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Enhanced Spin Figure of Merit in Molecular Junction Yuanyuan Wang, Huaqing Xie, Zihua Wu, Jiaojiao Xing, Jianhui Mao, and Yihuai Li J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b02709 • Publication Date (Web): 12 Apr 2017 Downloaded from http://pubs.acs.org on May 2, 2017

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The Journal of Physical Chemistry

Enhanced Spin Figure of Merit in Molecular Junction Yuanyuan Wang, Huaqing Xie*, Zihua Wu, Jiaojiao Xing, Jianhui Mao, and Yihuai Li School of Environmental and Materials Engineering, Shanghai Polytechnic University, 2360 Jinhai Road, Shanghai 201209, China

ACS Paragon Plus Environment

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_____________________________ *

Electronic mail: [email protected]

ABSTRACT

We study the spin-dependent thermoelectric effect in a molecular junction where a semiconductor quantum dot in a magnetic field is trapped between two conducting polymer leads. The Green’s function method along with the Landauer formula based on the Holstein small polaron model is applied to study the thermo-spin effects in this system. The narrow bandwidth of small polaron band in the polymer leads results in sharp carrier density of states, which offers opportunity to enhance the spin Seebeck coefficient. At the same time, the spin conductance and electron thermal conductance can be tuned by the tuning the affinity mismatch and chemical potential flexibly. Consequently, significant enhancement of spin figure of merit can be achieved. Detailed calculation of the influence of band mismatch, width of small polaron band, chemical potential, temperature and magnetic field on the thermo-spin effects are shown in this work. Our results show that the value of spin figure of merit is larger than 1 at a wide parameter range. Specially, the spin figure of merit can be up to 9 when the band mismatch is 0.52 eV, the coupling strength is 5 meV at room temperature. The work indicates that the efficient generation and control of spin polarization can be realized in the polymersemiconductor-polymer hybrid nanoscale structure.


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I. INTRODUCTION The conventional thermoelectric (TE) effect, which directly converts heat to electricity and vice versa, plays an important role for waste heat recovery, solar thermal utilization and thermal management.1-3 However, widely applications of the TE effect are limited to its low efficiency,4 which is determined by the dimensionless figure of merit ZT. In the past two decades, significant progresses have been made for improving ZT, especially with the approach utilizing nanostructures, where the quantum effect and/or low-energy filtering effect of electrons introduced in the low-dimensional structures enhance the thermopower while phonon-interface scattering decreases the phononic thermal conductivity.2 Recently, the TE effects turned out to be useful also for spintronics after the discovery of the spin Seebeck effect in metallic ferromagnets.5 Analogous to the conventional Seebeck effect generating electric voltages, the spin Seebeck effect refers to the generation of spin currents or voltages in the presence of a temperature gradient, which provides a new method to generate and control spin polarization by tuning the thermal bias and can be directly applied to construct thermal spin generators for spintronics devices. Therefore, the thermo-spintronics topic has been investigated intensely. Besides metallic ferromagnets,6-8 spin Seebeck effect has been observed on a variety of materials, including polarized semiconductors,9-10 insulators,11-13 and magnetic tunnel junctions.14-18 However, the measured spin thermopower in bulk samples is so weak that may be overwhelmed by its charge counterpart of several orders larger, which prevents its application. Therefore, similar to the essential task in charge TE effect, the crucial task in thermo-spin effect is to increase the spin figure of merit Z sT = Gs S s2T (κ el + κ ph ) , where Gs is


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the spin conductance, Ss is the spin thermopower, κ el and κ ph are the electron and phonon thermal conductance respectively, and T is the temperature. It has been know that, in analogous to the case of charge TE effect, the magnitude of spin figure of merit can also be enhanced effectively by reducing the dimensionality of the materials.19 The zero-dimensional quantum dot (QD) is one of the promising candidates for thermospin devices. A single semiconductor QD coupled to two ferromagnetic electrodes has been studied. The spin thermopower is reported to reach the values of orders of kB e ( kB is the Boltzmann constant and e is the unit charge of carriers),20-22 which is comparable with the Seebeck coefficient, and a spin figure of merit Z sT ≈ 0.17 is achieved at 4K.20 Qi et al. further found the spin polarization of thermal current has a rectification effect when a QD is connected to a normal metal and a ferromagnetic lead.23 Some other works focused on thermo-spin effects in double QDs linked with two ferromagnetic electrodes.

