Landau quantized dynamics and spectra for group-VI dichalcogenides, including a model quantum wire

Abstract

This work is concerned with the derivation of the Green’s function for Landau-quantized carriers in the Group-VI dichalcogenides. In the spatially homogeneous case, the Green’s function is separated into a Peierls phase factor and a translationally invariant part which is determined in a closed form integral representation involving only elementary functions. The latter is expanded in an eigenfunction series of Laguerre polynomials. These results for the retarded Green’s function are presented in both position and momentum representations, and yet another closed form representation is derived in circular coordinates in terms of the Bessel wave function of the second kind (not to be confused with the Bessel function). The case of a quantum wire is also addressed, representing the quantum wire in terms of a model one-dimensional δ(x)-potential profile. This retarded Green’s function for propagation directly along the wire is determined exactly in terms of the corresponding Green’s function for the system without the δ(x)-potential, and the Landau quantized eigenenergy dispersion relation is examined. The thermodynamic Green’s function for the dichalcogenide carriers in a normal magnetic field is formulated here in terms of its spectral weight, and its solution is presented in a momentum/integral representation involving only elementary functions, which is subsequently expanded in Laguerre eigenfunctions and presented in both momentum and position representations.

Theory of Friedel oscillations in monolayer graphene and group-VI dichalcogenides in a magnetic field

“…where n ≥ 1, u = a l t/ ≃ 0.66 × 10 6 m/s, see Table 1, and E w is defined in Eq. (31). The quantity 1/m * = u 2 /E w is the inverse of the energy effective mass of electron at the bottoms of conduction bands.…”

“…There is N n = 2E n (E n − E w ), where E w and E n are defined in Eqs. (31) and (33), respectively. For n = 0 there is where Ψ(a, c; t) is the second solution of the confluent hypergeometric equation [60], and W κ,µ (t) is the Whittaker function.…”

Temperature Dependence of the Entropy and Magnetic Moment of Landau-Quantized Dichalcogenide Carriers in a Strong Magnetic Field

“…As indicated above, our approach to the determination of the role of a quantizing magnetic field in the entropy of charge carriers of the Group VI Dichalcogenides in the low energy regime (in which their Hamiltonian is "Dirac-like" with energy proportional to momentum) is undertaken using the retarded Green's function; In earlier work 15 , the associated Landau-quantized Green's function matrix was derived with full account of its pseudospin-1/2 and spin-1/2 features in the presence of a high magnetic field; and the pertinent diagonal elements of its retarded Green's function pseudospin matrix…”

“…It is also of interest to describe the thermodynamic Green's function matrix, G( x, x ′ ; T ), which is characterized by periodicity in imaginary time (period τ = −iβ = −i/k B T ′ ) instead of retardation. It may be written in terms of its "greater" (G > ) and "lesser" (G < ) constituents as 12,15…”

Effect of pseudospin polarization on wave packet dynamics in graphene antidot lattices (GALs) in the presence of a normal magnetic field

“…Clearly, the off-diagonal elements interchange with the interchange of Dirac points (K and K ). 22,23 The Green's functions matrix in time representation can be obtained by Fourier transform of Eqs. ( 5), ( 8), (9) as…”