劉志海, 劉江山, 馬建明, 鄭鐵軍, 張德剛

(1. 四川師范大學(xué) 物理與電子工程學(xué)院, 四川 成都 610101; 2. 成都紡織高等?？茖W(xué)校 基礎(chǔ)部, 四川 成都 611731)

鐵基超導(dǎo)體中非磁性雜質(zhì)引起的隙內(nèi)束縛態(tài)

劉志海1, 劉江山1, 馬建明1, 鄭鐵軍2, 張德剛

(1. 四川師范大學(xué) 物理與電子工程學(xué)院, 四川 成都 610101; 2. 成都紡織高等?？茖W(xué)校 基礎(chǔ)部, 四川 成都 611731)

鐵基超導(dǎo)體中單個(gè)非磁性雜質(zhì)引起的隙內(nèi)束縛態(tài)可以用來(lái)區(qū)分S-波和S±-波配對(duì)對(duì)稱性.基于一個(gè)兩軌道四帶緊束縛模型,研究在具有S±-波配對(duì)對(duì)稱性的鐵基超導(dǎo)體中單個(gè)非磁性雜質(zhì)對(duì)局域態(tài)密度的影響,獲得雜質(zhì)共振峰的高度、位置與雜質(zhì)勢(shì)的關(guān)系.發(fā)現(xiàn)在一定的雜質(zhì)勢(shì)范圍內(nèi)正、負(fù)能側(cè)雜質(zhì)共振峰出現(xiàn)的位置是對(duì)稱的,當(dāng)VS>0.40 eV時(shí),正能側(cè)的共振峰分裂為2個(gè)峰,VS=0.70 eV附近區(qū)間,在次近鄰點(diǎn)上的局域態(tài)密度中可以觀察到4個(gè)明顯的雜質(zhì)共振峰,分別位于ω±3.4 meV和ω±2.2 meV處，像這樣的隙內(nèi)束縛態(tài)可以通過(guò)掃描遂穿實(shí)驗(yàn)直接觀測(cè).

鐵基超導(dǎo)體; 超導(dǎo)序參量; 非磁性雜質(zhì); 隙內(nèi)束縛態(tài)

新型超導(dǎo)材料鐵基超導(dǎo)體的發(fā)現(xiàn)[1-5],為高溫超導(dǎo)電性的研究提供了新的平臺(tái).到目前為止,已獲得的鐵基超導(dǎo)材料的最高轉(zhuǎn)變溫度高達(dá)55 K[2].與銅氧化物超導(dǎo)體類似,鐵基超導(dǎo)體也有一個(gè)層狀結(jié)構(gòu),超導(dǎo)電性來(lái)自于FeAs層中的電子庫(kù)伯對(duì).與銅氧超導(dǎo)體不同的是,鐵基超導(dǎo)體中每個(gè)Fe原子位于相鄰的4個(gè)As原子組成的四面體的中心,每個(gè)元胞中的2個(gè)As原子分別位于Fe-Fe平面上方和下方.能帶計(jì)算[6-7]和ARPES實(shí)驗(yàn)[8-12]已經(jīng)揭示鐵基超導(dǎo)體中存在圍繞Γ(0,0)點(diǎn)的2個(gè)空穴型費(fèi)米面和圍繞M(π,π)點(diǎn)的2個(gè)電子型費(fèi)米面.