24-26

Swirkowicz et al.24 found that the

interference effects induce significantly increases of Z sT and the maximum value of Z sT is 1.8. In Ref. 25, Liu et al. reported the Seebeck coefficient can be generated by the coaction of the magnetic flux and the Rashba spin-orbit (RSO) interaction and the largest Z sT is about 0.65. Zheng et al.26 showed that Z sT can reach 3 by the coexistence of Rashiba spin-orbit coupling in the double QDs and the leads’ spin polarization. In the above works, the leads are all inorganic. In fact, in comparison with the inorganic materials, conducting polymers are low cost and environmentally friendly, which also exhibit high efficiency TE performance.27-28 Here we propose a study of the thermo-spin effect in the polymer-semiconductor-polymer (PSP) junction, where a semiconductor QD in a magnetic field is attached to two conducting polymer leads. In the conducting polymer, small polarons need to be considered since the electron-phonon interactions are usually too strong to be treated as a perturbation.29 Narrow


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small polaron band leads to sharp carrier density of states (DOS),30-31 which provides the possibility to enhance the spin Seebeck coefficient. In consideration that the carriers transport through the resonant tunneling process, the spin conductance can be tuned by the band mismatch. Consequently, the nanoscale PSP junction has potential and flexibility to achieve larger spin thermopower and spin conductance simultaneously and consequently larger spin figure of merit in comparison with the case of conventional nanoscale junction where a QD/QDs is linked with inorganic leads. In the calculation, the Green’s function method29 based on the Landauer formula32-34 with Holstein small polaron model adopted is applied.35 The rest of this paper is organized as follows. In Sect. II, we present the Hamiltonian for the PSP junction based on the Holstein small polaron Hamiltonian and show the derivations of thermo-spin properties using the Landauer formula and Green’s function method. Then we study the influences of parameters on the thermo-spin effects in Sec. III, including affinity mismatch (Sec. IIIA), the bandwidth of the small polaron band in polymer leads (Sec. IIIB), the chemical potential (Sec. IIIC), and the magnetic field and the temperature (Sec. IIID). Finally, we conclude this study in Sec. IV.

II. THEORETICAL MODEL Figure 1(a) shows the schematics of the PSP junction, where a cubic semiconductor QD with size l in a magnetic field B is trapped between two polymer leads made of the same material. The temperature of the left (right) polymer lead is TL ( TR ). Figure 1(b) shows the band structure of this system. ε 0 is the band offset between the polymer leads and the semiconductor QD. Once the conduction band edge of the semiconductor QD is chosen as the energy reference (energy zero), the small polaron band locates at ε ′ = ε 0 − ∆ , where ∆ is the small polaron selfenergy. In the semiconductor QD, electrons are assumed to be confined by a square hard wall


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potential with electron eigenstates n and corresponding eigenenergies ε nQD , where n = 1,2,3L is the index of energy levels. Once a magnetic field B is applied, the orbitals n split into spinQD QD up and spin-down states ( n ↑ and n ↓ ) whose energy are ε nQD is σ = ε n + ε B , where ε n

obtained by the Schrödinger equation and ε B = gµ B Bσ 2 is the Zeeman splitting energy. In the above equation, σ = ± 1 is the spin quantum number, g is the g-factor of the QD, and µ B is the Bohr magnetron. To simplicity, here we only consider the PSP junction with n-type materials, while the case with p-type materials can be considered similarly. We also assume there are no electrons trapped at the semiconductor-organic interface, when the Schottky barrier can be neglected. Our starting point is the Hamiltonian of this system, L(R) H = H Lead + H QD + H IL ( R )

(1)

L(R) where H Lead , HQD , and H IL ( R ) describe the left (right) polymer lead, the semiconductor QD, and

the interactions between left (right) leads and the semiconductor QD, respectively. The Holstein small polaron model35 is applied to describe the polymer leads

(

L(R) H Lead = ε 0 ∑ c j+ c j + ∑ tξ c j+ c j + ∑ M Lead ,qλ e iq⋅j c j+ c j a qλ + a −+qλ j

jδξ

)

(2)

j

where ε 0 is the electron energy in the leads and cj+ ( cj ) is the creation (annihilation) operator of the electron at position j . Here δ is the nearest site around one site j . tξ = (t // , t ⊥ , t ⊥ ) is the anisotropy inter-site coupling with intra-chain coupling tz and inter-chain coupling t // , while

aq+λ ( aqλ ) is the creation (annihilation) operator of the λ -branch phonon with wave vector q and frequency ω qλ . M Lead , qλ is the electron-phonon interaction matrix in the lead. The Hamiltonian of the QD can be written as


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+ H QD = ∑ ε nQD σ d nσ d n σ + nσ

M ∑ σσ λ

nn′

′q

(

n′σ ′ e iq⋅rn nσ d n+′σ ′ d nσ aqλ + a −+qλ

QD ,qλ

)

(3)

where dn+σ ( d nσ ) is the creation (annihilation) operator of the electron with eigen state nσ .

