Magnetic field dependence of conductivity and effective mass of carriers in a model of Mott-Hubbard material
The effect of external magnetic field h on a static conductivity of MottHubbard material which is described by the model with correlated hopping of electrons has been investigated. By means of canonical transformation, the effective Hamiltonian is obtained which takes into account strong intra-s...
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| Zitieren: | Magnetic field dependence of conductivity and effective mass of carriers in a model of Mott-Hubbard material / L. Didukh, O. Kramar, Yu. Skorenkyy, Yu. Dovhopyaty // Condensed Matter Physics. — 2005. — Т. 8, № 4(44). — С. 825–834. — Бібліогр.: 39 назв. — англ. |
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irk-123456789-1210572017-06-14T03:04:38Z Magnetic field dependence of conductivity and effective mass of carriers in a model of Mott-Hubbard material Didukh, L. Kramar, O. Skorenkyy, Yu. Dovhopyaty, Yu. The effect of external magnetic field h on a static conductivity of MottHubbard material which is described by the model with correlated hopping of electrons has been investigated. By means of canonical transformation, the effective Hamiltonian is obtained which takes into account strong intra-site Coulomb repulsion and correlated hopping. Using a variant of generalized Hartree-Fock approximation the single-electron Green function and quasiparticle energy spectrum of the model have been calculated. The static conductivity σ has been calculated as a function of h, electron concentration n and temperature T . The correlated hopping is shown to cause the electron-hole asymmetry of transport properties of narrow band materials В статтi досліджено вплив зовнішнього магнiтного поля на статичну провідність Мотт-Габбардiвського матеріалу в моделi з корельованим переносом електронів. Ефективний гамiльтонiан отримано iз застосуванням канонічного перетворення та з використанням узагальненого наближення Гартрi-Фока знайдено функцію Грiна i енергетичний спектр. Провідність розрахована як функція магнiтного поля, концентрації електронів та температури. 2005 Article Magnetic field dependence of conductivity and effective mass of carriers in a model of Mott-Hubbard material / L. Didukh, O. Kramar, Yu. Skorenkyy, Yu. Dovhopyaty // Condensed Matter Physics. — 2005. — Т. 8, № 4(44). — С. 825–834. — Бібліогр.: 39 назв. — англ. 1607-324X PACS: 72.15.-v, 72.80.Ga DOI:10.5488/CMP.8.4.825 http://dspace.nbuv.gov.ua/handle/123456789/121057 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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| description |
The effect of external magnetic field h on a static conductivity of MottHubbard
material which is described by the model with correlated hopping
of electrons has been investigated. By means of canonical transformation,
the effective Hamiltonian is obtained which takes into account strong
intra-site Coulomb repulsion and correlated hopping. Using a variant of
generalized Hartree-Fock approximation the single-electron Green function
and quasiparticle energy spectrum of the model have been calculated.
The static conductivity σ has been calculated as a function of h, electron
concentration n and temperature T . The correlated hopping is shown to
cause the electron-hole asymmetry of transport properties of narrow band
materials |
| format |
Article |
| author |
Didukh, L. Kramar, O. Skorenkyy, Yu. Dovhopyaty, Yu. |
| spellingShingle |
Didukh, L. Kramar, O. Skorenkyy, Yu. Dovhopyaty, Yu. Magnetic field dependence of conductivity and effective mass of carriers in a model of Mott-Hubbard material Condensed Matter Physics |
| author_facet |
Didukh, L. Kramar, O. Skorenkyy, Yu. Dovhopyaty, Yu. |
| author_sort |
Didukh, L. |
| title |
Magnetic field dependence of conductivity and effective mass of carriers in a model of Mott-Hubbard material |
| title_short |
Magnetic field dependence of conductivity and effective mass of carriers in a model of Mott-Hubbard material |
| title_full |
Magnetic field dependence of conductivity and effective mass of carriers in a model of Mott-Hubbard material |
| title_fullStr |
Magnetic field dependence of conductivity and effective mass of carriers in a model of Mott-Hubbard material |
| title_full_unstemmed |
Magnetic field dependence of conductivity and effective mass of carriers in a model of Mott-Hubbard material |
| title_sort |
magnetic field dependence of conductivity and effective mass of carriers in a model of mott-hubbard material |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2005 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/121057 |
| citation_txt |
