Superfluidity of dipolar excitons in a transition metal dichalcogenide double layer

Berman, Oleg L.; Kezerashvili, Roman Ya.

doi:10.1103/physrevb.96.094502

Cited by 62 publications

(49 citation statements)

References 81 publications

(133 reference statements)

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“…Therefore, we can perform the Taylor's series expansion for the Coulomb potential and keep the first two terms only. We obtain

V false(r false) = - V_{0} + γ r^{2}

where

V_{0} = κ e^{2} false/ ε_{d} D

and

γ = κ e^{2} false/ 2 ε_{d} D^{3}

. Under this approximation, the solution of the Schr

\overset{o}{true}

dinger equation for the relative motion of the interlayer exciton is similar to a 2D harmonic oscillator; the corresponding eigenfunction can be given as

ϕ_{n m} (ζ, θ) = C ζ^{| m |} \exp (- ζ^{2} / 2 + i m θ) L_{n}^{| m |} (ζ^{2})

with the normalization constant

C = \sqrt{\frac{n!}{2 π a^{2} (n + | m |)!}}

where n = 0, 1,⋯ is the radial quantum number, m = 0, ± 1,⋯ is angular quantum number, θ is the polar angle,

a = false[ℏ false/ false(2 \sqrt{2 μ γ} {false) false]}^{1 false/ 2}

is the Bohr radius of the interlayer exciton, and

L_{n}^{false| m false|} false(ζ^{2} false)

is the associated Laguerre polynomials with the ratio constant

ζ = r false/ false(\sqrt{2} a false)

.…”

mentioning

confidence: 88%

Multiphonon Raman Scattering in Transition Metal Dichalcogenide Double Layers

Wang

Deng

Xiao

et al. 2020

Physica Rapid Research Ltrs

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Herein, multiphonon Raman scattering assisted by the interlayer excitons in double transition metal chalcogenide (TMD) layers based on the Huang–Rhys's model is studied. The processes of multiple longitudinal optical (LO) phonons Raman scattering are presented due to the strong exciton–LO phonon coupling. It is found that the Raman scattering intensity and orders of LO phonon overtones depend on the obtained value of Huang–Rhys factor, which can be tuned obviously by the strength of exciton–LO phonon coupling and interlayer distance between two TMD layers. Meanwhile, temperature dependence of scattering intensities for different orders of LO phonon overtones in the multiphonon processes is discussed. The theoretical results provide significant insight not only for the analysis of multiphonon Raman spectroscopy in experiments, but also for the modulation of optical properties in a series of TMD double layers and Van der Waals heterostructures.

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“…Therefore, we can perform the Taylor's series expansion for the Coulomb potential and keep the first two terms only. We obtain

V false(r false) = - V_{0} + γ r^{2}

where

V_{0} = κ e^{2} false/ ε_{d} D

and

γ = κ e^{2} false/ 2 ε_{d} D^{3}

. Under this approximation, the solution of the Schr

\overset{o}{true}

dinger equation for the relative motion of the interlayer exciton is similar to a 2D harmonic oscillator; the corresponding eigenfunction can be given as

ϕ_{n m} (ζ, θ) = C ζ^{| m |} \exp (- ζ^{2} / 2 + i m θ) L_{n}^{| m |} (ζ^{2})

with the normalization constant

C = \sqrt{\frac{n!}{2 π a^{2} (n + | m |)!}}

where n = 0, 1,⋯ is the radial quantum number, m = 0, ± 1,⋯ is angular quantum number, θ is the polar angle,

a = false[ℏ false/ false(2 \sqrt{2 μ γ} {false) false]}^{1 false/ 2}

is the Bohr radius of the interlayer exciton, and

L_{n}^{false| m false|} false(ζ^{2} false)

is the associated Laguerre polynomials with the ratio constant

ζ = r false/ false(\sqrt{2} a false)

.…”

mentioning

confidence: 88%

Multiphonon Raman Scattering in Transition Metal Dichalcogenide Double Layers

Wang

Deng

Xiao

et al. 2020

Physica Rapid Research Ltrs

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“…На графике хорошо видно выполнение этого условия. Напомним, что потенциал двумерного гармонического осциллятора интересен 1 Отметим, что в статьях [22,23] использовался потенциал Рытовой−Келдыша, в котором в качестве аргумента выступает Подчеркнем, что выбор пробной функции именно в виде (12) обусловлен тем, что в области значений d отличие энергий связи экситона в двух рассмотренных случаях максимально. Если же зафиксировать подгоночный параметр δ = 0, то рассчитанная энергия связи экситона уменьшится чуть более чем на 10%.…”

Section: энергия связи экситонаunclassified

“…Для двухслойных систем, где два монослоя ДПМ разделены туннельно-непрозрачным барьером, вопрос об энергиях связи экситона и триона не был подробно исследован. В работах [20,21] особенности экранировки кулоновского взаимодействия во внимание не принимались, а в статьях [22,23] использовалось упрощенное выражение, не учитывающее самосогласованное экранирование двумя слоями. Цель настоящей работы -восполнить указанный пробел.…”

Section: Introductionunclassified

Экситоны И Трионы В Двухслойных Ван-Дер-Ваальсовых Гетероструктурах

Семина¹

2019

Физика Твердого Тела

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Поступила в Редакцию 24 июня 2019 г. В окончательной редакции 24 июня 2019 г. Принята к публикации 24 июня 2019 г.Теоретически исследованы экситоны и трионы в двухслойных структурах на основе дихалькогенидов переходных металлов. Получены выражения для эффективного потенциала межчастичного взаимодействия в такой системе с учетом значительного диэлектрического контраста в гетероструктуре. Предложены простые и физически оправданные вариационные функции для электрон-дырочных комплексов. Выполнен вариационный расчет энергий связи экситона и триона в зависимости от расстояния между слоями с учетом особенностей экранировки кулоновского взаимодействия. Точность вариационного подхода подтверждена прямым численным расчетом энергии связи экситона в зависимости от расстояния между слоями.Ключевые слова: пространственно непрямой экситон, трион, монослои дихалькогенидов переходных металлов, двухслойные структуры, потенциал Рытовой−Келдыша

