潘慧雯,劉 柳,胡亞云,徐金良,李曉薇

(淮陰師范學(xué)院 物理與電子電氣工程學(xué)院,江蘇 淮安 223300)

有限溫度下石墨烯上鐵磁超導(dǎo)隧道結(jié)中微分電導(dǎo)的研究

潘慧雯,劉 柳,胡亞云,徐金良,李曉薇

(淮陰師范學(xué)院 物理與電子電氣工程學(xué)院,江蘇 淮安 223300)

石墨烯; 鐵磁體;p-波超導(dǎo)體; 超導(dǎo)隧道結(jié); 微分電導(dǎo)

0 引言

單層石墨片是只有一個原子層厚度的蜂窩狀的碳原子晶體,這種理想二維體系顯示了不同尋常的奇異特性[1-6],實(shí)驗(yàn)上已經(jīng)發(fā)現(xiàn)該體系具有很多新穎的物理性質(zhì),例如強(qiáng)磁場下反常的量子霍耳效應(yīng)[1]、彈道輸運(yùn)[3,4]、Josephson效應(yīng)[5]、雙極性超導(dǎo)特性[6]等.理論上,由于單層石墨片獨(dú)特的電子結(jié)構(gòu)和無質(zhì)量費(fèi)米子的特征,使得人們可以利用低能的凝聚態(tài)物理來模擬一些量子場論所預(yù)言的相對論量子現(xiàn)象[1,3,4],例如克萊因佯謬[7](Klein paradox).近幾年來,有關(guān)石墨層上超導(dǎo)隧道結(jié)的研究已成為當(dāng)前凝聚態(tài)物理的熱點(diǎn)之一.

近來,有很多關(guān)于基于石墨層上超導(dǎo)隧道結(jié)中準(zhǔn)粒子輸運(yùn)性質(zhì)的研究報道,人們研究了基于石墨層上正常金屬/s波和d波超導(dǎo)隧道結(jié)、石墨層上鐵磁體/s波超導(dǎo)體隧道結(jié)中準(zhǔn)粒子輸運(yùn)性質(zhì)[4,9-16],但有限溫度下有關(guān)基于石墨層上鐵磁/p波超導(dǎo)體隧道結(jié)中準(zhǔn)粒子輸運(yùn)性質(zhì)的研究還比較少.

本文利用推廣的BTK理論討論有限溫度下石墨層上鐵磁/p波超導(dǎo)體隧道結(jié)中準(zhǔn)粒子輸運(yùn)過程,計算結(jié)的微分電導(dǎo).計算結(jié)果表明,在有限溫度下,微分電導(dǎo)譜的電導(dǎo)峰對應(yīng)的偏壓位置隨α的增大從eV=Δ0處向零偏壓處移動,磁交換能EhEF時電導(dǎo)隨著磁交換能的增強(qiáng)而增大,此時鏡面Andreev反射起主導(dǎo)作用.在相同條件下,有限溫度下的微分電導(dǎo)隨溫度T的增大而減少.

1 模型

我們所研究的石墨層上鐵磁/p波超導(dǎo)體隧道結(jié)的結(jié)構(gòu)如圖1所示,x<0處為鐵磁態(tài),x>0處為p波超導(dǎo)體.當(dāng)不考慮準(zhǔn)粒子的自旋反轉(zhuǎn)效應(yīng)時,在石墨層上鐵磁/p波超導(dǎo)體隧道結(jié)中準(zhǔn)粒子的狀態(tài)可以由DBdG方程描述[8,15]:

(1)

h=EhΘ(-x)

(2)

Δk=Δ±(θ)Θ(x)

(3)

其中Θ(x)是階躍函數(shù),p波超導(dǎo)體的配對勢是各向異性的,電子、空穴的有效配對勢是不同的,分別是[19-21]:

Δ±(θ)=±Δ0cos(θ?α)

(4)

(5)

式中θ為準(zhǔn)粒子輸運(yùn)方向相對x軸的夾角,α是p波超導(dǎo)體的a軸與x軸的夾角,由于石墨層上蜂窩狀的碳原子晶體結(jié)構(gòu),α取0和±2π/3[24].式(4)(5)分別是零溫和有限溫度下的配對勢.

考慮電子型準(zhǔn)粒子從左邊入射的情況,在x<0處的鐵磁區(qū)域,電子型和空穴型準(zhǔn)粒子E>0的本征矢和波矢為:

(6)

(7)

(8)

EF是鐵磁區(qū)域的費(fèi)米能,平行于結(jié)方向的粒子的動量是守恒的,滿足條件:

(9)

其中θAσ最大值為900,超過900時,Andreev反射是一虛過程虛Andreev反射對電流沒有貢獻(xiàn).因此,θσ不能超過:

(10)

(1) 自旋向上的入射電子空穴 (2) 自旋向下的反向Andreev反射空穴(3) 自旋向上的反射電子 (4) 自旋向下的鏡面Andreev反射空穴(5) 自旋向上的透射電子型準(zhǔn)粒子 (6) 自旋向下的透射空穴型準(zhǔn)粒子

在x>0處的超導(dǎo)體區(qū)域,電子型和空穴型準(zhǔn)粒子E>0的本征矢和波矢為:

(11)

(13)

(14)

(15)

(16)

(17)

波函數(shù)滿足的邊界條件為[8]:

ψsσ(x=0-)=ψFσ(x=0+)

(18)

(19)

(20)

(21)

(22)

(23)

(24)

這里G0是常量,G1G2分別為零溫和有限溫度下的微分電導(dǎo).

(25)

Bσ(eV,θ)=|bσ(eV,θ)|2

(26)

圖2 微分電導(dǎo)隨偏壓V的變化關(guān)系曲線

2 計算結(jié)果和討論

3 結(jié)論

本文利用推廣的BTK理論討論石墨層上鐵磁/p波超導(dǎo)體隧道結(jié)中準(zhǔn)粒子輸運(yùn)過程,計算了結(jié)的微分電導(dǎo).計算結(jié)果表明,在有限溫度下,微分電導(dǎo)譜的電導(dǎo)峰對應(yīng)的偏壓位置隨α的增大從eV=Δ0處向零偏壓處移動,磁交換能EhEF時電導(dǎo)隨著磁交換能的增強(qiáng)而增大.微分電導(dǎo)隨溫度T的增大而減少;EF≠0的零偏壓電導(dǎo)值比零溫度下的對應(yīng)值小.

圖3 微分電導(dǎo)隨偏壓V的變化關(guān)系曲線

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[責(zé)任編輯：蔣海龍]

Tunneling Conductance in Graphene Ferromagnet/pWave Superconductor Junctions at Finite Temperature

PAN Hui-wen,LIU Liu,HU Ya-yun,XU Jin-liang,LI Xiao-wei

(School of physics and electronic electrical engineering,Huaiyin Normal University,Huaian Jiangsu 223300,China)

Using the extended Blonder-Tinkham-Klapwijk formalism,we investigate the conductance spectra of graphene ferromagnet/pwave superconductor junctions at finite temperature.It is found that the conductance spectra at finite temperature are affected by the p wave pairing symmetry.The ferromagnetic exchange energy in the ferromagnet can suppress Andreev retroreflection but enhance the specular Andreev reflection in graphene ferromagnet/pwave superconductor junctions.The conductance decreases at finite temperature with increasing exchange energyEhforEhEF.

graphene; ferromagnet;p-wave superconductor; superconductor junctions; differential conductance

O511

:A

:1671-6876(2015)01-0024-06