The ground state of the "frozen" electron phase in two-dimensional narrow-band conductors with a long-range interelectron repulsion. Stripe formation and effective lowering of dimension
In narrow-band conductors a weakly screened Coulomb interelectron repulsion can supress narrow-band electrons` hopping, resulting in formation of a "frozen" electron phase which differs principally from any known macroscopic self-localized electron state including the Wigner crystal. In a...
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| Published in: | Физика низких температур |
|---|---|
| Date: | 1999 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
1999
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/139014 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The ground state of the "frozen" electron phase in two-dimensional narrow-band conductors with a long-range interelectron repulsion. Stripe formation and effective lowering of dimension / A.A. Slutskin, V.V. Slavin, H.A. Kovtun // Физика низких температур. — 1999. — Т. 25, № 8. — С. 936-943. — Бібліогр.: 13 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860209993759850496 |
|---|---|
| author | Slutskin, A.A. Slavin, V.V. Kovtun, H.A. |
| author_facet | Slutskin, A.A. Slavin, V.V. Kovtun, H.A. |
| citation_txt | The ground state of the "frozen" electron phase in two-dimensional narrow-band conductors with a long-range interelectron repulsion. Stripe formation and effective lowering of dimension / A.A. Slutskin, V.V. Slavin, H.A. Kovtun // Физика низких температур. — 1999. — Т. 25, № 8. — С. 936-943. — Бібліогр.: 13 назв. — англ. |
| collection | DSpace DC |
| container_title | Физика низких температур |
| description | In narrow-band conductors a weakly screened Coulomb interelectron repulsion can supress narrow-band electrons` hopping, resulting in formation of a "frozen" electron phase which differs principally from any known macroscopic self-localized electron state including the Wigner crystal. In a zero-bandwidth limit the "frozen" electron phase is a classical lattice system with a long-range interparticle repulsion. The ground state of such systems has been considered in the case of two dimensions for an isotropic pair potential of the mutual particle repulsion. It has been shown that particle ordering into stripes and effective lowering of dimension resides universally in the ground state for any physically reasonable pair potential and for any geometry of the conductor lattice. On the basis of this fact a rigorous general procedure to describe the ground state fully has been formulated. Arguments have been adduced that charge ordering into stripes in high-Tc superconductors testifies to the presence of a "frozen" electron phase in these systems.
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| first_indexed | 2025-12-07T18:13:53Z |
| format | Article |
| fulltext |
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r�s � oQq g l g t h�x �I� w i p g t�w�p�q y�x � lC� � i p '=(+* p�t x'� � p�l�n1l>w�s
s�|
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s�r'pCv�nFq
p¾|�suq w i p � �
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w)p � lz~ g w i x
� sQt h�j q x t h p g tEw�p�q�o x q
w g r � p,q
p�o�n � l g sut ¦�>H².?E¨ �
@F\<ACB�D,eFE3_�a�^FeGB
^=\)HNeGD�I,EFJ$dK`�K,L�_2B%EFL
� i p f*x���g � w�sut g3x tD�<M��Fs�|0w i p,l � l
