Electronic properties and polaronic dynamics of semi-Dirac system within Ladder approximation

Abstract

We investigate the electronic properties of the semi-Dirac system and its polaronic dynamics when coupled with a fermi bath with quadratic dispersion. The electronic anisotropic transport properties and the semiclassical dynamics of the semi-Dirac system are studied, including the density-of-states, conductivity, transport relaxation rate, specific heat, electrical current denity, and free energy. The attractive polaron formed as the semi-Dirac impurity dressed with the particle-hole excitations in a two-dimensional system are studied both analytically and numerically. The pair propagator, self-energy, spectral function are being detailly calculated and discussed. The method of medium T -matrix approximation (non-self-consistent), which equivalent to the partially dressed interaction vertex by summing over all ladder diagrams, is applied, and compared with some other methods (for many-body problem), like the leading-order 1/N expansion (GW approximation), Hartree-Fock theory, and the Nozieres-Schmitt-Rink theory. Since we foucs on the weak-coupling region, the mean-field approximation is also applicable. The polaron properties is related to the anisotropic effective masses of the semi-Dirac system. That's in contrast to the polarons formed in the surface of normal Dirac systems which has an isotropic dispersion, since the anisotropic dispersion of the semi-Dirac systems results in anisotropic effective mass and anisotropic charge carrier transport. Besides, the symmetry between electron and hole is also broken since the effective masses of the electron and hole are different, which are affected by the polaronic effect when the semi-Dirac material is deposited on a polar substrate, like hBN. The self-localization, short-range potential, and experimental methods as well as the possible formation of the bose polaron on the surface of semi-Dirac system are also discussed in the end. Our results are useful also for the investigation of two/three-dimensional bosonic polaron as well as the polarons in other solid state systems, like the magnetic matter or the topological systems. *

Bipolaron formed through electron-hole excitation

“…ε k is energy of the electron before excitation. There are the four point vertices g ψf in the second line of above formula, which is widely seen in the T-matrix approximation [6][7][8][9][10]. Note that in many-particle generalization, we have the average † † † † † † y y y y y y y y y y y y á ñ = á ñá ñ -á ñá ñ + -+ -+ -+ p q k q k p p q p k q k p q k k q p…”

Bipolaron formed through electron-hole excitation

“…There are the four point vertices in the second line of above formula, which is widely seen in the T -matrix approximation [1,2,3,4,5]. Note that in many-particle generalization, we have the average ψ † p 1 −q ψ † k+q ψ k ψ p = ψ † p 1 −q ψ p ψ † k+q ψ k − ψ † p 1 −q ψ k ψ † k+q ψ p + Π(p 1 , k), where Π(p 1 , k) is the pair propagator.…”