TY - JOUR
T1 - Gauge invariance of excitonic linear and nonlinear optical response
AU - Taghizadeh, Alireza
AU - Pedersen, Thomas Garm
PY - 2018/5
Y1 - 2018/5
N2 - We study the equivalence of four different approaches to calculate the excitonic linear and nonlinear optical response of multiband semiconductors. These four methods derive from two choices of gauge, i.e., length and velocity gauges, and two ways of computing the current density, i.e., direct evaluation and evaluation via the time-derivative of the polarization density. The linear and quadratic response functions are obtained for all methods by employing a perturbative density-matrix approach within the mean-field approximation. The equivalence of all four methods is shown rigorously, when a correct interaction Hamiltonian is employed for the velocity gauge approaches. The correct interaction is written as a series of commutators containing the unperturbed Hamiltonian and position operators, which becomes equivalent to the conventional velocity gauge interaction in the limit of infinite Coulomb screening and infinitely many bands. As a case study, the theory is applied to hexagonal boron nitride monolayers, and the linear and nonlinear optical response found in different approaches are compared.
AB - We study the equivalence of four different approaches to calculate the excitonic linear and nonlinear optical response of multiband semiconductors. These four methods derive from two choices of gauge, i.e., length and velocity gauges, and two ways of computing the current density, i.e., direct evaluation and evaluation via the time-derivative of the polarization density. The linear and quadratic response functions are obtained for all methods by employing a perturbative density-matrix approach within the mean-field approximation. The equivalence of all four methods is shown rigorously, when a correct interaction Hamiltonian is employed for the velocity gauge approaches. The correct interaction is written as a series of commutators containing the unperturbed Hamiltonian and position operators, which becomes equivalent to the conventional velocity gauge interaction in the limit of infinite Coulomb screening and infinitely many bands. As a case study, the theory is applied to hexagonal boron nitride monolayers, and the linear and nonlinear optical response found in different approaches are compared.
UR - http://www.scopus.com/inward/record.url?scp=85047500808&partnerID=8YFLogxK
U2 - 10.1103/PhysRevB.97.205432
DO - 10.1103/PhysRevB.97.205432
M3 - Journal article
SN - 2469-9950
VL - 97
JO - Physical Review B
JF - Physical Review B
IS - 20
M1 - 205432
ER -