w�p � n1t1v�pCq�r's�tEl g3j
vQp�q x w g sQt iQx l�w i p,|�suq �
MON& ( P ) Q =
§
R ∑S ≠ S ′
� ( T ` −
`
′ T ) U (̀ ) ( ` ′) � ��§
�
~ i p�q
p `
=
�CV&W � +
� � B � x q)p q x v g n1l y p�r'w�s�q�l su|�w i pi s�l�w j � x w�w g r'p;l g w�p�l'� � �� � x q�p g t�w)p h p�q�lK� B �� � x q
p i sQl
w j � x w j
w g r'p*oQq g���g w g3y p�w�q x t9l � x w g s�t y p'r'w�suq�l ��¢?��X l ��7 w i p�sHr�r'n j
o x w g sut4t�n �@� pCq�lNsQ|Dw i p i sul)w j � x w g r'p�l g w�p�l'�Y (̀ ) = ¼ suq § �x q
p �*g rCq�s�l�r�sQo g r yQx q g�x'� � pCl2Z 7 w i p:l
n �7g lNw x
� p�t�s y p�q>w i p
~ i s � p i sQl
w � x w)w g r'pE� � i p�o x�g q�o�s�w)pCt�w g�x � g l x l)l�n � p�vmw�s� p x tÃp y p�q � ~ i pCq�p r�sQt y p�´ |�n1tEr�w g s�tÃsQ|}w i p¤|�s�q �� ( [ ) = \] ( ¬ )̂:[ �:~ i p�q)p¿w i pµ|�nFt�r�w g sut �] ( ¬ ) vQp�o�p�tQv9lmsQtw i p*r i1x q x r'w�p�q2sQ|0w i p,l
r�q�p'p�t g t h5� p�v g n �x t1v g w�l�oQs�l g3j
w g sQtz~ g w i q
p�l�o�p�r'w�w�s{w i p � � N¡0¢ �.�
t x t � r x l)p_�] ( ¬ )w
pÍt�v�l>w
s���p�q�s x l ¬ − � s
q0| x l�w
pÍq>~ i p�t ¬ → ∞
7 � ] ( ¼ ) =
� � « κ� � g l2w i p�p � p'r�w�q�s�tAr iQx q h pQ� κ
g l�w i p�v g p � p'r�w�q g r,o�p�q ��g w j
w g3y1g w � � � ( w i p�q
~ g l
pE�`�] ( ¬ ) r x t � p�q)p'r � s�tQp�v x l x q ��g3j
w�q x q � 5 x l�~ g �I� � pAl i s�~*t � p � sH~m� g w�l,l)o�p�r g | g rA|�sQq � g lg��*��x w�p�q gLx � w)s$s
nFq x oEoQq)s x r i �
� � sut h w i p ·*¸ r'sut9| g+h n1q x w g sQtQl N (
`
) Q ~ g w i v g |
|�p jq)pCt�w ρ w i pa��� � � �F� �'©*sutEp�l x q�p � � r�q � l�w x � l�~ g w i s�t�p
p � p'r�w�q)sut¾o�p�qmr'p ���,� � ¸ j rCq � l)w x � l�� � Z�Z � � i p g q g t y p�q�l
p ρy1x � nQp�l ��x�� p n9o x t g t1| g t g w�pÂl�p'wzsu| g tEw�p h pCq�lcb:d =
= T vEp�w (
�
κλ
d
(
B �:� B � ))T �1~ i pCq)p$e g t9v�p'´1p�l ¸ j r�q � l)w x � lK�1w i pg t�w)p h pCq)l �
κλ
d �
κ � λ =
§ � �9� x q)p;r's � oEsutEpCt�w�l0su| ¸ j r�q � l j
w x �,¢N�.X l g t w i p B
λ
�1x l g l 7 b d g l4w i pfe j w i ¸ j rCq � l)w x �
p � p � p�t�w x q �Qj r�p ��� x q�p x@� p x l
nFq
p�v g t,n9t g w�l>su|Dw i1x w�sQ|Dw i pi sul)w � x w)w g r'pE� σ S = T B � ×W%g�h �( nFq*l�w�q x w�p hQ�¿g l@w�szvQp�q g3y p$w i p�|�n �I� v�p�l)rCq g o�w g s�t su|
w i p ·*¸ |�suq x t � B �� � �=l
w x q
w g t h ~ g w i r'sut9l g v�pCq x w g sut5su|
l ��x ��� yQg r g t g w g pCl�su| ρ =
§ « b:d�� ¸ g t�r�pÂl�o�p'r g | g r �
κλ
d
y1x � nQp�l x q)p g q�q)p � p yQx tQw�w�smw iEg l�q)p x l�s�t g t h ��~�p,vQq)suo5w i pg tQvEp'´ie x w b x t9v x wzs
w i p�q{r i9x q x r�w)pCq g l
w g r�l{s�|5w i p¸ j rCq � l)w x � l�|�s�q x ~ i1g � pQ�* nQp{w�s�w i pÀv g l
r�q)p�w)pCt�p�l�l,s�|�w i pzl � l)w�p � ~ g w i w i pf*x
�@g � w)sQt g�x t �
§
� x �*x r�q)sul)r�s�o g r x �I� � l �*x ��� r iEx t h pE�
δρ � g t ρ (δρ → ¼4jk8 �mlQ� Tδρ T → ∞ ~ i pCt 8 → ∞
� oQq)s j
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l�o x r'p$l
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sQt�~ i p'w i p�qmw i p � q
p�l)n � w�|
q)s � x t g t�r�q�p x l
pzsQq x v�p j
r�q�p x l
p g t ρ � � iQg l�| x r'w g l�p�´FoQq)pCl)l)pCv �E� w i p g vEp�t�w g w �
p Û (8 ± Tδ 8 h j,9 ± Tδ 9 T ) −
p Û ( 8 � 9 ) =
= ± µ± Tδ 8 h +− q
± Tδ 9rT � ���Q�
~ i p�q)p p Û g l�w i p ·*¸ pCt�pCq hQ� � δ8 x t1v δ 9 x q�p:r i9x t h p�lg t 8 x t9v 9 oQq
sQv�n9r g t h δρ � � i p¶oQq
sQo�sQq�w g s�t x � g w �
r'sup�|
| g r g pCtEw�lC� µ−
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−
