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Уважаемые сотрудники ИТФ,<br>
<br>
На заседании Ученого совета в пятницу 31 января будут заслушаны
доклады:<br>
<br>
1) Я.В. Фоминов, А.А. Мазаник, М.В. Разумовский<br>
<font size="+1"><b>Поверхностная плотность состояний в
сверхпроводниках с неоднородной константой взаимодействия</b></font><br>
<br>
Рассмотрена задача о сверхпроводнике с поверхностным подавлением
константы взаимодействия БКШ <span class="MathJax"
id="MathJax-Element-1-Frame" tabindex="0" style="position:
relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo
stretchy="false">(</mo><mi>x</mi><mo
stretchy="false">)</mo></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-1" style="width: 1.424em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 1.563em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.666em, 1001.51em,
2.947em, -1000em); top: -2.557em; left: 0em;"><span
class="mrow" id="MathJax-Span-2"><span class="mi"
id="MathJax-Span-3" style="font-family: STIXGeneral;
font-style: italic;">λ</span><span class="mo"
id="MathJax-Span-4" style="font-family: STIXGeneral;">(</span><span
class="mi" id="MathJax-Span-5" style="font-family:
STIXGeneral; font-style: italic;">x<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.003em;"></span></span><span
class="mo" id="MathJax-Span-6" style="font-family:
STIXGeneral;">)</span></span><span style="display:
inline-block; width: 0px; height: 2.557em;"></span></span></span><span
style="display: inline-block; overflow: hidden;
vertical-align: -0.218em; border-left: 0px solid; width:
0px; height: 0.877em;"></span></span></nobr></span>.
Аналитически найдены щель в поверхностной плотности состояний,
поведение плотности состояний <span class="MathJax"
id="MathJax-Element-2-Frame" tabindex="0" style="position:
relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi>ν</mi><mo
stretchy="false">(</mo><mi>E</mi><mo
stretchy="false">)</mo></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-7" style="width: 1.566em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 1.776em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.668em, 1001.73em,
2.947em, -1000em); top: -2.557em; left: 0em;"><span
class="mrow" id="MathJax-Span-8"><span class="mi"
id="MathJax-Span-9" style="font-family: STIXGeneral;
font-style: italic;">ν</span><span class="mo"
id="MathJax-Span-10" style="font-family: STIXGeneral;">(</span><span
class="mi" id="MathJax-Span-11" style="font-family:
STIXGeneral; font-style: italic;">E<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.023em;"></span></span><span
class="mo" id="MathJax-Span-12" style="font-family:
STIXGeneral;">)</span></span><span style="display:
inline-block; width: 0px; height: 2.557em;"></span></span></span><span
style="display: inline-block; overflow: hidden;
vertical-align: -0.218em; border-left: 0px solid; width:
0px; height: 0.876em;"></span></span></nobr></span> выше
щели, "вертикальная" особенность плотности состояний на энергии,
равной объемному параметру порядка <span class="MathJax"
id="MathJax-Element-3-Frame" tabindex="0" style="position:
relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi
mathvariant="normal">Δ</mi><mn>0</mn></msub></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-13" style="width: 0.998em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 1.136em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(0.107em, 1001.14em,
1.367em, -1000em); top: -0.994em; left: 0em;"><span
class="mrow" id="MathJax-Span-14"><span class="msubsup"
id="MathJax-Span-15"><span style="display:
inline-block; position: relative; width: 1.151em;
height: 0px;"><span style="position: absolute; clip:
rect(3.09em, 1000.68em, 4.19em, -1000em); top:
-3.977em; left: 0em;"><span class="mi"
id="MathJax-Span-16" style="font-family:
STIXGeneral;">Δ</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span><span
style="position: absolute; top: -3.827em; left:
0.722em;"><span class="mn" id="MathJax-Span-17"
style="font-size: 70.7%; font-family:
STIXGeneral;">0</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span></span></span></span><span
style="display: inline-block; width: 0px; height:
0.994em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.203em;
border-left: 0px solid; width: 0px; height: 0.859em;"></span></span></nobr></span>,
а также пертурбативная поправка к плотности состояний на более
высоких энергиях. Щель в поверхностной плотности состояний
параметрически отличается от поверхностного значения параметра
порядка из-за различия пространственного масштаба <span
class="MathJax" id="MathJax-Element-4-Frame" tabindex="0"
style="position: relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>r</mi><mi>c</mi></msub></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-18" style="width: 0.714em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 0.781em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(0.34em, 1000.78em,
1.365em, -1000em); top: -0.994em; left: 0em;"><span
class="mrow" id="MathJax-Span-19"><span class="msubsup"
id="MathJax-Span-20"><span style="display:
inline-block; position: relative; width: 0.778em;
height: 0px;"><span style="position: absolute; clip:
rect(3.323em, 1000.41em, 4.19em, -1000em); top:
-3.977em; left: 0em;"><span class="mi"