Magnetic field dependence of conductivity and effective mass of carriers in a model of Mott-Hubbard material / L. Didukh, O. Kramar, Yu. Skorenkyy, Yu. Dovhopyaty // Condensed Matter Physics. — 2005. — Т. 8, № 4(44). — С. 825–834. — Бібліогр.: 39 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT didukhl magneticfielddependenceofconductivityandeffectivemassofcarriersinamodelofmotthubbardmaterial AT kramaro magneticfielddependenceofconductivityandeffectivemassofcarriersinamodelofmotthubbardmaterial AT skorenkyyyu magneticfielddependenceofconductivityandeffectivemassofcarriersinamodelofmotthubbardmaterial AT dovhopyatyyu magneticfielddependenceofconductivityandeffectivemassofcarriersinamodelofmotthubbardmaterial |
| first_indexed |
2025-07-08T19:07:05Z |
| last_indexed |
2025-07-08T19:07:05Z |
| _version_ |
1837106861439975424 |
| fulltext |
Condensed Matter Physics, 2005, Vol. 8, No. 4(44), pp. 825–834
Magnetic field dependence of
conductivity and effective mass of
carriers in a model of Mott-Hubbard
material
L.Didukh∗, O.Kramar, Yu.Skorenkyy, Yu.Dovhopyaty
Ternopil State Technical University,
Department of Physics,
56 Rus’ka Str., 46001 Ternopil, Ukraine
Received July 22, 2005
The effect of external magnetic field h on a static conductivity of Mott-
Hubbard material which is described by the model with correlated hopping
of electrons has been investigated. By means of canonical transformati-
on, the effective Hamiltonian is obtained which takes into account strong
intra-site Coulomb repulsion and correlated hopping. Using a variant of
generalized Hartree-Fock approximation the single-electron Green functi-
on and quasiparticle energy spectrum of the model have been calculated.
The static conductivity σ has been calculated as a function of h, electron
concentration n and temperature T . The correlated hopping is shown to
cause the electron-hole asymmetry of transport properties of narrow band
materials.
Key words: Mott-Hubbard material, conductivity, magnetic field
PACS: 72.15.-v, 72.80.Ga
The achievements of the recent years in the field of strongly correlated electron
systems enable us to understand the properties of narrow-band materials, in parti-
cular those in which metal-insulator transition under the action of external effects
(pressure, doping, temperature) is realized [1]. The strongly correlated electron sys-
tems demonstrate unusual transport properties [2]. In order to understand the phys-
ical mechanisms, which cause these peculiarities, the experimental and theoretical
research of the temperature dependence of conductivity is needed. The results con-
cerning the low-frequency behavior of conductivity are of prior importance, because
they provide the information about the scattering processes close to the Fermi sur-
face. The theoretical investigations of conductivity σ(ω, T ) are mainly concentrated
∗E-mail: didukh@tu.edu.te.ua
c© L.Didukh, O.Kramar, Yu.Skorenkyy, Yu.Dovhopyaty 825
L.Didukh et. al
on the limit T = 0. The behavior of the static conductivity σ(T ) = σ(ω = 0, T ) at
T > 0 has not been studied well enough.
Theoretical investigations of the optical conductivity in the Hubbard model [3]
within the framework of the Kubo linear response theory [4] have been going on for
many decades. Here we should note the investigations by analytical methods such
as: moment method [5], composite operators method [6], the mean-field theory [7,8],
the perturbative theory method [9,10] in the limit of weak interaction (|t| � U), the
method of the memory function [11,12] in the opposite limit (U � |t|). The conduc-
tivity has been intensively studied in the one-dimensional Hubbard model [13–15],
where the numerical results can be compared with the exact ones obtained by Bethe
ansatz application.
In order to numerically investigate the conductivity in the Hubbard model, the
exact diagonalization of finite clusters has been used [16] for 4 x 4 sites cluster,
quantum Monte-Carlo method for 8, 10 sites [17], 3 x 3 sites [15], 8 x 8 sites [18], 12
x 12 sites [19]. The investigations using numerical methods were mainly carried out
for a two-dimensional lattice (this is caused by the interest to the high-temperature
superconductivity phenomena [20] in the systems with CuO planes). The conduc-
tivity of three-dimensional system has been studied only in a narrow interval close
to half-filling at weak and intermediate interactions [21].
The optical conductivity has also been studied using the dynamical mean field
theory (DMFT) in the limit of infinite spatial dimension [22]. Different DMFT equa-
tions solvers were used: iterated perturbation theory IPT [23], non-crossing approx-
imation NCA [24], second order perturbation theory 2OPT [25]. The authors have
considered the symmetrical Hubbard model at half-filling close to metal-insulator
transition (intra-atomic Coulomb repulsion U ' 2w, where 2w is the bandwidth)
and have obtained a good agreement with experimental data for some Mott-Hubbard
systems. However, for realistic models the non-local (i.e., dependent on wave vec-
tor) contributions to self-energy and transport characteristics are important. Besi-
des, the investigations within the framework of DMFT consider mainly the case of
half-band filling.