¹ s
+
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w i p�r i p ��g r x � o�s�w�p�t�w g�x � � µ � x t9v®w i p o9q
p�l�l
n1q)pE�fs��
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p�tQp�q h1g p�l s�|¶|�s�q �*x w g sut su|7r's�q)q)pCl)oQs�t1v g t h vEp�|�p�r'w�lC�� i n9l'� g tÀl)s � p y1g r g t g w � su| ρ =
§ « b w i p ·�¸ g l � s�n1t9v
w�s � p x l
n1oEpCq)l)w�q
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s j v g�� pCt j
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w gØy p � � � ( tQp:r x t � p g t�r � g tQp�v4w�s,w iEg t � w i9x w δ8 l i sHn � v� p g vQp�t�w g | g pCvÃp'´ x r'w � � ~ g w i w i p w�s�w x � t�n �@� pCq su|
± v�p'|�p�r'w
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p�o x q x w)p�vD� ± µ±
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� f s
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l)p�p ��g t h � � p yQg v�p�tQw¿l)w x w)p � p�t�w g l x r'w�n x ��� �¶g tQr'suq�q�p�r'w
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ν ;�¼ � g l� sQq
pmw i1x t § � x�� �H�0 # �'©�¯E© � s�| Tν T ± vEpC|�p'r�w)sut9l x q g l)pCl~ i s�l)p�p�t�p�q h��¿g l � pCl�l@w iQx t Tν T � ±
�=¥�p iQx'y pmq
p y p x � p�v
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vQp�l
r�q g o�w g sut,s�|Nw i p ·,¸ ~ g w i ν = ±
§ � ±
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v g o�s � p x oQoQq)s x r i sQ|
|�p�q�l x r � p x q yQg p'~£s�| i s
~ w i p
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w i p�vEp�|�p�r'w�s�t1l{s�|Aw i p l xH� p l g6h t q)p�o�p � p x r i s
w i p�q'�� p g t h ~ g vEp � � l�o x r'pCv°�
�0w ν ≠ ¼ x oEpCq�w�n1q � p�v ¸ j rCq � l
w x � g l*|�s�q � p�vz~ i pCq�pQ�� p�l g v�pzp � p�r'w�q)s�t1lmo � x r�p�v x w i sQl
w j � x w�w g r�p¿l g w�p�l g t w i pg tQw)pCq)l)w g r�p�l2s�|�w i p ¸ j rCq � l)w x ��� ν ; ¼ � sQq0p � o�w � ¸ j rCq � l jw x � l g w)pClC� � i s � p�l��Z� � ν º ¼ � ��w i p�q
p x q)p h p�t�pCq x ��� �¶x
r�p�q)w x�g t�tEn �@� p�q$s�| ¸ j r�q � l)w x � p � p'r�w�q
sQtQlml i9g |�w�p�v |
q�s �
w i p g q2t x w g6y p ¸ j r�q � l
w x � l g w
p�lC� � i p � x w
w�p'q0r x t � p:r�s�tQl g v�p j
q�p�v x l � x tQw g o x q)w g r � p�l'�m~ i sul)p,r iEx q h p g l pC��n x � w�s5w i p
p � p�r'w�q)s�tmsQt�p g t ��x'h t g w�n1vEp � n9w g l0sQoQo�sQl g w�p g t5l g6h t°� x
o x�g q � x t,p � p�r'w�q)sutml iQg |�w)pCv �Q�$x@y p�r'w�sQq ξξ +
g w�l x tEw g o x q j
w g r � p � s
r x w�p�v x w x t ¸ j rCq � l
w x � l g w)p ` � � p g t h w i p � ` � ξξ
j
v g o�s � pu�Z� � i nFl'�1w i p*o�p�q)w�n1q �1x w g sutms�|�w i p ¸ j rCq � l�w x � r x t� pmp�t yQg l g sQt�pCv x l x t¿p�tQl)p �:� � pmr�sQtQl g l)w g t h su|�l
p y p�q x �
v g o�s � pCl x tQv Tν T g tQw)pCq)l)w g w g�x � o x q
w g r � p�l � i s � p�l � � ¢ � f l � �� i p*v g o�s � p�l g tEw�p�q x r'w2~ g w i w i p,� ¢ � f l x t9v4~ g w i p x r i
suw i p�q�� � i p,p�tEpCq h1� su| g tEw�p�q x r'w g sQt � p�w)~�p'pCt x t � ¢ � f� x w ` = ¼ � x tEv ` � ξξ
j v g o�s � p g l �
ξξ(̀ ) = l g�h t ν( � ( h P − ξξ T ) −
− � ( T ` h)) ≡
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�� ν∆� ξξ � ( T ` T ) 7 w i ppCt�p�q hQ� s�| g tQw)pCq x r'w g sQt� p'w�~:p'pCt ` � ξξ
j x tQv `
′ � ξξ′
j v g oQs � p g l �
ξξ
ξξ′(
`
−
`
′) =
= ∆
�
ξξ∆
�
ξξ′
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| g p � v°�<� (
`
) �<~ i9g r i g l�pC�En x � w�s −
� � S |�sQq i s � p�l � i p�q