id="MathJax-Span-21" style="font-family:
STIXGeneral; font-style: italic;">r<span
style="display: inline-block; overflow:
hidden; height: 1px; width: 0.023em;"></span></span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span><span
style="position: absolute; top: -3.827em; left:
0.389em;"><span class="mi" id="MathJax-Span-22"
style="font-size: 70.7%; font-family:
STIXGeneral; font-style: italic;">c</span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span></span></span></span><span
style="display: inline-block; width: 0px; height:
0.994em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.201em;
border-left: 0px solid; width: 0px; height: 0.652em;"></span></span></nobr></span>,
на котором подавляется <span class="MathJax"
id="MathJax-Element-5-Frame" tabindex="0" style="position:
relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo
stretchy="false">(</mo><mi>x</mi><mo
stretchy="false">)</mo></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-23" style="width: 1.424em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 1.563em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.666em, 1001.51em,
2.947em, -1000em); top: -2.557em; left: 0em;"><span
class="mrow" id="MathJax-Span-24"><span class="mi"
id="MathJax-Span-25" style="font-family: STIXGeneral;
font-style: italic;">λ</span><span class="mo"
id="MathJax-Span-26" style="font-family: STIXGeneral;">(</span><span
class="mi" id="MathJax-Span-27" style="font-family:
STIXGeneral; font-style: italic;">x<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.003em;"></span></span><span
class="mo" id="MathJax-Span-28" style="font-family:
STIXGeneral;">)</span></span><span style="display:
inline-block; width: 0px; height: 2.557em;"></span></span></span><span
style="display: inline-block; overflow: hidden;
vertical-align: -0.218em; border-left: 0px solid; width:
0px; height: 0.877em;"></span></span></nobr></span>, и длины
когерентности. Вертикальная особенность означает точку перегиба с
бесконечной производной на кривой <span class="MathJax"
id="MathJax-Element-6-Frame" tabindex="0" style="position:
relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi>ν</mi><mo
stretchy="false">(</mo><mi>E</mi><mo
stretchy="false">)</mo></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-29" style="width: 1.566em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 1.776em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.668em, 1001.73em,
2.947em, -1000em); top: -2.557em; left: 0em;"><span
class="mrow" id="MathJax-Span-30"><span class="mi"
id="MathJax-Span-31" style="font-family: STIXGeneral;
font-style: italic;">ν</span><span class="mo"
id="MathJax-Span-32" style="font-family: STIXGeneral;">(</span><span
class="mi" id="MathJax-Span-33" style="font-family:
STIXGeneral; font-style: italic;">E<span
style="display: inline-block; overflow: hidden;
height: 1px; width: 0.023em;"></span></span><span
class="mo" id="MathJax-Span-34" style="font-family:
STIXGeneral;">)</span></span><span style="display:
inline-block; width: 0px; height: 2.557em;"></span></span></span><span
style="display: inline-block; overflow: hidden;
vertical-align: -0.218em; border-left: 0px solid; width:
0px; height: 0.876em;"></span></span></nobr></span> при <span
class="MathJax" id="MathJax-Element-7-Frame" tabindex="0"
style="position: relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><msub><mi
mathvariant="normal">Δ</mi><mn>0</mn></msub></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-35" style="width: 2.773em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 3.125em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.67em, 1003.13em,
2.93em, -1000em); top: -2.557em; left: 0em;"><span
class="mrow" id="MathJax-Span-36"><span class="mi"
id="MathJax-Span-37" style="font-family: STIXGeneral;
font-style: italic;">E<span style="display:
inline-block; overflow: hidden; height: 1px; width:
0.023em;"></span></span><span class="mo"
id="MathJax-Span-38" style="font-family: STIXGeneral;
padding-left: 0.313em;">=</span><span class="msubsup"
id="MathJax-Span-39" style="padding-left: 0.313em;"><span
style="display: inline-block; position: relative;
width: 1.151em; height: 0px;"><span style="position:
absolute; clip: rect(3.09em, 1000.68em, 4.19em,
-1000em); top: -3.977em; left: 0em;"><span
class="mi" id="MathJax-Span-40"
style="font-family: STIXGeneral;">Δ</span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span><span
style="position: absolute; top: -3.827em; left:
0.722em;"><span class="mn" id="MathJax-Span-41"
style="font-size: 70.7%; font-family:
STIXGeneral;">0</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span></span></span></span><span
style="display: inline-block; width: 0px; height:
2.557em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.203em;
border-left: 0px solid; width: 0px; height: 0.859em;"></span></span></nobr></span>
с зависимостью, определяемой квадратным корнем при отклонении <span
class="MathJax" id="MathJax-Element-8-Frame" tabindex="0"
style="position: relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-42" style="width: 0.572em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 0.639em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.691em, 1000.64em,