在鐵基超導(dǎo)電性的研究中,超導(dǎo)序參量的配對(duì)對(duì)稱性一直是一個(gè)核心的問(wèn)題.大量的理論研究[13-17]以及通過(guò)STM實(shí)驗(yàn)描繪的Fe(Te,Se)材料中準(zhǔn)粒子干擾模式與磁場(chǎng)的關(guān)系[18]都表明,鐵基超導(dǎo)體中電子型費(fèi)米面和空穴型費(fèi)米面上的超導(dǎo)序參量帶有相反的符號(hào).眾多實(shí)驗(yàn)[19-23]也揭示了各個(gè)費(fèi)米面上的超導(dǎo)能隙是無(wú)節(jié)點(diǎn)的、接近各向同性的,因此d-波及p-波配對(duì)可以被排除.所以一般認(rèn)為鐵基超導(dǎo)體中的超導(dǎo)序參量為具有帶間符號(hào)反轉(zhuǎn)的S±-波配對(duì),但也有研究[24-25]認(rèn)為其超導(dǎo)序參量可能為S++-波配對(duì),即各向異性的S-波配對(duì).相對(duì)于d-波及p-波配對(duì),S-波和S±-波配對(duì)更難以區(qū)分,因?yàn)槌搜刂鳰點(diǎn)的2個(gè)費(fèi)米面上的超導(dǎo)序參量反號(hào)外,二者具有相似的對(duì)稱性.

眾所周知,雜質(zhì)的研究是高溫超導(dǎo)電性研究的一個(gè)重要手段[26].在鐵基超導(dǎo)體的超導(dǎo)序參量的研究中,非磁性雜質(zhì)散射會(huì)在S±-波配對(duì)對(duì)稱性中引起隙內(nèi)束縛態(tài),而這樣的束縛態(tài)不會(huì)出現(xiàn)在S-波配對(duì)對(duì)稱性中[27-29],通過(guò)STM實(shí)驗(yàn)描繪鐵基超導(dǎo)體中雜質(zhì)點(diǎn)及其鄰近點(diǎn)上的局域態(tài)密度可以直接地觀測(cè)非磁性雜質(zhì)引起的隙內(nèi)束縛態(tài).鐵基超導(dǎo)體中單個(gè)非磁性雜質(zhì)引起的隙內(nèi)束縛態(tài)可以作為S±-波配對(duì)對(duì)稱性存在的信號(hào).

本文的研究將基于一個(gè)兩軌道四帶緊束縛模型[27].該模型充分考慮了Fe-Fe平面上、下方配體As原子對(duì)該平面內(nèi)電子態(tài)的影響,對(duì)于研究鐵基超導(dǎo)材料晶體裂開(kāi)的表面層或表面敏感實(shí)驗(yàn)中的層是十分必要的.該模型不僅成功地解釋了STM實(shí)驗(yàn)所觀察到的間隙鐵雜質(zhì)引起的零能束縛態(tài)[30]、疇壁結(jié)構(gòu)[31-32],重復(fù)了核磁共振以及中子散射實(shí)驗(yàn)獲得的超導(dǎo)相圖[33-34],也成功地解釋了STM實(shí)驗(yàn)觀察到的渦流核中的負(fù)能共振峰[35-36].本文將基于該理論模型,通過(guò)調(diào)節(jié)非磁性雜質(zhì)勢(shì)的大小,研究鐵基超導(dǎo)體中單個(gè)非磁性雜質(zhì)引起的隙內(nèi)束縛態(tài).

1 理論模型

在兩軌道四帶緊束縛模型中,考慮了每個(gè)元胞中包含2個(gè)Fe原子和2個(gè)As原子,每個(gè)Fe原子包含2個(gè)簡(jiǎn)并軌道dxz、dyz.因?yàn)榕cFe原子相鄰的4個(gè)As原子有2種不同的排列方式,所以可將其晶格劃分為亞晶格A和亞晶格B,每個(gè)亞晶格中包含一種Fe(A或B)原子和一種As(A或B)原子,As原子位于Fe-Fe平面上方(A)或下方(B).

兩軌道四帶緊束縛模型的哈密爾頓量為

(1)

利用傅里葉變換式

將實(shí)空間的哈密爾頓量變換到動(dòng)量空間并化簡(jiǎn)得

(2)

作參數(shù)替換

(3)

并將H0寫成矩陣形式,可得到如下方程

(4)

由于波函數(shù)不為零,解方程可得

(5)

解得的對(duì)應(yīng)本征函數(shù)為

(6)

其中,下腳標(biāo)0、1分別代表簡(jiǎn)并軌道dxz、dyz,u(ν)=0、1代表不同的能帶,晶格常數(shù)取a=1.

