Nonequilibrium spin-polarized thermal transport in ferromagnetic-quantum dot-metal system

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• 作者：Li Xu^a ; ^b ; ^c ; ^{xuli715628@126.com" class="auth_mail" title="E-mail the corresponding author} ; Zhi-Jian Li^a ; Pengbin Niu^b ; ^c ; Yi-Hang Nie^a ; ^{nieyh@sxu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Nonequilibrium spin-polarized transport ; Thermoelectric effect ; Electrostatic potential ; Nonequilibrium Green function
• 刊名：Physics Letters A
• 出版年：2016
• 出版时间：14 October 2016
• 年：2016
• 卷：380
• 期：42
• 页码：3553-3558
• 全文大小：562 K

文摘

We use nonequilibrium Green function to analyze the nonequilibrium spin-polarized thermal transport through the ferromagnetic–quantum dot–metal system, in which a quantum dot (QD) is coupled to the ferromagnetic and metal electrodes with the voltage bias and the temperature shift. The differential thermoelectric conductance class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0375960116306302&_mathId=si1.gif&_user=111111111&_pii=S0375960116306302&_rdoc=1&_issn=03759601&md5=229d2b4f9d7b281ad9a757e3138257c7" title="Click to view the MathML source">L(θ)class="mathContainer hidden">class="mathCode">$L(\theta )$ is always zero and has no relation with the temperature shift when ε   is equal to the Fermi level. The positive and negative values of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0375960116306302&_mathId=si1.gif&_user=111111111&_pii=S0375960116306302&_rdoc=1&_issn=03759601&md5=229d2b4f9d7b281ad9a757e3138257c7" title="Click to view the MathML source">L(θ)class="mathContainer hidden">class="mathCode">$L(\theta )$ manifest the thermoelectric characteristic of electron-like (or hole-like) carrier when the temperature shift is nonzero. The electrostatic potential U   becomes spin-dependent, and makes the dot level renormalization when the ferromagnetic–quantum dot–metal system is driven by the voltage bias and the temperature shift. We define that the spin polarization of the currents between the spin current class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0375960116306302&_mathId=si2.gif&_user=111111111&_pii=S0375960116306302&_rdoc=1&_issn=03759601&md5=d2e3136de9eb3999448a157983c2e1ba" title="Click to view the MathML source">I_sclass="mathContainer hidden">class="mathCode">$I_s$ and the electric current class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0375960116306302&_mathId=si3.gif&_user=111111111&_pii=S0375960116306302&_rdoc=1&_issn=03759601&md5=3d695631c248fc264644f1a767cbbc21" title="Click to view the MathML source">I_cclass="mathContainer hidden">class="mathCode">$I_c$ is denoted as class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0375960116306302&_mathId=si4.gif&_user=111111111&_pii=S0375960116306302&_rdoc=1&_issn=03759601&md5=99116644e181e0101dcaf94b7ace12bd" title="Click to view the MathML source">I_s/I_cclass="mathContainer hidden">class="mathCode">$I_s/I_c$. The spin polarization class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0375960116306302&_mathId=si4.gif&_user=111111111&_pii=S0375960116306302&_rdoc=1&_issn=03759601&md5=99116644e181e0101dcaf94b7ace12bd" title="Click to view the MathML source">I_s/I_cclass="mathContainer hidden">class="mathCode">$I_s/I_c$ shows novel and unique physical phenomenon when the voltage bias and the temperature shift are changed in the nonequilibrium state. Another interesting phenomenon is that we can obtain the pure spin current and a zero point of the thermocurrent class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0375960116306302&_mathId=si6.gif&_user=111111111&_pii=S0375960116306302&_rdoc=1&_issn=03759601&md5=9688a40c8258610c617e7122d452f6a9" title="Click to view the MathML source">I_thclass="mathContainer hidden">class="mathCode">$I_{th}$ by adjusting the voltage bias and the temperature shift.