2.77em, -1000em); top: -2.557em; left: 0em;"><span
class="mrow" id="MathJax-Span-43"><span class="mi"
id="MathJax-Span-44" style="font-family: STIXGeneral;
font-style: italic;">E<span style="display:
inline-block; overflow: hidden; height: 1px; width:
0.023em;"></span></span></span><span style="display:
inline-block; width: 0px; height: 2.557em;"></span></span></span><span
style="display: inline-block; overflow: hidden;
vertical-align: -0.063em; border-left: 0px solid; width:
0px; height: 0.7em;"></span></span></nobr></span> от <span
class="MathJax" id="MathJax-Element-9-Frame" tabindex="0"
style="position: relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi
mathvariant="normal">Δ</mi><mn>0</mn></msub></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-45" style="width: 0.998em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 1.136em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(0.107em, 1001.14em,
1.367em, -1000em); top: -0.994em; left: 0em;"><span
class="mrow" id="MathJax-Span-46"><span class="msubsup"
id="MathJax-Span-47"><span style="display:
inline-block; position: relative; width: 1.151em;
height: 0px;"><span style="position: absolute; clip:
rect(3.09em, 1000.68em, 4.19em, -1000em); top:
-3.977em; left: 0em;"><span class="mi"
id="MathJax-Span-48" style="font-family:
STIXGeneral;">Δ</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span><span
style="position: absolute; top: -3.827em; left:
0.722em;"><span class="mn" id="MathJax-Span-49"
style="font-size: 70.7%; font-family:
STIXGeneral;">0</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span></span></span></span><span
style="display: inline-block; width: 0px; height:
0.994em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.203em;
border-left: 0px solid; width: 0px; height: 0.859em;"></span></span></nobr></span>.
Коэффициенты при этой зависимости различны при <span
class="MathJax" id="MathJax-Element-10-Frame" tabindex="0"
style="position: relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo><</mo><msub><mi
mathvariant="normal">Δ</mi><mn>0</mn></msub></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-50" style="width: 2.773em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 3.125em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.67em, 1003.13em,
2.93em, -1000em); top: -2.557em; left: 0em;"><span
class="mrow" id="MathJax-Span-51"><span class="mi"
id="MathJax-Span-52" style="font-family: STIXGeneral;
font-style: italic;">E<span style="display:
inline-block; overflow: hidden; height: 1px; width:
0.023em;"></span></span><span class="mo"
id="MathJax-Span-53" style="font-family: STIXGeneral;
padding-left: 0.313em;"><</span><span
class="msubsup" id="MathJax-Span-54"
style="padding-left: 0.313em;"><span style="display:
inline-block; position: relative; width: 1.151em;
height: 0px;"><span style="position: absolute; clip:
rect(3.09em, 1000.68em, 4.19em, -1000em); top:
-3.977em; left: 0em;"><span class="mi"
id="MathJax-Span-55" style="font-family:
STIXGeneral;">Δ</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span><span
style="position: absolute; top: -3.827em; left:
0.722em;"><span class="mn" id="MathJax-Span-56"
style="font-size: 70.7%; font-family:
STIXGeneral;">0</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span></span></span></span><span
style="display: inline-block; width: 0px; height:
2.557em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.203em;
border-left: 0px solid; width: 0px; height: 0.859em;"></span></span></nobr></span>
и <span class="MathJax" id="MathJax-Element-11-Frame" tabindex="0"
style="position: relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>></mo><msub><mi
mathvariant="normal">Δ</mi><mn>0</mn></msub></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-57" style="width: 2.773em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 3.125em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.67em, 1003.13em,
2.93em, -1000em); top: -2.557em; left: 0em;"><span
class="mrow" id="MathJax-Span-58"><span class="mi"
id="MathJax-Span-59" style="font-family: STIXGeneral;
font-style: italic;">E<span style="display:
inline-block; overflow: hidden; height: 1px; width:
0.023em;"></span></span><span class="mo"
id="MathJax-Span-60" style="font-family: STIXGeneral;
padding-left: 0.313em;">></span><span
class="msubsup" id="MathJax-Span-61"
style="padding-left: 0.313em;"><span style="display:
inline-block; position: relative; width: 1.151em;
height: 0px;"><span style="position: absolute; clip:
rect(3.09em, 1000.68em, 4.19em, -1000em); top:
-3.977em; left: 0em;"><span class="mi"
id="MathJax-Span-62" style="font-family:
STIXGeneral;">Δ</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span><span
style="position: absolute; top: -3.827em; left:
0.722em;"><span class="mn" id="MathJax-Span-63"
style="font-size: 70.7%; font-family:
STIXGeneral;">0</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span></span></span></span><span
style="display: inline-block; width: 0px; height:
2.557em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.203em;
border-left: 0px solid; width: 0px; height: 0.859em;"></span></span></nobr></span>,
поэтому особенность оказывается асимметричной.<br>
Доклад основан на работе [Ya.V. Fominov, A.A. Mazanik, M.V.