px tQv¾|�n1q�w i pCq4sQtÂ� Â� s�|�w i p ¸ j r�q � l�w x � g lmvEpCt�s�w)pCv �Q�
� S � � x tEvz|�s�q�� ¢ l g w g l:w i pm| g p � v¿oQq�s�v�n1r'pCv x w x oEs g t�w` �Q�$x ��� p � p�r'w�q)sut9l>su|Dw i p ¸ j rCq � l�w x � �9��t�w i pCl�p�w�p�q � l>w i p
r i9x t h p g t4w i p ·*¸ p�t�pCq hQ�$x w x2hFg-y pCt ν �����6à (ν) ��w xH� pClw i p*|�sQq �
� ��à (ν) =
�*g t ( ����� � + � Ø + � ú2��� + � ) � ��±F�
f p�q
p � üBú
� = Σ
α ! β
� ( T ` αβ T) g l4w i pÀp�tQp�q h9� sQ|�w i p � nEw�n x �
q�p�o�n � l g sut{sQ|�w i pm� ¢ � f l 7 � Ø = Σ
α
Å � ξξ " ( ` α Å ) g l:w i p,pCt�p j
q hQ� su| w i p g q g tQw)pCq x r�w g sQt ~ g w i w i p v g o�s � p�l 7
� ú&�'� = ΣÅ δ � ξξ # + ΣÅ ! Ä � ξξ " ξξ $ ( `&%(' ) ; ¼ g l w i p p'´1r g w x w g sQt
pCtEpCq h1� sQ| x t ¸ j rCq � l
w x � ~ g w i Ø v g o�s � p�l x w ν = ) 7
δ � ξξ ∼ � S hξξ T � «.¬ Â_Â� ;�¼ g l5w i p�pCtEpCq h1� s�|m|�s�q ��x w g sut¾s�|
s�t�p�v g oQs � p 7 � = Σ
α
� (̀ α)
g l�w i p�p�t�pCq hQ� su|0w i p$� ¢ � f l
g t w i pÂp'´1w)pCq)t x � | g p � v � p�t�w g sutEpCv 7 w i p g t9v g r'pCl α =
=
§ �*������� Tν h x tQv � =
§ �*�+�,�3� U.- pCt�n � p�q x w�p}w i pÂ� ¢ � f
q x v�n g l jLy p�r'w�sQq�l x tQv¾v g oQs � p�lK�;q�p�l�o�p�r'w g3y p � � � Ø g lmw i p
w�s�w x � tQn �@� p�qNsQ|Fw i p�v g oQs � p�l 7 ` Ó / ≡
` Ó −
` / � � i p ��g t gLj� n � g l�w x�� p�tz~ g w i q)p�l�o�p'r�w�w�sO Ø �?w i p$v g o�s � p y1x q gLj
x'� � p�l'� ` Å � ξξ Å � x t9v `
α
� � i p�q
p�|�sQq
pE�*w i p�v g o�s � p x o j
oQq)s x r i¶x �I� s
~*l w�s¾~�sQq � ~ g w i s�t � � x |�p'~ v g l)rCq�p�w)py1x q g�x'� � p�l'� � iEg l$| x r g � g w x w)pCl�r�s�t1l g vQp�q x'� � � w i p10 s�t�w�p j�<x q � s r�s � o�n9w�p�q l g�� n � x w g s�t sQ| w i p ± vEpC|�p'r�w)sut9l
( � �#à (± § ) = ± �
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|�p'r�w g-y p § � ?¡0¢ 5
� Ñ =
¦ � ^ ± ��7�� ± = Tθ − � h ^ σ± j σ± = T b ±×ξξ±
h � ?9�
~ i p�q
p ¦ ����� ¨ g lzw i p g tQw)p h q x � o x q)w¿su| x t�n �@� p�q�� �
pCtEn � pCq x w�p�l>w i p ± l)w�q g o�p�l 7 g tEw�p h pCq � Ñ g l>w i p:r�sHs�q)v g t x w�ps�| � j w i l�w�q g o�pQ�N~ i9g r iÀg l x o x�g q�sQ|�t�p g6h1iQ� s�q g t h � g tEpCl
su|2p � p�r!w�q
sutEl ` Ñ -� ( � ) = � b ± +
� Ñ z
± +
�
ξξ±
x t�v ` Ñ � ( � ) =
=
` Ñ 3� ( � ) +
z
± + ξξ±
� � = ¼ � ±
§ �,�I��� � � � i p¿l
n1oEpCq)l)w�q
nEr j
w�nFq
p�vEpCl�rCq g6� p�v �Q� ¡ �D� � ?9� g l�w i n1l x���g ´Qw�nFq
p¾s�|² l
w�q g oEp�l � θ − b ; ¼ � s�q + l)w�q g o�pCl � θ − b º ¼ � x t9vn�tQo�pCq)w�n9q � pCv,l)w�q g o�p�lNsQ|Dw i p ¸ j rCq � l)w x � ~ i9g r i,x q)p�o x q x � j� p � w�s b
±
�Zl)s4w i9x w
± = 8 È « 9 È g l�w i p�r's�t�r�p�tQw�q x w g sQt
s�|0w i p ± l)w�q g o�pCl 7 8 È g l�w i p g q:t�n �:� p�q 7 9 È g l2w i p�w�sHw x �
tQn �@� p�q:sQ|�w i p ± l
w�q g oEpCl x t1v{w i p ¸ j r�q � l
w x � sQt�pClK� � i ptQn �@� p�qAsQ|4n1t9o�p�q�w)n1q � p�v¾l�w�q g o�pCl � p'w�~�p'pCt � j w i�x t9v�
+
§ j w i ± l
w�q g oEp�l2p���n x � l � Ñ +
� −
���
− � �
� m¯ � ! � ¬ �)©&/ � � � ¬ ¯ ¬�¬ ¯0 6! ����� 9©$� � ���G� �© ¬ �� ���� � �& � �¸ g3� o � p�r�q � l�w x � l0~ g w i z
± = ±ξξ±
�Q~ i p�q�p ± = b « σ±g l x t g tEw�p h p�q'� x q�pÀsQ|,|
q�pC��n9p�t�w$sHr�r'n�q)q)pCt�r'pE� ¢ x q�w g r'n j� x q � � ��w i1g l�s
r'r'n1q�l�s�|�t�p'r�p�l�l g w � |�suq x w�q g3x t h n � x q i sQl
w� x w�w g r'p �
¸ p�rE� >1� � x t9v x � l)sA|�sQq σ± = σ
� x l g l:w � o g r x �s�| ¸ j rCq � l)w x � l2sQt x,i sQl
w � x w)w g r'p�su| x � su~:p�q:l �Q�*� p'w�q � �
