Magnetobreakdown oscillations of Nernst-Ettingshausen field in layered conductors
In the presented report, the Nernst-Ettingshausen effect in layered conductors is investigated. Considering a Fermi surface (FS) consisting of a slightly corrugated cylinder and two corrugated planes distributed periodically in the momentum space, the thermoelectric effects are considered under ge...
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Інститут фізики конденсованих систем НАН України
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irk-123456789-1542312019-06-16T01:26:04Z Magnetobreakdown oscillations of Nernst-Ettingshausen field in layered conductors Galbova, O. In the presented report, the Nernst-Ettingshausen effect in layered conductors is investigated. Considering a Fermi surface (FS) consisting of a slightly corrugated cylinder and two corrugated planes distributed periodically in the momentum space, the thermoelectric effects are considered under general assumptions for the value of a magnetic breakdown probability. As a result of an external generalized force, the FS sheets in layered conductors with a multisheet FS appear to be so close that the charge carriers (as a result of magnetic breakdown) can move from one FS sheet to another. In addition, the distribution functions of the charge carriers and the magnetic breakdown oscillations of thermoelectrical field along the normal to the layer, under different values and orientations of the magnetic field, B, are calculated. It is shown that if the magnetic field is deflected from the xz-plane at an angle ϕ, the oscillation part of a thermoelectrical field along the normal to the layer under condition sinϕtanϑ À 1 is mainly determined with the Nernst-Ettingshausen effect. В цiй статтi дослiджується ефект Нерста-Еттiнгсгаузена в шаруватих провiдниках. Розглядаючи поверхню Фермi (ПФ), що складається зi слабо гофрованого цилiндра i двох гофрованих площин, розподiлених перiодично в iмпульсному просторi, вивчаються термоелектричнi ефекти, роблячи загальнi припущення для значень ймовiрностi магнiтного пробою. В результатi зовнiшньої узагальненої сили, шари ПФ в шаруватих провiдниках з багатошаровими ПФ виникають так близько один до одного, що носiї заряду (в результатi магнiтного пробою) можуть переходити з одного шару ПФ до iншого. Крiм того, обчислено функцiї розподiлу носiїв заряду та осциляцiї термоелектричного поля магнiтного пробою вздовж нормалi до шару для рiзних значень i орiєнтацiй магнiтного поля B. Показано, що якщо магнiтне поле вiдхиляється вiд xz-площини на кут ϕ, осциляцiйна частина термоелектричного поля вздовж нормалi до шару при умовi sinϕtanϑ À 1 визначається в основному ефектом Нерста-Еттiнгсгаузена. 2016 Article Magnetobreakdown oscillations of Nernst-Ettingshausen field in layered conductors / O. Galbova // Condensed Matter Physics. — 2016. — Т. 19, № 3. — С. 33701: 1–7. — Бібліогр.: 28 назв. — англ. 1607-324X DOI: 10.5488/CMP.19.33701 PACS: 72.15.Gd, 74.70.Kn arXiv:1609.04710 http://dspace.nbuv.gov.ua/handle/123456789/154231 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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In the presented report, the Nernst-Ettingshausen effect in layered conductors is investigated. Considering a
Fermi surface (FS) consisting of a slightly corrugated cylinder and two corrugated planes distributed periodically
in the momentum space, the thermoelectric effects are considered under general assumptions for the value of
a magnetic breakdown probability. As a result of an external generalized force, the FS sheets in layered conductors with a multisheet FS appear to be so close that the charge carriers (as a result of magnetic breakdown)
can move from one FS sheet to another. In addition, the distribution functions of the charge carriers and the
magnetic breakdown oscillations of thermoelectrical field along the normal to the layer, under different values
and orientations of the magnetic field, B, are calculated. It is shown that if the magnetic field is deflected from
the xz-plane at an angle ϕ, the oscillation part of a thermoelectrical field along the normal to the layer under
condition sinϕtanϑ À 1 is mainly determined with the Nernst-Ettingshausen effect. |
| format |
Article |
| author |
Galbova, O. |
| spellingShingle |
