Namangan Institute of Engineering and Technology
nammti.uz
10.25.2023
Pg.226
max
0
1
1
,
,
,
,
,
2
1
(
)
2
k
N
m
s
i
i
N
i
eH
N
Gauss E E T
H
K
Gauss E E T
mc
eH
E
N
mc
(8)
max
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1
(
, , )
(
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1
,
2
1
(
)
2
k
N
m
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s
N
i
f
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f
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eH
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H
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E
mc
E
eH
E
N
mc
(9)
max
0
1
1
,
,
,
,
,
2
1
(
)
2
k
N
m
s
i
i
N
i
eH
N
Lorentz E E T
H
K
Lorentz E E T
mc
eH
E
N
mc
(10)
Using formulas (8) and (10), we consider graphs of the spectral density of states. Figures 1 and
2 show oscillations of the density of states in two-dimensional space for
InAs (
(0)
0.414
g
E
eV
) [5]
at a magnetic field
H=40 kOe (or
B=4 T).
Fig.1. Energy and temperature dependence of
the spectral density of states in InAs calculated
using formula (10).
Fig.2. Energy and temperature dependence of
the spectral density of states in InAs calculated
using formula (8).
These figures show the temperature and energy dependences of the oscillations of the
spectral density
of states for the narrow-gap InAs semiconductor. The graph in Fig. 1 is built
according to the formula (10), and the graph in Fig. 2 is built according to the formula (8). As can be
seen from these figures, at low temperatures (T < 5 K), discrete Landau levels appear sharply. In
addition, the height of discrete Landau levels looks almost the same in the temperature range 1 K <
T < 4 K. When the energy spectrum is calculated by formula (10) (Fig. 1) in the temperature range
50 K < T < 60 K, the Landau levels are not discrete, and in Fig. 2 it is in this temperature range that
oscillations of the spectral density of states can be observed.
Thus, some experimental results for quantum oscillation phenomena can be explained using
the distribution of the Gaussian function.
References:
Namangan Institute of Engineering and Technology
nammti.uz
10.25.2023
Pg.227
1.
Erkaboev, U.I., Rakhimov, R.G. Determination of the dependence of the oscillation of
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2.
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