��t4l)nQr imx r x l)p:w i p x'� s y p jI� pCtEw g s�tQp�v,p � p�r'w�q)sut � g tQp�l�s�|� sHw i w � o�pClK� ` Ñ -� ( � )
x tQv ` Ñ � ( � ) ��| x ��� g tEw�s,w i p�r � x l�l2s�|p � p�r'w�q)s�t � g t�p�l � b
± +
�
ξξ±
� � = ¼ � ±
§ �2���I� 7 � g l x t g t�w)p jh pCq � ��~ iQg r i r x t � p}r�sQtQl g v�p�q)pCv x l §�� � o x q
w g r � p�l��
~ g w i � r's
sQq�v g t x w)pCl'� � � � i p g q x q�q x t h1� p�t�wK� x l:|�s �I� s
~*l
|
q�s � ¡ �D� ��?9� �1s � p � l�w i p x � h suq g w iQ� 5
� Ñ =
¦ � � ¨ �f� = � ± +−
±
�
~ i p�q
p � Ñ g l�w i p � r's�suq�v g t x w�p��AsQ|�w i p � j w i � g t�pQ�)� g l
w i p � p x t � g tEp*l)pCo x q x w g sut � p x l�n9q
p�v g tmn1t g w�l2su| Tξξ± T �
\��fJ��1eFE=L!_�BEe�`�d�ByL J
� i p;vEpCo�p�tQvEpCt�r�p:su|
±
� s�q ρ
� s�t µ � � n1r i w i p�l x�� pw�s}w i p § � N¡0¢¤¦&>u²,?9¨ � g l x ~�p ��� j vQp y p � sQo�p�v�|
q x r�w x �
l)w�q�nQr�w)n�q�pQ� x v�p y1g � l�w x�g q
r x l�p,~ i sQl
p$l�w�p�o1l�sHr�r'n�q x w x ���
¬ ¯E©-�&�� E¯ �
± = �}« � ≤
§ � � � � x q�p�r's�oEq g�� p g t�w�p jh pCq�l � �°�2w h1g3y p�t � � � w i p ·*¸ r�s�t1| g6h n1q x w g sut�su|@w i p�K� N¡.¢ g l�w i n1l x � N¡.¢ r�q � l�w x � �5~ g w i � p � p'r'w�q)sut9l
o�p�q2r'p ��� x t1vm~ g w i ¢?��X l b
±
� � z
± + � ξξ±
�
��tmw i p*r's ��� sut � � sur'r'n1q�q g t h r x l)p�w iQx w z
±
g l x,� n � j
w g o � p2s
| ξξ±
��¸ p�r�� ?4� w i p�l�w
p�o�l �
~ g v�w i l!� ∆µ = ∆µ(� ^�� ) �r x t � p�|�s�n1tQv �1� v g q�p�r'w x oQo � g r x w g sQt4su|>w i p § � w i p�s�q �¦ �Z� ?9¨ �=r�s�t1l g v�p�q g t h w i p,pCt�pCq hQ� su|�w i p � g tQp j � g tEp�q)p�o�n � j
l g s�t?�
�
(
�
) = ∑Ä
=−∞
∞ � ( T � b ± + � ξξ±
h
)
� � g l�w i p$v g l
w x t�r'p � p�w)~:p�p�t g t�w�p�q x r�w g t h � g t�p�l � � x l�w i p§�� o x�g q�o�s�w�p�t�w g�x � � � iEg l�oQq)s�vQnQr'p�l
∆µ =
= � ∑Ñ
=
�
∞ �
(
�
( � �
−
§
) −
���
( � �
) +
�
( � �
+
§
)) �
~ i p�q)p � = ±
�
+− � g l�w i p o�p�q g s�v sQ|}w i p � g tEpCl��
o x w�w�p�q�t°� � i p,p'´FoQq)pCl)l g sQt g t{w i p � q x r � p'w�l g l�o�sQl g w g3y pE�
l g tQr'p �
(
�
)
g l x r�sQt y p'´�|�n�t�r�w g sut g t¿w i p5r x l�pAn�tEvQp�q
r's�tEl g vEpCq x w g sQtD� · p�t�p�q x �I� � � ∆µ( ��« � )
x q
p:p'´1oQq)p�l�l)pCv g t
w�p�q � l,s�|8� ÈBȱ (
�
)
�E�µx l � g�h�i w � suv g | g r x w g sQt�su|@w i p § �
w i p'suq � �
�F\��Yv��9`�B
^Fd�}4J�L|B
^Qb z!e-`�L!_ov
a�`�bxJK`�_)`oBH^xLKe�_!eØa�^4L,e-^5_o}4J
�9`�a�cE^1b LÍ_oBH_oJ4a0z2_2}xJC@ �! z
`�a0L�J�^�" J�EFJHd�_�`�a�^I }kB%L�J
� i p x � h sQq g w i9� � ?9� r x t � p�p'´Qw�p�t1v�pCvs y pCq w i p
~ i s � p
±
q x t h pQ� ¼ ¹
±
º � ��oQq�s yQg vEp�v�w i p rCq � l)w x �
~ g w i sQtEp*o x q)w g r � p�oQp
q0r'p �
�N� � ¸ ′
j r
q � l�w x � �*~ g w i ¢°��X lb
±
� z
± + ξξ±
� ~ iQg r i}x q g l)p�l x w
± =
§A�
θ = b ± σ±
� g l
l)w x'� � p � g � pE� g w g l x tQsHw i pCq ¸ j r�q � l�w x ��� s�q � p'w x l)w x'� � pE�� i1g l{|�s �I� s
~*l{|
q
s � w i p}| x r'wAw iQx w g � s�~ g t h w�sÂw i p
r's x � l
r'p�tQr'p$s�|;vEp�|�p�r'w�s�t1l ��x r�q�s�l)r�s�o g r x ��� � l ��x �I� y1x q gLjx w g s�tEl g t θ
h p�t�pCq x w)pQ� x w x t �
±
� § � v�p�|�p'r�w�l0s�t � � 7 g�g �
w i p�l
p §�� vEpC|�p'r'w�l'� x r�r'suq�v g t h w�s5s
n1q:r's � o�nQw)pCq r x � r�n j� x w g sQtQlK� i9x'y p*w i p�l x
� p ¢?��X � b
±
�=|�suq x ���
±
�
0{s�q
p�s y p'q'�=v�n�p,w
s � � p�w x � l�w x!�1g � g w � s
|�w i p ¸ ′
j r�q � l
w x �
w i p x � h s
q g w iE� ��?E� i s � vQlDs y p�q x θ q x t h p x v � x r�p�t
w>w
s�w i pg t�w