M QD, qλ is the electron-phonon interaction matrix in the QD. In Eqs. (2) and (3), both the electron-optical-phonon interaction and electron-acoustic-phonon interaction are included. We neglect electron-electron Coulomb interaction in the QD due to the relatively large dielectric constant of QD materials studied in this work. The coupling Hamiltonian between the QD and two leads is

(

H IL = H IR = ∑ V0 cj+0 d nσ + d n+σ c j0

)

(4)

nσ

where V 0 represents the coupling strength between the leads and the QD, which is assumed as energy and spin independent.21, 26 After knowing the Hamiltonian of the system (Eq. (1)), we apply standard canonical transformation29, 35-37 to diagonalize the electron-phonon interaction term in the small polaron Hamiltonian since the electron-phonon interaction is too strong to be treated as a perturbation. The transformed lead Hamiltonian can be written as: L(R) H Lead = ∑ ε (k )ck+ ck

(5)

k

where ε (k ) = ε 0 − ∆ + Γ ′(T ) ∑ δξ t ξ e − ik ⋅δ is the energy distribution of the small polaron band in polymer leads.29 Γ ′(T ) = exp [− ξ (T ) / 2 ] is the diagonal part of the hopping probability with

ξ (T ) = ∑ M Lead ,qλ (e q⋅δ − 1) hω qλ (1 + 2 N q ) , N q is the Bose-Einstein distribution function and h 2

qλ

is the Planck constant. The small polaron band width is 2(2t // + t z )Γ′(T ) , which increases with


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the intra-chain coupling tz and inter-chain coupling t // , and decrease with the increasing temperature.29-30 Using the Landauer formula,32-34 the spin-dependent electric current J σ and heat current Qσ can be expressed as

 Jσ   e  1   = τ σ (ε )( f L (ε ) − f R (ε )) dε  ∫  Qσ  2πh  ε − µσ 

(6)

where f L(R) (ε ) is the Fermi-Dirac distribution of the left (right) lead and ε is the energy. τ σ (ε ) is the transmission coefficient, which can be calculated by the Green’s function method as29, 32  ΓσL (ε )ΓσR (ε )  G σr (ε ) − G σa (ε )  L R  Γσ (ε ) + Γσ (ε ) 

(

τ σ (ε ) = Trace 

where the trace is taken over the eigen space n σ

)

(7)

in the QD. ΓσL ( R ) (ε ) is the effective width

functions of the tunneling processes between semiconductor QD and the left (right) polymer lead. Gσr (ε ) and Gσa (ε ) are the retarded and advanced Green’s function of the junction respectively. As we are interested in the linear-response regime, after expanding the Fermi-Dirac distribution function to the first order in temperature difference and spin bias, we can obtain the spin-resolved conductance Gσ , thermopower Sσ , and electron thermal conductance κ elσ as

Gσ = e 2 K 0σ Sσ =

κ elσ =

(8a)

K1σ eK 0σ T

1 K2  K 2σ − 1σ T K 0σ

(8b)   

(8c)

where


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K mσ =

1 ∞  ∂f (ε ) (ε − E f )m dετ σ (ε )− ∫  − ∞ πh  ∂ε 

(9)

in which m = 0,1,2 . Finally, one can define the spin conductance Gs , spin thermopower Ss , and electron thermal conductance κ el in the forms of Gs = G↑ − G↓ , S s = (S ↑ − S ↓ ) 2 , and

κ el = κ el ↑ + κ el ↓ , respectively. Then the spin figure of merit can be calculated as

Z sT = Gs S s2T κ el . Since there is a significant mismatch in the elastic properties of the QDs and the lead materials, the phonon contribution to the thermal conductance is much smaller than the electron contribution.26, 38-40 Therefore the phonon thermal conductance is neglected in this work.

III. RESULTS AND DISCUSSIONS In this work, we choose GaN as the QD material since the shape and size of GaN QD can be well controlled41 and its g-factor is relatively large.42 The size of the QD is fixed to be 5 nm. Different types of conducting polymers have been reported as high efficiency organic TE materials, which can be used as the lead materials.43 Thus the affinity mismatch ε 0 between polymer leads and GaN QD is in a wide range and can be tuned flexibly.31 We choose poly-3hexylthiophene (P3HT) as the lead material. The parameters of GaN and P3HT can be found in Ref. 42.