Galbova, O. Magnetobreakdown oscillations of Nernst-Ettingshausen field in layered conductors Condensed Matter Physics |
| author_facet |
Galbova, O. |
| author_sort |
Galbova, O. |
| title |
Magnetobreakdown oscillations of Nernst-Ettingshausen field in layered conductors |
| title_short |
Magnetobreakdown oscillations of Nernst-Ettingshausen field in layered conductors |
| title_full |
Magnetobreakdown oscillations of Nernst-Ettingshausen field in layered conductors |
| title_fullStr |
Magnetobreakdown oscillations of Nernst-Ettingshausen field in layered conductors |
| title_full_unstemmed |
Magnetobreakdown oscillations of Nernst-Ettingshausen field in layered conductors |
| title_sort |
magnetobreakdown oscillations of nernst-ettingshausen field in layered conductors |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/154231 |
| citation_txt |
Magnetobreakdown oscillations of Nernst-Ettingshausen field in layered conductors / O. Galbova // Condensed Matter Physics. — 2016. — Т. 19, № 3. — С. 33701: 1–7. — Бібліогр.: 28 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT galbovao magnetobreakdownoscillationsofnernstettingshausenfieldinlayeredconductors |
| first_indexed |
2025-07-14T04:40:52Z |
| last_indexed |
2025-07-14T04:40:52Z |
| _version_ |
1837595941348048896 |
| fulltext |
Condensed Matter Physics, 2016, Vol. 19, No 3, 33701: 1–7
DOI: 10.5488/CMP.19.33701
http://www.icmp.lviv.ua/journal
Magnetobreakdown oscillations of
Nernst-Ettingshausen field in layered conductors
O. Galbova∗
Faculty of Natural Sciences and Mathematics, Institute of Physics,
P.O. Box 162 1001 Skopje, Republic of Macedonia
Received February 23, 2016, in final form April 25, 2016
In the presented report, the Nernst-Ettingshausen effect in layered conductors is investigated. Considering a
Fermi surface (FS) consisting of a slightly corrugated cylinder and two corrugated planes distributed periodically
in the momentum space, the thermoelectric effects are considered under general assumptions for the value of
a magnetic breakdown probability. As a result of an external generalized force, the FS sheets in layered con-
ductors with a multisheet FS appear to be so close that the charge carriers (as a result of magnetic breakdown)
can move from one FS sheet to another. In addition, the distribution functions of the charge carriers and the
magnetic breakdown oscillations of thermoelectrical field along the normal to the layer, under different values
and orientations of the magnetic field, B , are calculated. It is shown that if the magnetic field is deflected from
the xz-plane at an angle ϕ, the oscillation part of a thermoelectrical field along the normal to the layer under
condition sinϕ tanϑÀ 1 is mainly determined with the Nernst-Ettingshausen effect.
Key words: layered conductor, Fermi surface, magnetic breakdown oscillations
PACS: 72.15.Gd, 74.70.Kn
1. Introduction
The electronic phenomena that occur in degenerate conductors, in the presence of strong magnetic
fields, are highly dependent on the electron energy spectrum. The experimental study of these phe-
nomena enables us to gain important information on the topology of the Fermi surface (FS) — a ba-
sic/fundamental characteristic of the electron energy spectrum. Theoretical investigations of the metal
magnetic permeability, under general assumptions for the type of energy spectrum of the conduction
electrons (taken a priori as the known one), were done by Lifshicz and Kosevich [1]. It was shown that
the period of oscillations of magnetization in a quantized magnetic field, B , as a function 1/B is propor-
tional to the extreme FS section. The investigation of these oscillations, under different orientations of
a magnetic field, allows for a complete determination of the form of the Fermi surface [2]. The analo-
gous information of the FS could be gained from the investigation of the Shubnikov de Haas magneto-
resistance oscillations [3, 4] in degenerate conductors [5]. The investigation of galvanomagnetic phenom-
ena in a strong magnetic field (classical case), where the circular frequency ωc = eH/(m∗c) is much
bigger than the relaxation frequency, 1/τ, enables one to determine the FS topology structure [6, 7]. In
the low-dimensional conductors, the oscillation effects are numerous.