p�q y�x � T b − σ−
� b + σ+ T �,�
t�l
nEr i�x r x l
p ¡ �Z� ��?E�
vEp�w)pCq �*g t�pCl x��@g ´1w)n1q
p}sQ|ml)w�q g o�pCl{s�|At�p'~ h p's � p�w�q �
~ iQg r izx q)p,r iQx q x r�w)pCq g ��p�v �Q� x t�p'~¤w�q g o � p,s�| y p'r'w�suq�lC�b
±′ �
z
±′ � ξξ±′ �.w i p x t x
� s h nQp�l�su| b
±
� z
±
� ξξ±
� x t9vzw i p
± l�w�q g o�p�l r�sQt�r'p�tQw�q x w g s�t
±′ = Tθ − b ± σ± T «$T b ±′ ×ξξ±′ T �
Ú$#&% � Î ��Î Ì�Ò���Î ��Ì�Î Ìo�������������-ÒÍÊØÉ��IÐCÙ�Ú'Ú�ÚuÐ�Ó�Æ����
Ð��u×$���
Ú
� q x t9l g w g sutm|
q�s � s�tQp h p�s � p'w�q � w)s x t�s�w i p�q g l0r�s�tQw g t�n j
sun9l g t θ l g tEr'p ±′
h s�p�l2w)s$��pCq)s4~ i p�t θ → b + σ±
�� sQt�w g tQnEs
nFl � � p'´1w)pCtQv g t h w i p x � h sQq g w iQ� � ?Q� g t4w i p�*x t9t�p�q.l i s�~�t x'� s y pE�u~@p�s � w x�g t�w i p � e jL� q x t�r i � � ~:pg tQw�q
sQv�nQr'p}w i p g t9v�p�´ e x!h�x�g t � ~ iQg r i r's � oQq g l)pCl x �I�� � p'w x � l�w x�� � p,l
w�q�nEr�w)n1q)pCl ¡ �D� � ?Q� r'sut9t�p'r�w)pCv g tAr'sutEw g3j
tQn g w � ~ g w i w i p:l)w x q
w g t h ¸ j r�q � l�w x � � � i p�r'sQq�q)pCl)o�sQtQv g t h
pCtEpCq h1� � p d (θ) �{r x t � p p x l g � � |�s
nFtQv g tÃw�p�q � lÂs�|
� ÈBȱ (
�
) ��n�l g t h ¡ �D� ��?9� ����l x q)n � pE�uw i p�q
p:p�´ g l)w.v g |
|�p�q)pCt�w¸ j r�q � l�w x � l � p � sut hEg t h w)szw i p�l x�� p�e jL� q x t�r i � ( t�w i p
suw i p�q iQx tQv°� x l�~@p i9x'y pmr�s � o�nQw�p�v°� g tEw�p�q�l)p'r�w g sut9l�s�|
v g |
|�p�q
p�tEw p d (θ) � x t9v i p�tEr�pE� ��� ¬ ���
© ��� � � ¬ ¯E©�� ¬ � � � ¬ �'©-�� ¬ #,� ¬ © ¬ ¯y ����)©&�
�� �� �& �Q¯ ¬ �
¯ �k�F� � µ � ¬ s � x w � o�pµs�|
oQs � �Q� s�q)o i9g l � � � x q)p{n1t g-y pCq)l x ��� � oQq
p�l)pCt�w g t w i p � � ?¡0¢ � �
¸ p�pmp'´ x�� o � p g t ¸ p'rQ� >9� � � i p�v�pCo�p�t9v�pCtEr'p�s�|p Û�sQt θ
g l@w i p�|�nFt�r�w g sut ~ i9g r i r's � oEq g l)p�l x ��� l)w x'� � p
oQs�q�w g s�tEl2sQ| x �I� p d (θ) �� i n1lK�Qs�~ g t h w)s*w i p ')(+* v�p�l)rCq g3� p�v x'� s y p:w i p ·*¸
s�|°w i p � � N¡�¢ g l2|�n �I� � v�p'w�p�q ��g tEpCv �1� w i p ¸ j r�q � l�w x � l¢?��X lK� �
κλ
d �=w i p � v g q)p�r'w�s�q�l��Z� b
±
d � x t9vAw i p$v g l�o � x r'p j� p�tQw y p�r'w�sQq)l�� ξξ±
d � w)s h p'w i pCq{~ g w i w i p�l)p�w{su| p d (θ)g tQw)pCq)l)p�r'w g sQt�o�s g tQw�l,~ iEg r i x q�p5w i pAsQt � � ·*¸ r iQx q x r j
w�p�q g l
w g rClmr iQx t h1g t h s�tÂl �*x ��� y1x q g�x w g sQtQl g t � ( [ ) ��� �I�w i pCl�p;�En x tQw g w g p�l�r x t � p�r's � o�nQw�p�v,s�t�w i p �1x l g l>su| ¡ �°���³1� x t1v ¡ �D� � ?9� �Q�¤x l�p � | j r'sQtQl g l
w)pCtEw�oQq)s
r'pCvEn1q�pQ�
| g t1v g t h w i p ¸ j r�q � l)w x � l�w)s h p'w i pCq�~ g w i w i p�e jL� q x tQr i p�lK�
¥�p iQx'y p¿|�sHn1t9v�w i p ·�¸ |�s�qmw�q g�x t h n � x q x tEv¾l���n x q
pi s�l�w � x w)w g r'pCl x l:~�p ��� x l�|�sQq x t�n �:� pCq:s�|�w i sul)p,~ g w i
r�p�tQw�q x � l �1��� p�w�q � sut � � � � i p}r�s � o�nQw x w g sQt i9x lÀtEs
w
q�p y p x � p�v�o9q g t�r g o x � v g |
|�p�q�p�t�r'pCl � p'w�~@p�p�t ·�¸ o9q
sQo�p�q j
w g p�lzs�| � � ?¡0¢ ~ g w i v g |
|�pCq)p�t�w h p�s � p�w�q � s�| i sQl
w� x w�w g r'pClK� x w � p x l)wz|�suq{w i sul)p}~ iQg r i¶x q
pÂt�s�w l g6h t g | g3j
r x t�w � �Ax t g l)s
w�q�s�o g rE�
�9\����0B�D I4EFJ
f p�q
p�~@p g �I� n1l)w�q x w�p�w i p x'� s y p h pCt�pCq x � q)pCl�n � w�l>~ g w ix w�q g�x t h n � x q i s�l)w � x w�w g r'p ��� f '0� �=� ��� w�q g�x t h n � x q � x w j
w g r'pCl5sQt¾w i p � f ' x q
p�tEp�r'pCl)l x q g � � ¸ j r�q � l)w x � l'� � iQg l