A. Dependence on the Band Mismatch As described in Sec. I, the band mismatch plays a pivotal role in determining spin TE properties. The coupling V0 between inorganic and organic materials which depends on the overlap integrals between electronic wavefunctions in these two types of materials lacks detailed calculations and is only assumed smaller than 50 meV.44-45 Thus it is treated as an input


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parameter in this work. The magnetic field is firstly set to be 50 T here, which is acceptable for the first-step modeling investigation,9, 46-47 although it is not realistic in experiments. Detailed study of dependence of thermo-spin effects on the magnetic field will be addressed in Sec. IIID. The temperature is set to be room temperature (T = 300 K). Further investigation of influence of temperature will also be found in Sec. IIID. In figure 2, we present the dependence of the absolute spin conductance Gs , spin thermopower Ss , electron thermal conductance κ el , and the spin figure of merit Z sT of nanoscale PSP junctions on the energy difference ε ′ with different coupling strength ( V0 = 5 mV, 10 meV, 15 mV and 20 mV). Since ε ′ = ε 0 − ∆ , it reflects the influence of the band mismatch ε 0 on the spin TE properties. The chemical potential E f is aligned to the small polaron band ( E f = ε ′ ). Fig. 2(a) shows that the absolute spin conductance has two maximum values besides each orbital energy level, no matter what the value of coupling QD strength V0 is. For example, two maximums locate at ε ′ = ε1 ± 0.05 eV with the lowest orbital QD QD level ε1 = 0.3 eV and another two are at ε ′ = ε 2 ± 0.05 eV with the second lowest orbital QD level ε 2 = 0.6 eV. When the small polaron band is aligned with the energy level in QD, the

resonant tunneling occurs, when the transmission coefficient reaches its maximum value. As we know, the transmission coefficient τ σ (ε ) is approximately a summation of a series of Lorenztype functions whose peaks are at the energy levels in QD.31 Once a spin-up energy level n ↑ is QD aligned with the small polaron band ( ε ′ = ε n↑ ), the spin-dependent transmission coefficient

, while the transmission coefficient τ ↓ (ε ) is orders of τ ↑ (ε ) reaches the maximum value at ε 1QD ↑ magnitude smaller than τ ↑ (ε ) since the corresponding energy ε 1QD is away from the small ↓ polaron band ε ′ by 2ε B . Then spin-resolved conductances G↑ reaches its maximum and G ↓ is


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much smaller than G↑ at ε ′ = ε n↑ . Therefore, the absolute spin conductance Gs = G↑ − G↓ has two peaks near to energy levels n ↑ and n ↓ respectively. It is also seen in Fig. 2(a) that the absolute spin conductance increases with coupling strength V0 . This because that the increase of the coupling strength leads to the increase of the width of the transmission coefficient. Fig. 2(b) shows the spin Seebeck coefficient also has two maximum values besides each orbital level QD QD ( ε ′ = ε1 ± 0.08 eV and ε 2 ± 0.08 eV). In terms that the spin-resolved Seebeck coefficient

S↑ (↓ ) is the average entropy of the spin-up (-down) carriers and implies the spin-up (-down)

carrier distribution asymmetry, the farther the small polaron band is from the spin-up (-down) energy level in QD, the more unsymmetrical the transmission coefficient τ ↑(↓ ) is to the energy level ε n↑(↓ ) . Then spin-resolved Seebeck coefficient S↑ (↓ ) increases with the energy difference

ε ′ − ε n↑(↓ ) between spin-up (-down) energy level and small polaron band. Then in consideration that ε n↑ and ε n↓ locate besides ε n , the spin Seebeck coefficient Ss reaches two maximums besides ε n . We can also find that the absolute spin Seebeck coefficient Ss decreases with the increase of coupling strength V0 in Fig. 2(b). This comes from that weaker coupling strength results in narrower transmission coefficient and sharper DOS. Fig. 2(c) shows that the electron thermal conductance has two peaks at the lowest and second lowest orbital energy levels when the band alignment is satisfied. The electron thermal conductance is the summation of thermal conductance induced by spin-up and -down electrons. Although κ el ↑ and κ el ↓ reach their maximum values when the small polaron band is aligned with energy levels n ↑ and n ↓ in QD respectively, the peaks of κ el appears at orbital level n , which is in the middle of n ↑ and


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n ↓ . Accordingly, the properties of the spin conductance, spin thermopower and electron

thermal conductance determine that spin figure of merit Z sT has two peaks near to each orbital levels, which is shown in Fig. 2(d). The maximum spin figure of merit Z sT can reach 9 when the energy difference ε ′ = 0.52 and coupling strength is weak ( V0 = 5 meV).