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“…The second term

H_{e x}^{true(r true)}

describes the relative motion of exciton with the reduced mass

μ = m_{e}^{- 1} + m_{h}^{- 1}

. In general, the relative distance r of electron‐hole pair is much smaller than the internal distance D , thus the harmonic oscillation approximation

V^{'} true(r true) = - V_{0} + γ r^{2}

for the Coulomb interaction

V true(r true) = - κ e^{2} / ϵ_{d} \sqrt{D^{2} + r^{2}}

is adopted extensively, where

V_{0} = κ e^{2} / ϵ_{d} D

and

γ = κ e^{2} / 2 ϵ_{d} D^{3}

as well as ϵ d is the dielectric constant determined by the dielectric environment and

κ = 9 \times 10^{9} N {normalm}^{2} / {normalC}^{2}

. In this approximation, the eigenfunctions and eigenenergies for the relative motion of interlayer exciton can be solved exactly (see the Supporting Information).…”

Section: Effective Masses Of Electron (Hole) and The Energies Of Lo Pmentioning

confidence: 99%

“…It can be seen that: 1) Δ T K BT increases obviously with increasing D , which because of the larger D leads to the increase of the exciton effective radius, and consequently the critical value of

{n a}_{B}^{* 2}

for the dilute exciton condensation; 2) Δ T K BT increases with increasing η , which attributes to the increasing of exciton–LO phonon coupling enhances the screening effect, implying the exciton Bohr radius is enlarged. In addition, interlayer excitons in these TMDS double layers embedding with insulator, for example hexagonal boron nitride (hBN), have been investigated extensively . In these structures, beside the influence of LO phonon, the excitons coupling with the interface optical phonons induced by the embedding insulator have potential influence on the properties of excitonic states, and need to be explored further.…”

Section: Effective Masses Of Electron (Hole) and The Energies Of Lo Pmentioning

confidence: 99%

Effect of Exciton–Phonon Coupling on the Interlayer Excitons in Transition Metal Dichalcogenides Double Layers

Wang

Dong

et al. 2018

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We investigate the correction of interlayer exciton binding energy in transition metal dichalcogenides double layers arising from the exciton-optical phonon coupling using the method of Lee-Low-Pines unitary transformation. We find that the binding energy varies in several tens of meV, depending on the polarizability of materials and the interlayer distance between double layers. Moreover, the correction of binding energy results in a remarkable increase of the critical temperature for the condensation of dilute excitonic gas basing on the Berezinskii-Kosterlitz-Thouless model. These results not only enrich the knowledge for the modulation of interlayer excitons, but also provide potential insights for the Bose-Einstein condensation and superfluid transport of interlayer excitons in two-dimensional heterostructures.Structure of the double layer consisting of different monolayer transition metal dichalcogenides (TMDS), that is called as van der Waals heterostucture, [1,2] provides an excellent platform to study the interlayer exciton physics, [3,4] in which an electron and a hole reside in different monolayers, bounded by attractive Coulomb interaction as illustrated in Figure 1(a). Due to the spatial charge separation, the recombination lifetimes of interlayer excitons are in the range of nanoseconds, several orders of magnitude longer than intralayer excitons shown in Figure 1(b). [5][6][7] More important is that optical properties of interlayer excitons can be easily modulated by some external ways, [4,[6][7][8][9][10][11] such as the gate voltage, temperature, and power of optical excitation, which provides an ideal candidate for realization of many excitonic devices, [3,12,13] such as excitonic photon storage, excitonic transistor, and excitonic light emission dipole. On the other hand, based on excitons are the nature of Bosonic particles, the Bose-Einstein condensation and superfluid transport of the dilute exciton gas in these double layers were proposed extensively in both recent experiments [13,14] and theories. [15][16][17][18][19] Of key importance to this species of exciton is its large binding energy, which determines above mentioned potential applications.Amount of experiments [20][21][22][23] and theories [17][18][19][22][23][24] have focused on the binding energies of interlayer excitons in different TMDS double layers in recent years. Wilson et al. deduced that the binding energy of interlayer exciton is large than 200 meV in MoSe 2 -WSe 2 heterobilayers by using rational device design and submicrometer angle-resolved photoemission spectroscopy in combination with photoluminescence. [20] But Mouri et al. found that the exciton binding energy is only 90 meV in MoS 2 -WSe 2 heterobilayers, determining from its thermal dissociation behavior. [21] The striking discrepancies between them can be attributed to the differences of the interlayer distance and the effective mass of exciton as theories predicted. Recently, Latini et al. developed the quantum electrostatic heterostructure model to calculate t...

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Superfluidity of dipolar excitons in a transition metal dichalcogenide double layer

Cited by 62 publications

References 81 publications

Multiphonon Raman Scattering in Transition Metal Dichalcogenide Double Layers

Multiphonon Raman Scattering in Transition Metal Dichalcogenide Double Layers

Экситоны И Трионы В Двухслойных Ван-Дер-Ваальсовых Гетероструктурах

Effect of Exciton–Phonon Coupling on the Interlayer Excitons in Transition Metal Dichalcogenides Double Layers

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