為了將哈密爾頓量H0對(duì)角化,作如下正則變換

(7)

最終得到哈密爾頓量H0的如下對(duì)角形式

(8)

其中

為了探究鐵基超導(dǎo)體的超導(dǎo)電性,引入平均場(chǎng)BCS哈密爾頓量

(9)

H=H0+HBCS+HNMI,

(10)

作波戈留波夫變換,令

(11)

可將總的哈密爾頓量H對(duì)角化得

(12)

為了解出局域態(tài)密度的表達(dá)式,構(gòu)造格林函數(shù)

(13)

求解可得

(14)

兩軌道四帶緊束縛模型中亞晶格A、B上的局域態(tài)密度分別為:

(15)

(16)

式中

在本文的計(jì)算中,采用文獻(xiàn)[27]中給出的參數(shù),取Δ05.8meV,t1=0.5,t2=0.2,t3=-1.0,t4=0.02,μ=-0.49eV對(duì)應(yīng)于理想電子摻雜(15%).

2 非磁性雜質(zhì)引起的隙內(nèi)束縛態(tài)

圖1中描述的是根據(jù) (15)和(16) 式計(jì)算得到的無(wú)雜質(zhì)時(shí)(Vs=0)亞晶格A和B原點(diǎn)處的局域態(tài)密度,可以明顯地觀察到無(wú)雜質(zhì)時(shí)亞晶格A、B原點(diǎn)處的局域態(tài)密度曲線基本重合.存在一大一小2個(gè)能隙Δ=5.8meV,Δ2=4.8meV,這與鐵基超導(dǎo)體的多費(fèi)米面結(jié)構(gòu)有關(guān),較小能隙來(lái)自于β費(fèi)米面[19-20],該計(jì)算結(jié)果與S.Grothe等[37]通過(guò)STM實(shí)驗(yàn)觀測(cè)到的結(jié)果吻合.

圖 1 無(wú)雜質(zhì)時(shí)亞晶格A、B原點(diǎn)處的局域態(tài)密度

下面計(jì)算一個(gè)位于亞晶格A原點(diǎn)處的單個(gè)非磁性雜質(zhì)對(duì)局域態(tài)密度的影響.圖2為雜質(zhì)勢(shì)(VS>0,排斥勢(shì))取不同值時(shí)在雜質(zhì)點(diǎn)、最近鄰點(diǎn)以及次近鄰點(diǎn)上的局域態(tài)密度.在雜質(zhì)點(diǎn)上,當(dāng)VS=0.13 eV時(shí),僅能在ω-3.4 meV處觀察到明顯的雜質(zhì)共振峰.隨著VS的增大,在正能側(cè)對(duì)稱的位置也出現(xiàn)共振峰;當(dāng)VS=0.22 eV時(shí)雜質(zhì)共振峰分別出現(xiàn)在ω±2.8 meV處,正、負(fù)能側(cè)共振峰高度的變化趨勢(shì)均為先增大然后逐漸減小;當(dāng)VS<0.40 eV時(shí),兩側(cè)峰的位置都逐漸向零能移動(dòng);VS<0.80 eV時(shí),較高的峰均出現(xiàn)在負(fù)能側(cè).