B. Dependence on the Small Polaron Band Width The narrow band width of the small polaron band in polymer leads to sharp DOS in the leads, which makes it is possible to obtain large spin thermopower. Consequently, the small polaron bandwidth is one of the most important factors to affect the thermo-spin transport properties. In this subsection, the dependence of the thermo-spin properties on small polaron band width is studied. As discussed in Section II, the small polaron band width 2(2t// + t z )Γ′(T ) is proportional to the coupling constants for a given temperature. Usually the inter-chain coupling t// due to van de Waals interaction is very small (1~25 meV).48 The intra-chain coupling tz due to covalent bonding varies in a wide range, from tens of meV to hundreds of meV49-51 and controls the band width. To study the effect of the small polaron band width on the thermo-spin properties of the nanoscale PSP junction, we here change tz in the known data range (from 50 meV to 200 meV) and assume inter-chain coupling t // = 10 meV. The small polaron bands in the polymer leads align with the lowest spin-down level in the QD ( ε ′ = E f = ε1QD ). The ↓ temperature is 300 K and the magnetic field is 50 T. Figure 3 shows the dependence of spinthermo properties on small polaron band width with varying V0 . From figure 3(a), it is seen that the spin conductance decreases with the increasing tz . Since the half width of the transmission


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coefficient through the n-th energy level in QD decreases with the increase of tz , the transmission coefficient through every energy levels in QD is over smaller energy range with the increase of tz . Consequently, the increase of tz results in the non-zero transmission coefficient QD through ε1 is over smaller energy range, which in turn reduces the spin conductance. Fig. 3(a)

also shows that the spin conductance increases with the coupling strength as explained in the previous subsection. Figure 3(b) shows that the absolute spin Seebeck coefficient S s increases with tz . With the increase of tz , which implies the increase of the small polaron band width, the transmission coefficients for spin-up and spin-down carriers which locates at 1 ↑ and 1 ↓ both become thinner. Then the transmission coefficients for spin-up and spin-down carriers become more asymmetrical to the chemical potential at ε 1QD and thus the spin Seebeck coefficient becomes larger. Fig. 3(c) also shows that the absolute spin Seebeck coefficient S s decreases with the increase of coupling strength V0 as in Fig. 2(c). Fig. 3(d) shows that the spin figure of merit Z sT for smaller coupling strength ( V0 = 5 meV, 10 meV) increases with tz , while that for larger coupling strength ( V0 = 15 meV, 20 meV) has a peak.

C. Dependence on the Chemical Potential Chemical potential is another important factor to affect the spin Seebeck effect, which can be controlled by tuning doping concentration. In this subsection, we study the dependence of the spin conductance Gs , spin Seebeck coefficient Ss , electron thermal conductance κ el , and the spin figure of merit Z sT of nanoscale PSP junctions on the chemical potential E f with different coupling strength V0 . The small polaron band in the polymer leads is aligned with the lowest


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orbital energy in the QD ( ε ′ = ε 1QD ). The temperature is 300 K and the magnetic field is 50 T. Fig. QD 4(a) shows the absolute spin conductance has two maxima which locate at E f = ε1 ± 0.04 eV QD where ε1 = 0.3 eV. This result comes from the resonant tunneling between the small polaron

band in polymer leads and the spin-up and spin-down energy levels in the QD. It can also found that the absolute spin conductance increases with the coupling strength. Figure 4(b) shows that QD the absolute spin Seebeck coefficient has a maximum at ε1 . Although the spin-dependent

Seebeck coefficient S↑ (↓ ) increases with the energy difference between spin-up (-down) energy level ε n↑(↓ ) and small chemical potential E f , the distribution difference of spin-up and spindown electrons is only obvious near to ε n↑ and ε n↓ , and hence spin thernmopower ε s reach its QD maximum value at ε1 . Fig. 4(b) also shows that the increase of coupling strength leads to the

decrease of absolute spin Seebeck coefficient. Fig. 4(c) shows that the electrical thermal conductance has a maximum value at the lowest orbital energy level. Because κ el↑ and κ el↓ QD QD reach their maximum at E f = ε1↑ and E f = ε1↓ respectively. Then the superposition of these

two peaks formed a larger peak of the electron thermal conductance. Finally, in Fig. 4(d) it can QD be seen that the spin figure of merit has two peaks at energy levels at E f = ε1 ± 0.04 and

smaller coupling strength is beneficial to obtain larger spin figure of merit.

