile tool toward the calculation of various transport properties, such as mobilities in realistic semiconductors involving multiple electronic energy bands, high-frequency optical and low-frequency acoustic phonons, different forms of dynamic and static disorders, and anisotropy.

B. Krämer

Tommaso Maria Mazzocchi, Daniel Werner, Enrico Arrigoni

We characterize the current-carrying nonequilibrium steady state (NESS) in a single-band Hubbard model confronted with a static electric field in the presence of quenched disorder. Beyond the linear response regime, the electric field amplitude must compensate for at least half of the band gap to have a non-negligible stationary current. As the disorder is not expected to dissipate the extra energy injected by the field, optical phonons assisted by a fermionic heat bath serve as dissipation channels for the current-induced Joule heat generated by the accelerated electrons. The NESS of the system is addressed employing the dynamical mean-field theory using the so-called auxiliary master equation approach as impurity solver. Disorder effects are treated locally via the coherent potential approximation (CPA) and the self-consistent Born (SCB) approach. In the regime in which the two schemes yield similar results, we employ the SCB as it is computationally cheaper than the CPA. We show that, in a purely electronic setup, the disorder-induced dephasing cannot contribute states within the gap but only smear out the edges of the Hubbard bands. When phonons are taken into account, the different nature of disorder-induced dephasing and phonon-related dissipation becomes clear. We show that although both disorder and electron-phonon interaction enhance the current at off-resonant fields, disorder effects play a marginal role since they cannot provide in-gap states which are instead brought about by phonons and represent the privileged relaxation pathway for excited electrons.