Luttinger parameters

The applied voltage renormalizes other terms in the action too (for example, the Luttinger parameter g). Power counting shows that some of them could also give rise to ratchet current contributions of the order of U2V29 lns V, s = const. 

Here are Luttinger parameters, and me is an electron effective mass, av, b, d and ac are Bir-Pikus deformation potentials. As0 is a spin-orbit splitting energy. L and a denote orbital and spin angular momentum operators, respectively. [Lf, LJ is defined as [Lf, LJ = (LjLj + LjLj)/2. The summation of i,j runs through x, y, z. 

Here Ai are inverse mass parameters in WZ structure, corresponding to Luttinger parameters in ZB structure, me11 and me1 are k-dependent electron effective masses. D , aic and a2c are Bir-Pikus deformation potentials. Ai and 3A2,3 correspond to the crystal-field and spin-orbit splitting energies, respectively. The definition of several operators is given as L+ = (U iLy)/V2, a+ = (ax iay)/2,... 

TABLE 2 Luttinger parameters of zincblende GaN and AIN. All values are in units of h2/2mo. 

Table 3.6. Experimentally-determined effective masses (in units of me) at k = 0 extrema and VB Luttinger parameters for some direct-band-gap cubic semiconductors...

The value of Tc calculated form the mean-field theory for three-dimensional (3D) case (Dietl et al. 2000, 2001c) is 18 K for (In,Mn)As with x = 0.03 and the hole density 1 x 102° cm-3, which corresponds to p = 5 x 1013 cm-3 in a 5 nm-thick film. For this calculation the Luttinger-Kohn parameters given in by Wiley (1975), the energy of the exchange interaction between the holes and Mn spins NoP = —0.98 eV (Dietl et al. 

The parameter A here is related to the conventional interaction parameter g of the Luttinger liquid g = 1/A. This relation follows from the definition g = vp/u in terms of the velocity of the collective mode (plasmon) u, and its value u = (7m/m)A in the Calogero-Sutherland model [14, 13]. For the rational values of A and at T = 0 the density-density correlation function is known exactly [14, 13]. Due to the integrability of the model, Ai k,w) 0 only in a finite interval of u> around u> = Uik [15]. We found this interval for k < 27rnj ... 

It is thus desirable to examine the resonant tunneling in a Luttinger liquid in a broad range of temperature down to T = 0 and for various parameters of the barriers. Our purpose in this paper is to analyze transport through a double barrier of arbitrary strength, strong or weak, symmetric or asymmetric, within a general analytical method applicable to all these situations. 

A6.4 Luttinger and Bir-Pikus parameters of GaN and AIN A6.5 Electron and hole effective masses of GaN and AIN A6.6 Deformation potentials of GaN and AIN A6.7 Momentum matrix elements of GaN A6.8 Subband structures of GaN/AlGaN quantum wells A6.9 Optical gain of bulk GaN and GaN/AlGaN quantum wells... 

Renormalization group method can be used to determine the flow of renormalization for (g, gj, g 4) when these act as perturbations for the Luttinger liquid parameters (K, uf) as a function of energy. 

Given the values of the Luttinger liquid parameters, we can now look at the properties of the system using the harmonic part of the Hamiltonian. Thus the... 

These parameters , M and N can be replaced by modified Luttinger constants,... 

New VB parameters 71, 72, and 73 were introduced by Luttinger [60] in his description of holes in the silicon VB. These so-called Luttinger VB parameters, which have been adopted for other semiconductors, are different from the ones in (3.25) as holes were considered instead of electrons ... 

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