Dependence of energy gap on magnetic field in semiconductor nano-scale quantum rings

Exact solutions of deformed Schrödinger equation with a class of non-central physical potentials

“…Later on, this formalism has been widely used in different fields of physics such as quantum liquids 2 , 3 H e clusters 3 , quantum wells, wires and dots 4,5 , metal clusters 6 , graded alloys and semiconductor heterostructures [7][8][9][10][11][12][13] , the dependence of energy gap on magnetic field in semiconductor nano-scale quantum rings 14 , the solid state problems with the Dirac equation 15 and others [16][17][18][19][20][21] . Recently, it has been applied to study nuclear collective states within Bohr Hamiltonian with Davidson potential and Kratzer potential [22][23][24] .…”

Magneto-optics of layers of semiconductor quantum dots and nano-rings

“…1 (a). Previously we have treated theoretically torus (cut-torus) shaped nano-scale rings in external magnetic fields, using an effective Hamiltonian with position dependent electronic and hole effective masses [4,14]. It was found that experimentally relevant simulations of the behavior of nano-rings can only be obtained with three-dimensional models using the experimentally determined shape, strain and composition of the rings [9].…”

“…Here we calculate electron and hole energies/envelope wave functions, adjacent to the energy gap, for these "eye" shaped dots and rings as a function of a magnetic field in the z-direction. Details of the method of calculation can be found in [4,14]. For frequencies ω close to the energy gap of the nano-objects, the size of the object is small as compared to the wavelength and the dipole approximation can be used.…”

Exact solutions of the position-dependent-effective mass Schrödinger equation

“…The concept of a position-dependent effective mass (PDEM) in the Schrödinger equation has gained much interest [1][2][3][4][5][6][7] in the last two decades, because of its applications in several fields of physics [8][9][10][11][12][13][14] from semiconductors 15,16 to quantum fluids. 17,18 For example, the transport proprieties in semiconductors, 19 the effective interaction in nuclear physics, 20 and the dynamical properties of a neutron superfluid in a neutron star 21 are described by the PDEM Schrödinger equation.…”