Cyclotron effective mass

To illustrate the effect of finite temperatures on the dHvA amplitude further, Fig. 3.1 shows an actual measurement of the dHvA effect in K-(ET)2l3 for different temperatures. This organic superconductor has a simple FS so that for the chosen field and temperature range only one extremal orbit is dominant (see Sect. 4.2.3). With increasing temperature the strong decrease of the oscillating magnetization is clearly seen. From this dependence, the cyclotron effective mass, fj,c, can be extracted either by fitting the relation... 

Table 4.1. Band-structure parameters of a-(ET)22f obtained from dHvA and SdH experiments. A-p is the FS area and Abz denotes the 2D Brillouin zone area which is approximate 40.7nm and only slightly changing for the different compounds Fo is the fundamental oscillation frequency at 6> = 0 mc/me is the cyclotron effective mass extracted from the temperature dependence of the oscillation amplitude gub is obtained from the angular dependence of the spin-splitting zeros...

Determination of the density of states, the Fermi surface and the cyclotron effective mass... 

The interpolation scheme for each band is used to display a perspective view of the Fermi surface and to calculate the extremal (maximum or minimum) cross-sectional area of the Fermi surface. It is also used to calculate a cyclotron effective mass fficb which is defined for a given orbit on the Fermi surface by... 

The experimental cyclotron effective mass m is also usually larger than the theoretical value TWcb defined in eq. (51). Therefore, the enhancement factor for the cyclotron effective mass can be defined in the same way, such as... 

As for an appropriate band theory for the localized 4f-electron system, an attractive approach based on the p-f mixing model was proposed, and was plied to CeSb. A future problem is to refine the approach so as to carry out quantitative calculations in a self-consistent way. The anomalously large enhancement factors for the cyclotron effective masses and the y values observed in the Ce compounds cannot be explained by band structure alone. Quantitative analysis of the mass enhancement factor is a problem challenging to many-body theory. There is still much room for improvement for a complete understanding of the electronic structures of lanthanide compoimds. 

F2 F4 - 2F and F3 F4 - Fi, correspond to the forbidden orbits. From a quantum-mechanical point of view there is no semiclassical closed orbit to explain these frequencies. However, they can be understood in the frame of the quantum interference (QI) model [10] as two-arms Stark interferometers [11]. Within the QI model [10] the temperature damping of the oscillation amplitude is given by the energy derivative of the phase difference ((pi -cpj ) between two different routes i and j of a two-arms interferometer. This model states that 5(cpi - cpj) / de = ( /eB) <3Sk / de, where Sk is the reciprocal space area bounded between two arms. Since 3(difference between the effective masses of the two arms of the interferometer, the associated effective mass is given by m = mj - mj, where nij and mj are the partial effective masses of the routes i and j. In our case an interferometer connected with the frequency F3 consists of two routes, abcdaf and abef and another interferometer, connected with the frequency F2, includes two cyclotron orbits, abcdaf and abebef (see Fig 5). 

According to Falicov and Stahowiak [12] the contribution of every segment of the cyclotron orbit to the cyclotron mass parameter is proportional to the subtended angle of this segment, and the total cyclotron mass parameter equals the sum of the partial cyclotron mass parameters. We have estimated the effective mass parameters from the temperature dependence of the SdH oscillation amplitude using the standard formula... 

It is interesting to compare the temperature dependence of the amplitude for all frequencies (see Fig. 6 for T = 1.5 K and Fig. 7 T = 4.2 K). At 1.5 K the a and (P-a) oscillation amplitudes dominate whereas the (P-2a) amplitude oscillation is very small. However, the (P-2a) amplitude oscillation dominates and the P one disappears completely at 4.2 K. These results are in agreement with the effective mass values corresponding to these oscillation frequencies and satisfy the necessary relations between effective masses for the QI effect. Noting that below 4.2 K the oscillation amplitude connected with the (P-2a) frequency is constant within the experimental error (i.e., a zero cyclotron mass), we may assume that this oscillation can survive to considerably higher temperatures. An analogous situation has been previously found for the (k-BEDT-TTF)2Cu(NCS)2 salt [13],... 

The electron effective mass in GaN is now reasonably well established by cyclotron resonance measurements [14-16] asm, = (0.22 0.0 l)m, and the low frequency dielectric constant (appropriately averaged spatially) e(0) = 9.5 0.2, from infrared refractive index and optic phonon energy measurements [17]. We can therefore derive a reliable value for the hydrogenic donor ionisation energy of EDH = (33.0 1.5) meV which compares well with IR absorption measurements, giving Ed = (35 1) meV [18] (see below). The discrepancy is readily explained in terms of a small chemical shift. 

The on-line interfacing of capillary isoelectric focusing with Fourier-transform ion cyclotron resonance-mass spectrometry (FTICR-MS) was shown to be effective for separating minor components of protein mixtures for on-line mass spectral analysis [62-64],... 

This effective mass, m, describes the movement of an electron under the influence of the periodic potential in the lattice. The value of can be calculated from the band structure of the semiconducting solid, and can also be measured experimentally using cyclotron methods. ... 

A large discrepancy is reported for the values of the effective cyclotron masses of the different orbits. Due to the non Lifshitz-Kosevich behavior of the temperature-dependent dHvA amplitude in [336] only data above 1K were analyzed resulting in effective masses between 2me and 3.5 me- In [334] in the low-field region all data down to the lowest temperature followed the usual behavior and yielded values of 0.66rUe, 0.92 me, and 1.2 me for the a,... 

Some discrepancies concerning the effective cyclotron mass were found. In contrast to the first published result, all later experiments consistently report a value of rric = (3.9 0.1) me for the large orbit at 0 = 0° and fields below 13T (see also Fig. 4.6) [192, 362, 363]. The effective mass for... 

Table 4.2. Experimentally obtained FS parameters of a-Me2Et2N[Ni(dmit)2]2- Fi is the SdH frequency i = a, P, 7, S), ai/BZ is the corresponding area divided by the area of the first Brillouin zone (= 4.47 x 10 cm ) in percent, and rric/rne is the effective cyclotron mass in relative units. For the 6 orbit no effective mass could be extracted. From [380]...

Table 4.3. Experimental and calculated values of dHvA frequencies and effective cyclotron masses in undeuterated (DMe-DCNQI)2Cu. For the e orbits no effective masses have been calculated. From [388]...

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