Experimental observations (1998) performed in the Shegoleva (Chernogolovka) laboratory, at mag-
netic field strengths of up to 14 T, show the existence of resistance oscillations with a varying angle be-
tween the magnetic field, ~H , and the normal to the layer, ~n, in the layered organic conductor β-(BEDT-
TTF)2JBr2 [8, 9]. Then, the angle oscillations were observed in multilayered conductors of organic origin
(see, for example the articles [10–19]) and in different quasi-two-dimensional conductors. This oscilla-
tion effect is essentially expressive under the tanϑ À 1 condition, where the cross section of the FS
with the plane pB = (~p~B)/B = const is strongly extended along the axis pz = ~p~n, and the velocity of
∗
E-mail: galbova@pmf.ukim.mk
© O. Galbova, 2016 33701-1
http://dx.doi.org/10.5488/CMP.19.33701
http://www.icmp.lviv.ua/journal
O. Galbova
the electrons, vz , along the trajectories in the momentum space ε(~p) = const, pB = const, frequently
changes the sign. Under certain orientations of the magnetic field, the mean value of the velocity vz may
be small enough to cause a sharp increase of the current resistance which is repeated periodically as
tanϑ functions. Out of the period of these oscillations, an important information on the form of FS could
be gained [20–23]. The inverse problem, i.e., calculation of the electron energy spectrum, is most effec-
tively performed using experimental investigations of thermomagnetic effects in a strong magnetic field.
An enormous number of the theoretical and experimental works are devoted to the investigation of the
Nernst-Ettingshausen effect (see, for example [24–26]).
2. Formulation of the problem
In the present report we consider the linear response of an electronic system to the perturbation by
an electric field, ~E , and temperature gradient, ∂T /∂r :
Ji =σi j E j −αi j
∂T
∂x j
(2.1)
in layered conductors. The quasi-two-dimensional electronic energy spectrum of charge carriers is taken
in a general form:
ε(p) =
∞∑
n=0
εn(px , py )cos
[ anpz
ħ +αn(px , py )
]
, (2.2)
εn(−px ,−py ) = εn(px , py ), αn(−px ,−py ) =αn(px , py ).
In the above equation, a is the separation between the layers, ħ is Plank constant divided by 2π, while
εn(px , py ) and αn(px , py ) are arbitrary functions. The quasi-two-dimensionality parameter of the elec-
tronic energy spectrum, η, is defined as a ratio between themaximum value of the electron velocity along
the normal of the layers:
vz =−
∞∑
n=1
an
ħ εn(px , py )sin
[ anpz
ħ +αn(px , py )
]
É ηvF (2.3)
and the Fermi velocity vF with which the electrons move within the layer.
In the absence of the current density, the electric field generated by the temperature gradient, is given
by
Ei = %i kαk j
∂T
∂x j
, (2.4)
where %i k , σi j and αi j are the resistivity tensor, conductivity tensor and thermoelectricity tensor, re-
spectively:
σi j =−
∫
σi j (ε)
∂ f0
∂ε
dε, (2.5)
αi j =−
∫
σi j (ε)
ε−µ
T
∂ f0(ε)
∂ε
dε. (2.6)
Here,
f0(ε) =
[
1+exp
(ε−µ
T
)]−1
is the equilibrium Fermi distribution function for the charge carriers, µ is the chemical potential of the
electrons, and T is temperature in units of energy.