D. Dependence on the temperature and magnetic filed The magnetic field, leading to splitting of spin-up and spin-down levels in QD, induces the asymmetry transport of spin-up and spin-down electrons, which is the key point why the thermospin effect exists. The temperature is another important parameter which affects the thermo-spin


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transport. In the previous three subsections, the magnetic field is set to be 50 T and the temperature is fixed to 300 K. To understand the influence of these two parameters, we present a magnetic field and temperature dependence study of the thermo-spin effect in this subsection, which could be helpful for further experimental investigation in this system at low temperature with low magnetic filed applied. In the calculation, the small polaron band in the polymer leads ). and the chemical potential are aligned with the lowest spin-up level in the QD ( ε ′ = E f = ε1QD ↑ Fig. 5(a) shows that the spin conductance increases with the magnetic field B . Since the small polaron band is aligned with the spin-down energy level, the conductance of spin-up electron G↑ keeps constant with increasing magnetic field. The energy difference between ε 1QD and ε 1QD is ↑ ↓

2ε B , which is proportional to the magnetic field. Then the electrical conductance of spin-down electron G↓ decreases with increasing magnetic field and is smaller than the electrical conductance of spin-up electron ( G↓ < G↑ ) because of band mismatch. Consequently, the spin conductance Gs = G↑ − G↓ increases with the magnetic field. Fig. 5(a) also shows that the spin conductance has a maximum at 325 K. From equations 8(a) and 9, the spin conductance Gσ is determined by the integral of the product of transmission coefficient τ σ (ε ) and the gradient of Fermi-Dirac distribution − ∂f (ε ) ∂ε . The transmission coefficient τ σ (ε ) is approximately a summation of a series of Lorenz-type functions whose width increases with the width of small polaron band 2(2t// + t z )Γ′(T ) .31 The term Γ′(T ) decreases with the increasing temperature and hence the non-zero transmission τ σ (ε ) covers narrower energy with the increasing temperature. Nevertheless, the gradient of Fermi-Dirac distribution − ∂f (ε ) ∂ε becomes wider with increasing temperature. These two competitive trend of τ σ (ε ) and − ∂f (ε ) ∂ε with increasing


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temperature leads to the integral of their product has a maximum value and therefore the spin conductance Gs has a maximum value at 325 K. Figure 5(b) shows that the spin thermopower increases with the magnetic field. The Seebeck coefficient of spin-down electrons S↓ keeps unchanging with magnetic field since the small polaron band is always aligned with the lowest spin-down level. Larger magnetic field leads to larger spin-splitting and consequently more asymmetry of the distribution of the spin-down electrons to the chemical potential. Therefore the Seebeck coefficient of the spin-up electrons S↑ increases with the magnetic field and larger than the Seebeck coefficient of the spin-down electrons ( S ↑ > S ↓ ). Then the spin thermopower S s = S ↑ − S ↓ 2 increases with the magnetic field. It can also been found in figure 5(b) that the

spin Seebeck coefficient S s has a maximum value at 230 K, which also comes from the competitive trend of τ σ (ε ) and − ∂f (ε ) ∂ε with increasing temperature. Figure 5(c) shows that the electron thermal conductance decreases with the the increasing magnetic field. The electron thermal conductance induced by the spin-down electron decreases with the magnetic field since the band mismatch ε 1↓ − ε ′ between the lowest spin-down energy level and the small polaron band becomes larger with the increasing magnetic field. The electron thermal conductance κ el , which is the summation of electron thermal conductance induced by spin-up and spin-down electrons, decreases with the magnetic field. Figure 5(c) also shows that κ el has a maximum at 260 K. This comes from the competing trend between τ σ (ε ) and − ∂f (ε ) ∂ε with increasing temperature too. Finally, the properties of Gs , S s and κ el determine the property of spin figure of merit, which is shown in figure 5(d). Z sT increases with increasing magnetic field and increasing temperature. The largest Z sT can reach 1.2. Z sT can be larger than 0.1 even with


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smaller magnetic field applied if one increase the temperature. For example, when the magnetic filed is 23 T and temperate is 600 K, Z sT is 0.1.