In works [26–28] the essential importance of taking into account the correlated
hopping has been emphasized and narrow-band model with non-equivalent Hubbard
subbands has been proposed. In such a model the hopping integrals which describe
the translational movement of holes and doublons differ from one another and from
the activation processes integral. Similar models have been studied intensively in
recent years [29–31]. For the generalized model which takes into account the non-
equivalency of Hubbard subbands, there are no reliable results for conductivity, so
the analytical study of conductivity within the framework of realistic models of
electronic subsystem is necessary.
In this work we show that the application of the variant of projection procedure
for the calculation of the Green function allows us to reproduce some peculiarities
of static conductivity of narrow-band material in the limit of strong Coulomb cor-
relation and to investigate the external effects such as temperature change, doping,
pressure and magnetic field. We apply our approach to the Hamiltonian, which, besi-
826
Magnetic field dependence of conductivity and effective mass of carriers
des the intra-site Coulomb repulsion U , strong in comparison with inter-site hopping
tij, describes the correlated hopping of electrons (the effect of electron concentration
n on the hopping processes) and show that it leads to the electron-hole asymmetry
of conductivity and other characteristics.
We write the Hamiltonian of the correlated electron system in representation of
Xkl
i Hubbard operators:
H = H0 + H1 + H ′
1 + Hex , (1)
where
H0 = −µ
∑
is
(
Xs
i + X2
i
)
+ U
∑
i
X2
i +
1
2
NV0κu2 + µBh
∑
is
ηsX
s
i ,
H1 =
∑
ijs
′
tij(n)Xs0
i X0s
j +
∑
ijs
′
t̃ij(n)X2s
i Xs2
j ,
H ′
1 =
∑
ijs
′ (
t′ij(n)ηsX
s0
i X s̄2
j + h.c.
)
.
Hex = −
1
2
∑
ijs
′
J(ij)
((
Xs
i +X2
i
) (
Xs
j +X2
j
)
+ Xss̄
i X s̄s
j
)
.
Here operator Xkl
i describes the transition of site i from state |l〉 to state |k〉, µ is the
chemical potential, U denotes the energy of intra-site Coulomb repulsion of electrons,
J stands for the direct inter-site exchange interaction, κ is the elastic constant, V0 is
the initial volume of the crystal, N is the number of lattice sites, µB is Bohr magne-
ton, h stands for the external magnetic field, ηs = 1 if s =↑ and −1 otherwise. Trans-
lation processes are characterized by different hopping integrals, namely tij(n) =
(1+αu)(1−τ1n)tij and t̃ij(n) = (1+αu)(1−τ1n−2τ2)tij are hopping parameters for
holes and doublons, respectively; t′ij(n) = (1+αu)(1−τ1n−τ2)tij is parameter of the
hopping of an electron between doublon and hole; correlated hopping parameters τ2
and τ1 describe the effect of the sites involved in the hopping process and neighboring
sites, respectively; parameter α < 0 takes into account the renormalization of band-
width 2w = 2z|tij| at strain u [32], z is the number of the nearest neighbor to a site.
We restrict ourselves to considering the strong correlation limit, namely U �
w(n). In such a system at partial filling of the band the conductance is mainly due
to electron hopping processes within the Hubbard subbands. Thus, the interband
hopping can be neglected. At these conditions we apply the canonical transformati-
on [28] to the Hamiltonian (1).
Heff = eSHe−S, (2)
where
S =
∑
ij
(
L(ij)
(
X↑0
i X↓2
j − X↓0
j X↑2
i
)
− h.c.
)
, (3)
827
L.Didukh et. al
with L(ij) = t′ij(n)/U . The operator S is taken to exclude the processes with pair
hopping of holes and doublons in the first order in the hopping parameter:
H ′
1 + [S; H0] = 0. (4)
Finally, we obtain the effective Hamiltonian:
Heff = H0 + H1 + Hex + H̃ex , (5)
where
H̃ex = −
1
2
∑
ijs
′
J̃(ij)
(
Xs
i X
s̄
j − Xss̄
i X s̄s
j
)
(6)
with the indirect exchange interaction parameter J̃(ij) = (t′ij(n))2/U .