By employing the kinetic equation solution for the distribution function of the charge carriers
f (~p) = f0(ε)−eE jψ
j ∂ f0(ε)
∂ε
in the τ-approximation for the collision integral, it is possible to calculate the conductivity tensor σi j (ε):
σi j (ε) = 2e3B
c(2πħ)3
∫
dpB
T∫
0
dt vi (t )
t∫
λ1
dt ′v j (t ′)+exp
(
λ1− t
τ
)
ψ j (λ1, pB )
= 〈viψ
j 〉, (2.7)
33701-2
Magnetobreakdown oscillations of Nernst-Ettingshausen field in layered conductors
where the function
ψ j (λ1, pH ) =
λ1∫
−∞
v j (t )exp
(
t −λ1
τ
)
dt (2.8)
describes the complex motion of the charge carriers along the magnetic breakdown trajectories, with
probabilities for a magnetic breakdown w and w ′
in the regions A and B (figure 1), respectively, at the
moments λ1, λ2, λ3, (λ1 being the closest to the moment when electrons move from a given sheet of FS
to the neighboring one, and also λk > λk+1). The tensor σ
′
i j (ε) coincides with the tensor σi j (ε) if in the
expression for σ′
i j (ε), τ is substituted by τε.
As a result of an external generalized force, the FS sheets in the layered conductors with a multisheet
FS appear to be close enough so that the charge carriers (as a result of magnetic breakdown) can move
from one FS sheet to another, and their motion along the magnetic-breakdown trajectories becomes com-
plex. The magnetic breakdown oscillations of the current resistance normal to the layer of conductors
with a multisheet FS, composed of a weakly corrugated cylinder and two corrugated planes, is period-
ically repeated in the momentum space, were theoretically investigated in the work [27]. It was shown
that the period of the magnetic breakdown oscillations of the kinetic coefficients contains important in-
formation for both the form of the FS planes (sheets) and the mutual positions of the FS planes (sheets)
in the momentum space. Furthermore, only the limiting cases when the probability for magnetic break-
down, w , is negligibly small and when w is close to 1, are considered.
In this report we consider the thermoelectric effects under a general assumption for the value of the
magnetic breakdown probability. Let the Fermi surface be composed of a cylinder and two planes, weakly
corrugated along the pz axis, and let the px axis be normal to the plane, figure 1.
When there are several groups of charge carriers, each of them contributes to the kinetic coefficient,
so that
〈viψ
j 〉 = 〈viψ
j 〉1+〈viψ
j 〉2+〈viψ
j 〉3 +〈viψ
j 〉4, (2.9)
where the terms 〈viψ
j 〉
1
+〈viψ
j 〉
3
define the current due to the electrons on the quasi-planar FS sheets
and the terms 〈viψ
j 〉
2
+ 〈viψ
j 〉
4
give the contribution of the conduction electrons belonging to the FS
section in the form of a corrugated cylinder.
1
3
2
4
Figure 1. Projections of the FS and the magnetic breakdown electron trajectories in the magnetic field
~H = (H sinϑ,0, H cosϑ) on the plane px py .
33701-3
O. Galbova
3. Calculations
In [28], a case was considered where the probabilities for magnetic breakdown w and w ′
are essen-
tially different, and the electron that was tunneled from the quasi FS plane sheet to the cylinder FS sheet,
after performing a rotation along the cross-section (as a result of magnetic breakdown) comes back to the
previous quasi FS plane sheet.
Here, we consider the case where in the magnetic field ~B = (B sinϑ,0,B cosϑ) the distance between
the regions A and B (when the FS sheets are at the closest distance along the pz axis) is equal to an
integer, N , of the unit cells in the momentum space, figure 1, i.e.,
tanϑ= 2πNħ
aDp
. (3.1)
In the above equation, Dp is the diameter of a cylinder along the px axis. In this case, the probability w ′
coincides with the probability w on all cross-sections of the FS and the plane pB = const, and the elec-
tron could move from one quasi-FS plane sheet to another quasi-FS plane sheet even in cases where the
corrugation along the px axis is pronounced.