IV. CONCLUSIONS To summarize, we have proposed the thermo-spin effect emerging in the organic-inorganic hybrid nanoscale PSP junction. The spin TE properties are studied by the Landauer formula and Green’s function method based on Holstein small polaron model. In the PSP junction, it is flexible to manipulate the DOS of the junction to obtain larger spin Seebeck coefficient and the spin conductance could also be maximized once the resonant tunneling is reached. The energy mismatch which can be controlled by material selection plays a key role to achieve better thermo-spin performance. The maximum spin figure of merit can reach 9 when the energy mismatch is 0.52 eV, the coupling strength is 5 meV and the magnetic field is 50 T at room temperature. The spin figure of merit Z sT for smaller coupling strength ( V0 = 5 meV, 10 meV) increases with the increasing small polaron band, while that for larger coupling strength ( V0 = 15 meV, 20 meV) has a peak. The chemical potential that can be tuned by doping concentration also affects the spin figure of merit. When the chemical potential is besides the orbital levels in the QD QD ( E f = ε1 ± 0.04 ), the spin figure of merit has two peaks. Smaller coupling strength is

beneficial to obtain larger spin figure of merit. Furthermore, high temperature and large magnetic field are beneficial to obtain large spin figure of merit. Z sT can be larger than 0.1 even with smaller magnetic field applied if one increase the temperature. For example, when the magnetic filed is 23 T and temperate is 600 K, Z sT is 0.1. The modeling study presented in this work is helpful to understand the thermo-spin transport mechanisms in the organic-inorganic nanoscale


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junction and indicates that the organic-inorganic hybrid low-dimensional structures have the potential to achieve fairly good thermo-spin properties.

ACKNOWLEDGMENT This work is supported by the National Natural Science Foundation of China (No. 51406111 and No. 51676117), the Major Program of the National Natural Science Foundation of China (No. 51590902), the Natural Science Foundation of Shanghai (No. 14ZR1417000), the Scientific Innovation Project of Shanghai Education Committee (No. 15ZZ100), and Young Eastern Scholar of Shanghai (No. QD2015052).


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FIGURE CAPTIONS Figure 1. (a) Schematic diagram of PSP junction where a cubic semiconductor QD in a magnetic field B is attached to conducting polymer leads. The temperature of the left and right leads are

TL and TR respectively. (b) Schematic diagram of energy levels in the PSP junction. ε 0 is the band offset between the polymer leads and the semiconductor QD. ∆ is the small polaron selfenergy. The small polaron band locates ε ′ = ε 0 − ∆ above the conduction band E c in the QD. The lowest orbital level is separated into spin-up and spin-down states with eigen energies ε 1QD ↑ and ε 1QD respectively by the magnetic field due to the Zeeman splitting effect. ↓ Figure 2. (a) absolute spin conductance Gs , (b) spin Seebeck coefficient S s , (c) electron thermal conductance κ el , and (d) spin figure of merit ZTs as functions of energy difference ε ′ with different coupling strength ( V0 = 5 meV, 10 meV, 15 meV, 20 meV). In the calculation, T = 300 K, E f = ε ′ , and B = 50 T.

Figure 3. (a) spin conductance Gs , (b) spin Seebeck coefficient S s , (c) electron thermal conductance κ el , and (d) spin figure of merit ZTs as functions of intra-chain coupling tz with different coupling strength ( V0 = 5 meV, 10 meV, 15 meV, 20 meV). In the calculation,

E f = ε1QD , T = 300 K, and B = 50 T. ↑ Figure 4. (a) absolute spin conductance Gs , (b) absolute spin Seebeck coefficient S s , (c) electrion thermal conductance κ el , and (d) spin figure of merit ZTs as functions of chemical


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potential E f with different coupling strength ( V0 = 5 meV, 10 meV, 15 meV, 20 meV). In the calculation, ε 1QD = ε ′ , T = 300 K, and B = 50 T. Figure 5. The magnetic field and temperature dependences of (a) spin conductance Gs , (b) absolute spin Seebeck coefficient S s , (c) electrion thermal conductance κ el , and (d) spin figure of merit ZTs . In the calculation, ε 1QD = ε ′ and V0 = 5 meV.


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FIGURES Figure 1


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Figure 2


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Figure 3


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Figure 4


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Figure 5


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Contents Image


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Figure 1. (a) Schematic diagram of PSP junction where a cubic semiconductor QD in a magnetic field B is attached to conducting polymer leads. The temperature of the left and right leads are TL and TR respectively. (b) Schematic diagram of energy levels in the PSP junction. ε0 is the band offset between the polymer leads and the semiconductor QD. ∆ is the small polaron self-energy. The small polaron band locates ε′ = ε0 - ∆ above the conduction band Ec in the QD. The lowest orbital level is separated into spin-up and spin-down states with eigen energies ε1↑QD and ε1↓QD respectively by the magnetic field due to the Zeeman splitting effect. 142x111mm (96 x 96 DPI)