|�s ��� s
~*l2|
q�s � w i p*| x r'w.w iQx w g w g l0w i p:w�q g3x t h n � x q � x w�w g r�p
w i9x w�q)p x � g ��pCl4w i p¿¯ � � � � �9© � p�t�p�q hQ�¾��g t g3� n � sQ|�w i p
l � l)w�p � ~ i s�l�p¶p � p'r'w�q)sut9l x q
p |
q)p�p¶w)s � s y pE� ¸ nQr i¸ j r�q � l�w x � l x q�p � �0� j r�q � l)w x � l!�m~ g w i ¢?��X l�� B � + W �4�� B � + W�� x tQv θ = � � + � − � � �0� x q�p x q �1g w�q x q �g tQw)p h p�q�lK� B �� �� � g l x w�q g o � pmsu| � f '¾¢N�.X l@~ i9g r i}x q
p
pC�En x � g t�w i p � s�vQn � n1l x tQv,|�sQq �¾x t x t h � p2s�| §�� ¼�� ~ g w ip x r i s�w i pCq � �.�*l g t h w i p�oQq�s�r�p�v�nFq
p�v g l)r�n1l)l)pCv g t ¸ p'rE�Á �9~�p iQxKy p�|�sun9tQvmw iEx w x ��� ¼ � j r�q � l�w x � l � p � sQt h w�s4w i pl x�� p:e j�� q x tEr i � w i p ��xHg t � q x t�r i � ��~ i9g r i r�s y pCq�l�w i p
q x t h p ? ≤ θ º ∞ � � i p ¸
′
j r�q � l)w x � l}s�|�w i p ¼ � j sutEpClx q
p ¸ j rCq � l)w x � lÃw�sHsD� � i p � sur'r'n1q x w θ = ( � +
§
)
(
�
≤ º ∞)
x tEv i1x'y p ¢N�.X l B κ
� ( +
§
)
B
λ
�
κ � λ =
§ �� � ±�7 κ ≠ λ
� � � i p:l�w�q g o�p l�w�q)nQr'w�n1q)p�l ��?9� i1x'y p�w i p;l x
� p¢��4X � B κ �
|3s
q x
���
θ s
|9w i p g tHw�pÍq yux ��¦ ( −
§
) � ( � +
§
)
¨ �
w i p g q ξξ±
� p g t h ±
W
λ (κ ≠ λ) �
¥ i pCt_�0� ≠ ¼ �xe jL� q x t�r i p�l@su|�v g |
|�pCq)p�t�w �<� � j r�q � l jw x � l x q
p,v g l)w g t�r�wK� � i p � vQsmt�s�w i1x'y p � nEw�n x � g t�w)pCq�l
p'r j
w g sut9l'� � n9w x ��� g tEw�p�q�l)p'r�w@w i p ��x�g t � q x t�r i �?w i p g tQw)pCq j
l)p�r'w g sQtQl�s�r�r'n1q�q g t h x w�q x w i p�q:l �@x ��� r'sutEr�p�t�w�q x w g sut9l�su|
w i p:�0� � j rCq � l�w x � l5� ± l)w�q g o�p�lK����t4s�w i p�q2~:sQq�v9l'�9w i p g tQw)pCq jy1x � l�su| �0� � j r�q � l
w x � l,l�w x'�Fg � g w � � �0� ≠ ¼ � � x t9v�r�s�q�q
p jl�o�sut9v g t h � �}�*x�g t jL� q x t�r i�� p'w x l�w xK�1g � g w � �.w)n1q�t}sHn1w,w)s� p,t x q)q)s
~m�
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| id | nasplib_isofts_kiev_ua-123456789-139014 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0132-6414 |
| language | English |
| last_indexed | 2025-12-07T18:13:53Z |
| publishDate | 1999 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Slutskin, A.A. Slavin, V.V. Kovtun, H.A. 2018-06-19T18:28:06Z 2018-06-19T18:28:06Z 1999 The ground state of the "frozen" electron phase in two-dimensional narrow-band conductors with a long-range interelectron repulsion. Stripe formation and effective lowering of dimension / A.A. Slutskin, V.V. Slavin, H.A. Kovtun // Физика низких температур. — 1999. — Т. 25, № 8. — С. 936-943. — Бібліогр.: 13 назв. — англ. 0132-6414 https://nasplib.isofts.kiev.ua/handle/123456789/139014 In narrow-band conductors a weakly screened Coulomb interelectron repulsion can supress narrow-band electrons` hopping, resulting in formation of a "frozen" electron phase which differs principally from any known macroscopic self-localized electron state including the Wigner crystal. In a zero-bandwidth limit the "frozen" electron phase is a classical lattice system with a long-range interparticle repulsion. The ground state of such systems has been considered in the case of two dimensions for an isotropic pair potential of the mutual particle repulsion. It has been shown that particle ordering into stripes and effective lowering of dimension resides universally in the ground state for any physically reasonable pair potential and for any geometry of the conductor lattice. On the basis of this fact a rigorous general procedure to describe the ground state fully has been formulated. Arguments have been adduced that charge ordering into stripes in high-Tc superconductors testifies to the presence of a "frozen" electron phase in these systems. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Низкоразмерные и неупорядоченные системы The ground state of the "frozen" electron phase in two-dimensional narrow-band conductors with a long-range interelectron repulsion. Stripe formation and effective lowering of dimension Article published earlier |
| spellingShingle | The ground state of the "frozen" electron phase in two-dimensional narrow-band conductors with a long-range interelectron repulsion. Stripe formation and effective lowering of dimension Slutskin, A.A. Slavin, V.V. Kovtun, H.A. Низкоразмерные и неупорядоченные системы |
| title | The ground state of the "frozen" electron phase in two-dimensional narrow-band conductors with a long-range interelectron repulsion. Stripe formation and effective lowering of dimension |
| title_full | The ground state of the "frozen" electron phase in two-dimensional narrow-band conductors with a long-range interelectron repulsion. Stripe formation and effective lowering of dimension |
| title_fullStr | The ground state of the "frozen" electron phase in two-dimensional narrow-band conductors with a long-range interelectron repulsion. Stripe formation and effective lowering of dimension |
| title_full_unstemmed | The ground state of the "frozen" electron phase in two-dimensional narrow-band conductors with a long-range interelectron repulsion. Stripe formation and effective lowering of dimension |
| title_short | The ground state of the "frozen" electron phase in two-dimensional narrow-band conductors with a long-range interelectron repulsion. Stripe formation and effective lowering of dimension |
| title_sort | ground state of the "frozen" electron phase in two-dimensional narrow-band conductors with a long-range interelectron repulsion. stripe formation and effective lowering of dimension |
| topic | Низкоразмерные и неупорядоченные системы |
| topic_facet | Низкоразмерные и неупорядоченные системы |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/139014 |
| work_keys_str_mv | AT slutskinaa thegroundstateofthefrozenelectronphaseintwodimensionalnarrowbandconductorswithalongrangeinterelectronrepulsionstripeformationandeffectiveloweringofdimension AT slavinvv thegroundstateofthefrozenelectronphaseintwodimensionalnarrowbandconductorswithalongrangeinterelectronrepulsionstripeformationandeffectiveloweringofdimension AT kovtunha thegroundstateofthefrozenelectronphaseintwodimensionalnarrowbandconductorswithalongrangeinterelectronrepulsionstripeformationandeffectiveloweringofdimension AT slutskinaa groundstateofthefrozenelectronphaseintwodimensionalnarrowbandconductorswithalongrangeinterelectronrepulsionstripeformationandeffectiveloweringofdimension AT slavinvv groundstateofthefrozenelectronphaseintwodimensionalnarrowbandconductorswithalongrangeinterelectronrepulsionstripeformationandeffectiveloweringofdimension AT kovtunha groundstateofthefrozenelectronphaseintwodimensionalnarrowbandconductorswithalongrangeinterelectronrepulsionstripeformationandeffectiveloweringofdimension |