Non-equilibrium distribution functions of the electrons on the FS sheet 1 after the magnetic break-
down in the region A:
φ1(λ1+0) =
λ1∫
−∞
dt exp
(
t −λ1
τ
)
(~E~v)1
E
(3.2)
are connected to the distribution functions of the electrons on the same FS sheet but prior to themagnetic
breakdown, φ1(λ1 −0), with the following equation:
φ1(λ1+0) = (1−w)φ1(λ1−0)+wφ2(λ1−0), (3.3)
and with the functions φ1 and φ2 at the previous moment λ2
φ1(λ1+0) = (1−w)
[
A1+exp
(−P
τ
)
φ1(λ2+0)
]
+w
[
A2+exp
(−P ′
τ
)
φ2(λ2+0)
]
. (3.4)
Similarly, the equation (3.4) at the earlier moments λ2, λ3, λ4, gain the forms:
φ2(λ2+0) = (1−w)
[
A4+exp
(−P ′
τ
)
φ4(λ3+0)
]
+w
[
A3+exp
(−P
τ
)
φ3(λ3+0)
]
, (3.5)
φ3(λ3+0) = (1−w)
[
A3+exp
(−P
τ
)
φ3(λ4+0)
]
+w
[
A4+exp
(−P ′
τ
)
φ4(λ4+0)
]
, (3.6)
φ4(λ4+0) = (1−w)
[
A2+exp
(−P ′
τ
)
φ2(λ5+0)
]
+w
[
A1+exp
(−P
τ
)
φ1(λ5 +0)
]
, (3.7)
φ1(λ5+0) = (1−w)
[
A1+exp
(−P
τ
)
φ1(λ6+0)
]
+w
[
A2+exp
(−P ′
τ
)
φ2(λ6 +0)
]
. (3.8)
In the above equations, the functions
Ai =
λ j∫
λ j +1
dt exp
(
t −λ j
τ
)
(~E~v)i
E
, i = 1,2,3,4, (3.9)
in the non-collision range (τ→∞) are equal to the drifting of the electrons along an electrical field for
a time period (λ j −λ j+1) between two instants of the magnetic breakdown. This period estimated with
accuracy to small corrections proportional to the quasi-two-dimensionality parameter of the electronic
energy spectrum, η, is independent of λ j , and corresponds to the period P of the electron drifting on
the FS sheets 1 and 3, i.e., to a half-period P ′
of the electron drifting along the closed sections of the
corrugated cylinder.
33701-4
Magnetobreakdown oscillations of Nernst-Ettingshausen field in layered conductors
One can easily find that the equation (3.8) corresponds to the equation (3.4) for some previous mag-
netic breakdownmoment. Going on with the above recursive relation, one moves back in time and, since
the functions on the right-hand side of the equations (3.3)–(3.8) decrease with each recursion (accumula-
tion of the effect of multipliers smaller than 1), they become sufficiently small after many recursive steps.
As a result, the functions φi on the left-hand side of the equations (3.4)–(3.7), proportional to A j , form
a geometric progression which can be easily calculated [25]. After several algebraic manipulations, one
comes to
φ1(λ1+0) = (1−w)A1+w A2
1−h1
+
∞∑
n=0
hn
1
gφ2(λn+2 +0), (3.10)
where h1 = (1−w)exp(−P/τ), g = w exp(−P ′/τ).
Substituting the function φ4(λ4 +0) in the equation (3.5) and using the expression (3.7), one gets
φ2(λ2+0) = (1−w)(A4+h A2)+w(A3+h A1)+h2φ2(λ4 +0)+ g1φ3(λ3+0)+hg1φ1(λ5+0), (3.11)
where g1 = w exp(−P/τ), h = (1−w)exp(−P ′/τ).