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Figure 2. (a) absolute spin conductance |Gs| as a function of energy difference ε’ with different coupling strength (V0 = 5 meV, 10 meV, 15 meV, 20 meV). In the calculation, T = 300 K, Ef = ε’, and B = 50 T. 161x148mm (100 x 100 DPI)


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Figure 2. (b) spin Seebeck coefficient Ss as a function of energy difference ε’ with different coupling strength (V0 = 5 meV, 10 meV, 15 meV, 20 meV). In the calculation, T = 300 K, Ef = ε’, and B = 50 T. 161x148mm (100 x 100 DPI)



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Figure 2. (c) electron thermal conductance κel as a function of energy difference ε’ with different coupling strength (V0 = 5 meV, 10 meV, 15 meV, 20 meV). In the calculation, T = 300 K, Ef = ε’, and B = 50 T. 161x148mm (100 x 100 DPI)


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Figure 2. (d) spin figure of merit ZsT as a function of energy difference ε’ with different coupling strength (V0 = 5 meV, 10 meV, 15 meV, 20 meV). In the calculation, T = 300 K, Ef = ε’, and B = 50 T. 161x148mm (100 x 100 DPI)



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Figure 3. (a) spin conductance Gs as a function of intra-chain coupling tz with different coupling strength (V0 = 5 meV, 10 meV, 15 meV, 20 meV). In the calculation, Ef = ε1↑QD, T = 300 K, , and B = 50 T. 166x149mm (100 x 100 DPI)


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Figure 3. (b) spin Seebeck coefficient Ss as a function of intra-chain coupling tz with different coupling strength (V0 = 5 meV, 10 meV, 15 meV, 20 meV). In the calculation, Ef = ε1↑QD, T = 300 K, , and B = 50 T. 166x149mm (100 x 100 DPI)



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Figure 3. (c) electron thermal conductance κel as a function of intra-chain coupling tz with different coupling strength (V0 = 5 meV, 10 meV, 15 meV, 20 meV). In the calculation, Ef = ε1↑QD, T = 300 K, , and B = 50 T. 163x151mm (100 x 100 DPI)


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Figure 3. (d) spin figure of merit ZsT as a function of intra-chain coupling tz with different coupling strength (V0 = 5 meV, 10 meV, 15 meV, 20 meV). In the calculation, Ef = ε1↑QD, T = 300 K, , and B = 50 T. 162x149mm (100 x 100 DPI)



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Figure 4. (a) absolute spin conductance |Gs| as a function of chemical potential Ef with different coupling strength (V0 = 5 meV, 10 meV, 15 meV, 20 meV). In the calculation, ε1QD = ε’, T = 300 K, and B = 50 T. 162x152mm (100 x 100 DPI)


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Figure 4. (b) absolute spin Seebeck coefficient |Ss| as a function of chemical potential Ef with different coupling strength (V0 = 5 meV, 10 meV, 15 meV, 20 meV). In the calculation, ε1QD = ε’, T = 300 K, and B = 50 T. 162x152mm (100 x 100 DPI)



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Figure 4. (c) electrion thermal conductance κel as a function of chemical potential Ef with different coupling strength (V0 = 5 meV, 10 meV, 15 meV, 20 meV). In the calculation, ε1QD = ε’, T = 300 K, and B = 50 T. 162x152mm (100 x 100 DPI)


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Figure 4. (d) spin figure of merit ZsT as a function of chemical potential Ef with different coupling strength (V0 = 5 meV, 10 meV, 15 meV, 20 meV). In the calculation, ε1QD = ε’, T = 300 K, and B = 50 T. 162x152mm (100 x 100 DPI)



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Figure 5. (a) The magnetic field and temperature dependences of spin conductance. In the calculation,ε1QD = ε’ and = 5 meV. 155x128mm (100 x 100 DPI)


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Figure 5. (b) The magnetic field and temperature dependences of absolute spin Seebeck coefficient. In the calculation,ε1QD = ε’ and = 5 meV. 148x128mm (100 x 100 DPI)



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Figure 5. (c) The magnetic field and temperature dependences of electron thermal conductance. In the calculation,ε1QD = ε’ and = 5 meV. 155x128mm (100 x 100 DPI)


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Figure 5. (d) The magnetic field and temperature dependences of spin figure of merit. In the calculation,ε1QD = ε’ and = 5 meV. 144x128mm (100 x 100 DPI)



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Content Image 192x80mm (150 x 150 DPI)


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Enhanced Spin Figure of Merit in a Molecular Junction - The Journal of

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