Using the projection procedure [33] for the case of n < 1 we obtain for the single
particle energy spectrum:
Es(k) = −µ − zJns − zJ̃ns̄ + αstk(n) + βs , (7)
where the correlated narrowing of the band and spin-dependent shift of subband
center are
αs =
2 − n + ηsm
2
+
n2 − m2
2(2 − n + ηsm)
, (8)
βs = −
2
(2 − n + ηsm)
∑
k
tk(n)〈X s̄0
i X0s̄
j 〉k , (9)
respectively. The respective results for n > 1:
Ẽs(k) = −µ + U − zJns − zJ̃ns̄ + α̃st̃k(n) + β̃s , (10)
α̃s =
n + ηsm
2
+
n2 − m2
2(n + ηsm)
, (11)
β̃s = −
2
(n + ηsm)
∑
k
t̃k(n)〈Xs2
i X2s
j 〉k , (12)
describe the upper Hubbard subband of halfbandwidth w̃(n) = z|t̃ij(n)|.
Using the method of works [34,35], we calculate the xx-component of static
electronic conductivity σxx = σ + σ̃, where
σ = −
e2τz
2Na
∑
ijs
〈
Xs0
i X0s
j
〉
tij(n), (13)
is the conductivity of lower (0 − s)-subband,
σ̃ = −
e2τz
2Na
∑
ijs
〈X2s
i Xs2
j 〉t̃ij(n), (14)
828
Magnetic field dependence of conductivity and effective mass of carriers
Figure 1. The concentration depen-
dencies of the conductivity at corre-
lated hopping τ1 = τ2 = 0.1 in the
absence of the external magnetic field
and exchange interactions: curve 1 cor-
responds to temperature Θ/w = 0.01,
curve 2 corresponds to Θ/w = 0.1,
curve 3 corresponds to Θ/w = 0.2.
Figure 2. The concentration depen-
dencies of the conductivity in the ex-
ternal magnetic field at Θ/w = 0.02,
zJeff/w = 0.02, τ1 = τ2 = 0: curve 1
corresponds to h/w = 0, curve 2 corre-
sponds to h/w = 0.005, curve 3 corre-
sponds to h/w = 0.02.
is the conductivity of upper (↑↓ −s̄)-subband.
The magnetization can be calculated from the equation
exp
(
2h + β↓ − β↑ + zJeffm
Θ
)
=
sinh
(
w(n)α↓
Θ
1−n
1−n↑
)
sinh
(
w(n)α↑
Θ
1−n
1−n↓
)
sinh
(
w(n)α↑
Θ
n↑
1−n↓
)
sinh
(
w(n)α↓
Θ
n↓
1−n↑
) (15)
for n < 1 and corresponding equation for n > 1 in which the substitutions n → 2−n,
w(n) → w̃(n), αs → α̃s, βs → β̃s are made. Here Jeff = J−J̃ . Using these expressions
we have numerically calculated the static conductivity σxx as a function of electron
concentration (figures 1, 2), temperature (figure 4), and magnetic field (figure 3).
From figure 1 one can see that in the considered model with correlated hop-
ping of electrons, the conductivity provided by the carriers in the upper subband is
lower than the conductivity, provided by carriers in the lower subband. This effect
was discussed in work [35]. This is a manifestation of the electron-hole asymme-
try inherent to real transition metal compounds. Another important feature is the
change of the current carrier type from metallic to semiconducting type in the vici-
nity of n = 2/3, 4/3 and from semiconducting type to the metallic one at n = 1.
Increasing the correlated hopping we shift the maxima of the conductivity closer to
the half-filling. The external magnetic field qualitatively changes the concentration
dependence of σ (see figure 2).
829
L.Didukh et. al
Figure 3. The dependencies of the
conductivity on magnetic field for the
electron concentration n = 0.3 and
zJeff/w = 0.01, τ1 = τ2 = 0: solid curve
corresponds to Θ/w = 0.02, dashed
curve – to Θ/w = 0.04, dashed-dotted
curve – to Θ/w = 0.06.
Figure 4. The dependencies of the con-
ductivity on temperature in the ex-
ternal magnetic field h/w = 0.01 at
zJeff/w = 0 and τ1 = τ2 = 0: curve
1 corresponds to n = 0.3, curve 2 – to
n = 0.35, curve 3 – to n = 0.45.
Figure 5. The dependence of current car-
riers effective mass meff/m0 on electron
concentration: upper curves correspond to
τ1 = τ2 = 0.3; middle curves – to τ1 =
τ2 = 0.2; lower curves – to τ1 = τ2 = 0.