Using the expression (3.7), the connection between the function φ3(λ3 +0):
φ3(λ3 +0) = (1−w)A3+w A4
1−h1
+
∞∑
n=0
hn
1
gφ4(λn+4 +0), (3.12)
and the function φ2 is as follows:
φ3(λ3 +0) = (1−w)A3+w A4
1−h1
+hg
(1−w)A2+w A1
1−h1
+
∞∑
n=0
hn
1
g hφ2(λn+5 +0)+
∞∑
n=0
hn
1
g g1φ1(λn+5 +0).
(3.13)
By substituting the functionsφ1 andφ3 from the equations (3.12)–(3.13) in the equation (3.11), we gain
the functional expression for only one functionφ2 whose solution under conditionsw À γ1 = exp(P/τ)−
1 and w À γ= exp(P ′/τ)−1 gains a simple form:
φ2(λ2+0) = A1+ A2+ A3+ A4
2(γ+γ1)
, (3.14)
φ1(λ1+0) = (1−w)A1+w A2
w +γ1
+ w
w +γ1
φ2(λ2+0). (3.15)
The functions φ3(λ3+0) and φ4(λ4+0) coincide with the functions φ1(λ1+0) and φ2(λ2+0) if we inter-
change the places therein: A1→ A3, A2→ A4. Now, if we know the functions φi , it is easy to calculate all
the components of the conductivity and thermoelectricity tensors under different values and orientations
of the magnetic field ~B = (B cosϕsinϑ,B sinϕsinϑ,B cosϑ).
4. Discussion and conclusion
The basic contribution to the average value of an electron velocity, vz , that is moving along a strongly
extended trajectories, under condition tanϑÀ 1, is given by small areas in the vicinity of the stationary
phases, where
dpz
dt
= eB
c
sinϑ(vx sinϕ− vy cosϕ) = 0. (4.1)
On the closed sections of a corrugated cylinder, there are at least two points of this kind. Under certain
orientations of the magnetic field with respect to the crystal axis of the single crystal conductor, the con-
tribution from these points to the average value of the electron velocity, vz , can be cancelled. This leads
to a sharp increase of the current resistance normal to the layer, %zz , whose asymptotic behavior under
η→ 0 is equal to 1/σzz . In the magnetic field normal to the y -axis, the components of the conductivity
tensor gain the form:
σzz = σ0η
2
tanϑ
{
β(1+ sinαDp )+2β1(1+ sinαδpx )+β2
[
2cosα(Dp +δpx +∆p )
+ sinα(Dp +2δpx +2∆p )− sinα(Dp +δpx )
]+β3 [cosα(δpx +∆p )
−sinα∆p + sinα(Dp +2δpx +∆p )+cosα(Dp +∆p )
]}
. (4.2)
33701-5
O. Galbova
Here, σ0 is the electro-conductivity of the quasi-two-dimensional conductor along the layer in the ab-
sence of amagnetic field;Dp is the diameter of a cylinder along the px axis;∆p = pminx2 −pminx1 = pminx3 −pminx2
is the minimum distance between the cylinder and the plane FS sheets; α = (a/ħ) tanϑ; the quantities
β, β1, β2 and β3 are all ∼ 1 and depend on a concrete type of the electronic energy spectrum. In the
formula (4.2), the non-oscillation terms of the diagonal electro-conductivity components σzz are not in-
cluded:
σzz =− 2e2
(2πħ)3
∫
dε
∂ f0(ε)
∂ε
∫
dpB
∣∣∣∣ tB
c
∣∣∣∣ (v̄z1 + v̄z2 + v̄z3 + v̄z4)2
2(γ+γ1)
> 0. (4.3)
The angular oscillation of a thermoelectric filed along the normal to the layer, Ez :
Ez = π2T
3e
%zk
∂σk j
∂µ
∂T
∂x j
(4.4)
gains a multiplier proportional to tanϑ as a result of the differention with respect to µ of the quickly
oscillating members in σ′
i j (ε) under condition tanϑÀ 1. It means that the thermoelectric filed, Ez , as
a function of tanϑ, can change the sign even in the case of a longitudinal thermoelectrical effect when
