On Behind the Physics of the Thermoelectricity of Topological Insulators

Abstract

Topological Insulators are the best thermoelectric materials involving a sophisticated physics beyond their solid state and electronic structure. We show that exists a topological contribution to the thermoelectric effect that arises between topological and thermal quantum field theories applied at very low energies. This formalism provides us with a quantized topological mass proportional to the temperature T leading, through an electric potential V, to a Seebeck coefficient where we identify an anomalous contribution that can be associated to the creation of real electron-hole Schwinger’s pairs close to the topological bands. Finally, we find a general expression for the dimensionless figure of merit of these topological materials, considering only the electronic contribution, getting a value of 2.73 that is applicable to the Bi 2 Te 3 , for which it was reported a value of 2.4 after reducing its phononic contribution, using only the most basic topological numbers (0 or 1).

Emergent topological fields and relativistic phonons within the thermoelectricity in topological insulators

“…Both things are conceptually very different, one worked with Chern numbers and the other with genus using Gauss–Bonnet theorem; but physically they are connected linking the singularities of the bands and the real spacetime. Consistently, by making the same substitution we also find an expression for the electric field inside TIs, obtaining a value that determines the field needed to force a topological phase transition and which is again related with the corresponding critical field in the vacuum needed to create electron–hole pairs 4 , 37 , 38 . This is all that we can have for the electromagnetic fields within the TI with constant , they are fixed and hence can not intervene in the dynamics, but we can overcome this difficulty just introducing phonons that move the different topological sectors.…”

“…The family of 3DTIs Bi Se , Bi Te , Sb Te has a special interest by the fact of being topological besides including on their members the most efficient thermoelectric material up to now. The highly conducting edge states, provided by the topology, are predicted to be responsible for their high figure of merit in low thermal conductivity conditions 4 , 20 . However, this must not be the unique ingredient to explain the thermoelectricity in these materials where the coexistence of time-reversal symmetry and non-zero temperatures, which usually involves entropy change, might cause a conflict.…”

“…Its highest value is around 2.4 at 300 K for Bi Te /Sb Te superlattices 2 . These structures are built with topological insulators for decreasing the thermal conductivity as much as possible and take advance of the highly conducting edge channels present in TIs to provide a high efficient thermoelectric response 3 , 4 . Nevertheless, the technological applications still need a higher value to the previously mentioned 5 .…”

Дефекты межслоевой поверхности и термоэлектрические свойства в слоистых пленках топологических изоляторов n-Bi-=SUB=-2-=/SUB=-Te-=SUB=-2.7-=/SUB=-Se-=SUB=-0.15-=/SUB=-S-=SUB=-0.15-=/SUB=-

“…Увеличение |r eff | в пленках n-Bi 2 Te 2.7 Se 0.15 S 0.15 определяет более резкую энергетическую зависимость времени релаксации τ по сравнению с объемным материалом, что объясняется эффектом фильтрации носителей заряда и приводит к росту коэффициента Зеебека в области температур 80−240 K (рис. 4, кривые 1, 2) в пленках благодаря более широкому энергетическому спектру электронов в топологических изоляторах [5,9,13,22]. n-Bi 2 Te 2.7 Se 0.15 S 0.15 , чем в объемном образце во всем исследованном интервале температур (рис.…”

“…Сильное спин-орбитальное взаимодействие и нетривиальная зонная структура фермионов Дирака в топологических изоляторах являются причиной усиления энергетической зависимости спектрального распределения длин свободного пробега электронов в исследуемых материалах и, соответственно, увеличения коэффициента Зеебека за счет фильтрации носителей заряда [11,12]. Аналогичное увеличение коэффициента Зеебека в топологических термоэлектриках на основе Bi 2 Te 3 [13] согласуется с оценками, выполненными в рамках теории теплового квантового поля при появлении электроннодырочных пар Швингера на горячей стороне термоэлектрика вдоль градиента температуры.…”