The higher is the electron concentra-
tion, the less pronounced is the effect
of the applied magnetic field. At small
concentration of electrons the band is
fully polarized. In such a ferromag-
netic system the conductivity is con-
siderably lower than in paramagnetic
state. If the electron concentration in-
creases, the decrease of magnetization
leads to the increase of conductivity,
σ approaches its value in the param-
agnetic state. At the same time, due
to the changes in the correlation band
narrowing factor and the shift of sub-
band center, the position of conduc-
tivity maximum changes from n = 2/3
in the saturated ferromagnetic state
(figure 2, 2) to n = 0.5 in the ferromag-
netic state (figure 2, 3). The change of
conductivity with the increase of the applied field can be very sharp at low temper-
ature, (figure 3, solid curve). The increase of temperature leads to the decrease of σ
830
Magnetic field dependence of conductivity and effective mass of carriers
Figure 6. The dependence of current
carriers effective mass meff/m0 on the
magnetization at n = 0.2, Θ/w = 0.02,
zJeff/w = 0: solid curves correspond to
τ1 = τ2 = 0; dashed curves – to τ1 =
τ2 = 0.1.
Figure 7. The dependence of current
carriers effective mass meff/m0 on the
applied magnetic field: solid curves cor-
respond to zJeff/w = 0, Θ/w = 0.02;
dotted curves – to zJeff/w = 0, Θ/w =
0.05; dash-dotted curves – to zJeff/w =
0.05, Θ/w = 0.02.
and its changes become more smooth. Plateau of σ(h) dependence signifies that at
low temperatures a fully polarized state is reached in a very low field. Much higher
field is needed to polarize spins at higher temperatures (figure 3, long-dashed and
short-dashed curves).
Sharp increase of σ with the increase of temperature is related to the transiti-
on from the polarized ferromagnetic state to the paramagnetic one. In each state
the conductivity decreases with the rise of temperature. Very small changes of elec-
tron concentration can greatly affect the temperature dependence of conductivity
(see figure 4).
Within the framework of the considered model one can naturally introduce the
notions of “wide” (lower) and “narrow” (upper) energy bands and, correspondingly,
“light” and “heavy” current carriers with the effective masses
m∗
s =
(
∂2Es(k)
∂k2
)−1
, m̃∗
s =
(
∂2Ẽs(k)
∂k2
)−1
, (16)
where Es(k) is the energy spectrum of current carriers in the lower (s − 0) band,
Ẽs(k) is the energy spectrum of current carriers in the upper (s̄− ↑↓) subband.
We have found that the effective mass of heavy carriers can increase substantially
with the increase of electron concentration. Due to the correlated hopping, the heavy
carriers can be realized in the lower (s−0) subband as well. It is worthwhile to note
that the notion “effective mass of current carrier” has a conditional sense, different
from the standard one, used in the band theory. The definitions (16) are related to
the expressions for band spectrum which describe the transitions between |s〉- and
831
L.Didukh et. al
|0〉-states as well as | ↑↓〉- and |s̄〉-states. In the paramagnetic state m∗ and m̃∗ are
effective masses of respective transitions; for the cases when subbands are almost
empty or almost full, m∗ and m̃∗ can be interpreted as effective masses of electronic
and hole states. For the case n � 1 the value m∗
1 = ~(2a2|t(n)|)
−1
' ~(2a2|t|)
−1
can
be identified as an effective mass of |s〉-states, i.e. electrons, for the case n = 1 − ε
(ε � 1) the value m∗
2 = ~(2a2|t(n)|)
−1
|n=1 is an effective mass of a hole. If n > 1,
then for n = 1 + ε we have translational motion of doublons (“extra electrons”)
with masses m̃∗
1 = ~(2a2|t̃(n)|)
−1
|n=1, and for n = 2 − ε we have the effective mass
of holes m̃∗
2 = ~(2a2|t̃(n)|)
−1
|n=2. From these results one can see that the effective
mass of carrier in the upper band can substantially differ from the effective masses
in the case when the conductivity is due to s− 0-transitions. It is important to note
that passing from the regime of conductivity provided by the carriers in the lower
band to the regime when it is provided by s̄− ↑↓-transitions, the effective mass
increases stepwise at the point n = 1 (the effective mass dependence on the electron
concentration is shown in figure 5).