the temperature gradient is directed along the normal of the layer. When the magnetic field is deflected
from the xz-plane by the angle ϕ different from zero, the drift of the charge carriers along the y -axis is
v̄y = v̄z sinϕ tanϑ, and, when sinϕ tanϑÀ 1, the oscillation part of the thermoelectrical field Ez :
Ez = π2T
3e
τ
τη
1
σzz
∂σosczz
∂µ
(
∂T
∂z
+ sinϕ tanϑ
∂T
∂y
)
(4.5)
is mainly determined with the Nernst-Ettingshausen effect. The magnetic breakdown oscillations could
not exist if sinϕ � 1 because in this case the relation (4.1), which is an imperative requirement for the
existence of stationary phase points on the FS plane sheets, is not fulfilled. Under the following conditions:
γ0 ¿ cosϑ ¿ sinϕ ¿ 1, (where γ0 is of the same order of magnitude with the quantities γ1 and γ2
under ϑ = 0), the stationary phase points on the electronic trajectories, under small deflection of the
magnetic field from the xz-plane, are insignificantly dislocated. This allows us to use the equation (4.2)
to calculate the angular oscillation of a thermoelectrical filed along the normal to the layer, Ez . There are
also angular oscillations of the thermoelectrical filed along the layer plane under condition tanϑÀ 1,
but their amplitudes are negligibly small (proportional to η2
) compared to the dominant background,
smoothly changing with the variation of the angle between the magnetic field and the layer plane.
References
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Осциляцiї магнiтного пробою поля Нерста-Еттiнгсгаузена в
шаруватих провiдниках
O. Галбова
Факультет природничих наук i математики, Iнститут фiзики,
P.O. Box 162 1001 Скоп’є, Республiка Македонiя
В цiй статтi дослiджується ефект Нерста-Еттiнгсгаузена в шаруватих провiдниках. Розглядаючи поверх-
ню Фермi (ПФ), що складається зi слабо гофрованого цилiндра i двох гофрованих площин, розподiлених
перiодично в iмпульсному просторi, вивчаються термоелектричнi ефекти, роблячи загальнi припущен-
ня для значень ймовiрностi магнiтного пробою. В результатi зовнiшньої узагальненої сили, шари ПФ в
шаруватих провiдниках з багатошаровими ПФ виникають так близько один до одного, що носiї заряду
(в результатi магнiтного пробою) можуть переходити з одного шару ПФ до iншого. Крiм того, обчислено
функцiї розподiлу носiїв заряду та осциляцiї термоелектричного поля магнiтного пробою вздовж нормалi
до шару для рiзних значень i орiєнтацiй магнiтного поля B . Показано, що якщо магнiтне поле вiдхиля-
ється вiд xz-площини на кут ϕ, осциляцiйна частина термоелектричного поля вздовж нормалi до шару
при умовi sinϕ tanϑÀ 1 визначається в основному ефектом Нерста-Еттiнгсгаузена.
Ключовi слова:шаруватий провiдник, поверхня Фермi, осциляцiї магнiтного пробою
33701-7
http://dx.doi.org/10.1088/0034-4885/74/12/124507
http://dx.doi.org/10.1063/1.2400694
http://dx.doi.org/10.1063/1.3253405
http://dx.doi.org/10.1103/PhysRevLett.107.016601
http://dx.doi.org/10.1103/PhysRevB.65.205119
http://dx.doi.org/10.1088/0034-4885/79/4/046502
http://dx.doi.org/10.1063/1.4816118
http://dx.doi.org/10.1063/1.4927316
Introduction
Formulation of the problem
Calculations
Discussion and conclusion
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