Razumovskiy, Phys. Rev. B 100, 224513 (2019)].<br>
<br>
<br>
2) Игорь Лукьянчук<br>
<font size="+1"><b>Ferroelectric as topological material: Hopf
fibrations, multilevel logic, negative capacitance and THz
vibrations</b></font><br>
<br>
Formation of unusual textures of polarization is imminent for
nano-scale ferroelectric samples, films, rods, and granules, where
the depolarization surface effects play the crucial role. The
topologically protected stability of such textures and security of
information storage is coming from polarization vorticity, provided
by condition of absence of the energetically-unfavorable
depolarization charge. The endurance of ferroelectric formations
with respect to high-energy irradiation makes them ideal for the
aerospace industry, and the periodic domain walls structures can be
used as a platform for terahertz radiation generators and detection
devices. Polarization domains that alternate the surface charge
distribution can be formed in ferroelectric thin films as an
effective mechanism to confine the depolarization field to the
near-surface layer and diminish the depolarization energy. However
their existence have long been considered as barely possible until
the direct theoretical predictions [1-3] and experimental evidences
[4-6] in thin oxide-based superlattices. Very recently we have
demonstrated that the effective capacitance of ferroelectric layers
with domains is negative [7]. This effect is explained by the
opposite orientation of the depolarizing field with respect to the
field-induced averaged polarization. This phenomenon is currently
considered as the platform for realization of the dissipation-free
high performance nano-circuits [8]. Moreover, in sub-THz region the
resonance plasmonic effect can be induced by oscillating domain
walls [9] and can be suitable for design of the ultra-small
low-energy THz chips. Multi-vortex [10] and skyrmion [11] states can
be formed inside ferroelectric cylindrical nano-dots and nanorods to
reduce the depolarization energy. We study the stability of such
states and demonstrate that the topological class of the most stable
topological excitations can be driven by the geometrical and
electrical parameters of the system, external field and temperature.
We target the multi-domain and topological excitations in FE
nanodots as a platform for IT-secured multivalued logic units,
breaking ground for neuromorphic computing [12,13].<br>
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(2000).<br>
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Rev. Lett., 94, 047601 (2005)<br>
[3] I. Luk'yanchuk, L. Lahoche, and A. Sene, Phys. Rev. Lett., 102,
147601 (2009)<br>
[4] S. K. Streiffer, J. A. Eastman, D. D. Fong et al., Phys. Rev.
Lett. 89, 067601 (2002);<br>
[5] S. O. Hruszkewycz, M. J. Highland, et al., Phys. Rev. Lett.110,
177601 (2013).<br>
[6] Yadav, A. K., Nelson,et al.. Nature, 530 (7589), 198. (2016)<br>
[7] P. Zubko, M. Hadjimichael, S. Fernandez-Pena, A. Sené, I.
Luk’yanchuk, J.-M. Triscone & J. Íñiguez, Nature, 534, 524
(2016)<br>
[8] Khan, A. I., Chatterjee, K., Wang B. et al. Nature Materials 14,
182–186 (2015).<br>
[9] I. Luk'yanchuk, A.Pakhomov, A.Sené, A. Sidorkin, V. Vinokur,
arXiv:1410.3124<br>
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