The effective mass dependencies on the magnetization and external magnetic fi-
eld are shown in figures 6 and 7, respectively. The rise of magnetization leads to the
rise of difference in the effective masses of spin-up and spin-down current carriers
(figure 6). The slope of the dependencies meff(m) changes with the rise of m as well.
This leads to the decrease of overall transport in ferromagnetic state, though the
effective mass of carriers with majority spin becomes lower. The results shown in fig-
ure 6 qualitatively agree with the corresponding plot of work [36], where Gutzwiller
approximation has been used to calculate effective masses of current carriers. The
correlated hopping, favoring localization, shifts the effective masses up. Different
possible scenarios of meff(h) dependence are shown in figure 7. At high temperature
meff changes monotonously (figure 7, dotted curve) while at low temperature the sys-
tem in unstable towards the transition to polarized state (figure 7, solid curve). The
direct exchange interaction can stabilize the ferromagnetically polarized state in the
less than half-filled band even in a weak magnetic field (figure 7, dash-dotted curve).
In this paper we have used a model with correlated hopping of electrons to study
the effect of the external magnetic field, temperature and doping on a static con-
ductivity of Mott-Hubbard material. In the regime of strong Coulomb interaction
hybridization of the Hubbard subbands does not contribute essentially to the trans-
port properties, so we have excluded it from the effective Hamiltonian by means
of canonical transformation. The single-electron Green function and quasiparticle
energy spectrum of the model have been calculated using a variant of generalized
Hartree-Fock approximation. This procedure has allowed us to obtain an analyti-
cal expression for the band narrowing factor and relatively simple and transparent
equations for calculation of spin-dependent shift of the band center, magnetization,
static conductivity and effective mass of the current carrier. The results of our study
generalize the results of works [6,16], where the static conductivity of the Hubbard
model has been calculated as a function of electron concentration n, for a wider
class of systems, for which the correlated hopping should be taken into account. In
the limiting case of the absence of correlated hopping our results agree with the
832
Magnetic field dependence of conductivity and effective mass of carriers
concentrational dependencies obtained in the composite operator method [6], exact
diagonalization [16] and Monte-Carlo simulations [18]. The temperature dependence
of conductivity in paramagnetic state, calculated in this work, agrees with the cor-
responding results of DMFT [24,37]. In the magnetic field, the static conductivity
reflects the changes of single electron energy spectrum through correlation narrowing
of the band and the shift of subband center. The temperature and concentration de-
pendencies of σ are governed by the changes of system magnetization in the external
magnetic field. We have found that in the ground state the saturated ferromagnetic
phase is stable while at non-zero temperature, the magnetization has the concen-
tration dependence which agrees with work [38]. Such a behavior of magnetization
leads to σ(n) dependence with maxima at quarter and three-quarter fillings unlike
in paramagnetic ones, obtained in work [35]. At non-zero temperatures the sharp
changes of σ(n) dependence are possible. It is due to the complicated character of
temperature dependence of the band narrowing factor. The effective mass of quasi-
particles appears to be spin-dependent and substantially varies with the magnetic
field. These results are in agreement with the analysis of work [36] and with the ex-
perimental data of work [39] for heavy-fermion compounds. The correlated hopping
inherent to real narrow band materials being taken into consideration enables us to
describe electron-hole asymmetry of the processes observed in real materials.
Acknowledgement
Authors are grateful to Prof. I.V.Stasyuk, Prof. J.Spa lek and Dr. A.M.Shvajka
for the enlightening discussions. This work was supported by Ukrainian Fund for
Fundamental Research under grant No. 02.07/266.
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Залежнiсть провiдностi та ефективної маси носiїв
вiд магнiтного поля в моделi Мотт-Габбардiвського
матеріалу
Л.Дiдух, О.Крамар, Ю.Скоренький, Ю.Довгоп’ятий
Тернопiльський державний технічний
унiверситет iм. I. Пулюя, кафедра фізики,
Україна, 46001 Тернопіль, вул. Руська, 56
Отримано 22 липня 2005 р.
В статтi досліджено вплив зовнішнього магнiтного поля на статичну
провідність Мотт-Габбардiвського матеріалу в моделi з корельова-
ним переносом електронів. Ефективний гамiльтонiан отримано iз
застосуванням канонічного перетворення та з використанням уза-
гальненого наближення Гартрi-Фока знайдено функцію Грiна i енер-
гетичний спектр. Провідність розрахована як функція магнiтного по-
ля, концентрації електронів та температури.
Ключові слова: Мотт-Габбардiвський матеріал, провідність,
магнітне поле
PACS: 72.15.-v, 72.80.Ga
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