圖 2 排斥勢(shì)(VS>0)時(shí)雜質(zhì)點(diǎn)、最近鄰點(diǎn)、次近鄰點(diǎn)上的局域態(tài)密度

在最近鄰點(diǎn)上,當(dāng)VS=0.13 eV時(shí),可以觀察到2個(gè)雜質(zhì)共振峰,分別位于ω±3.4 meV處,隨著VS的增大,共振峰高度的變化趨勢(shì)與雜質(zhì)點(diǎn)相同;VS<0.35 eV時(shí),正、負(fù)能側(cè)共振峰出現(xiàn)的位置也與雜質(zhì)點(diǎn)相同,但較高的峰出現(xiàn)在正能側(cè),負(fù)能側(cè)的峰較不明顯;當(dāng)VS在0.35 eV～1.0 eV范圍內(nèi)時(shí),在負(fù)能側(cè)觀察不到明顯的雜質(zhì)共振峰.

在次近鄰點(diǎn)上,當(dāng)VS=0.13 eV時(shí),也可在ω±3.4 meV處觀察到2個(gè)雜質(zhì)共振峰,但當(dāng)VS在0.17 eV～0.30 eV范圍內(nèi)時(shí)負(fù)能側(cè)的共振峰消失;VS>0.30 eV時(shí)在負(fù)能側(cè)重新出現(xiàn)可觀察到的雜質(zhì)共振峰,但負(fù)能側(cè)共振峰出現(xiàn)的位置與雜質(zhì)點(diǎn)不再相同,如圖2(e);當(dāng)VS<1.0 eV時(shí)較高的峰均出現(xiàn)在正能側(cè).

隨著VS繼續(xù)增大,3個(gè)點(diǎn)上的局域態(tài)密度值都逐漸降低,當(dāng)VS→+時(shí),雜質(zhì)點(diǎn)上的局域態(tài)密度趨于零.此外,在圖2(e)中可以明顯地觀察到在雜質(zhì)點(diǎn)、最近鄰點(diǎn)以及次近鄰點(diǎn)上的局域態(tài)密度中位于正能側(cè)的雜質(zhì)共振峰均分裂為2個(gè)峰.

為了詳細(xì)地研究圖2(e)中正能側(cè)共振峰的分裂,分析了VS>0.40 eV時(shí)3個(gè)點(diǎn)上的局域態(tài)密度的變化情況,隨著VS的增大,正能側(cè)2個(gè)共振峰的絕對(duì)高度都在降低,但靠近零能的峰相對(duì)于靠近能隙邊緣的峰變得更高;VS<1.0 eV時(shí)靠近零能的峰逐漸向零能移動(dòng),靠近能隙邊緣的峰則逐漸向能隙邊緣移動(dòng).圖3給出了VS=0.70 eV時(shí)在雜質(zhì)點(diǎn)、最近鄰點(diǎn)以及次近鄰點(diǎn)上的局域態(tài)密度.在次近鄰點(diǎn)上,可以明顯地觀察到在ω±3.4 meV和ω±2.2 meV處共存在4個(gè)雜質(zhì)共振峰.在最近鄰點(diǎn)上,可以觀察到2個(gè)雜質(zhì)共振峰分別位于ω+3.4 meV和ω+2.2 meV處,雖然在ω-3.4 meV和ω-2.2 meV處觀察不到明顯的共振峰,但經(jīng)過(guò)對(duì)數(shù)據(jù)仔細(xì)地分析可以發(fā)現(xiàn),在最近鄰點(diǎn)上的局域態(tài)密度中在上述2點(diǎn)都存在極大值.在雜質(zhì)點(diǎn)上,在ω±2.2 meV和ω+3.4 meV處共可觀察到3個(gè)雜質(zhì)共振峰,同樣分析數(shù)據(jù)可以發(fā)現(xiàn),在雜質(zhì)點(diǎn)上的局域態(tài)密度中在ω-3.4 meV處也存在極大值.

圖 3 VS=0.70 eV時(shí)雜質(zhì)點(diǎn)、最近鄰點(diǎn)、次近鄰點(diǎn)上的局域態(tài)密度

注：箭頭代表較小能隙(Δ2=4.8 meV)的相干峰

圖4中描述的是雜質(zhì)勢(shì)為吸引勢(shì)(VS<0)時(shí)的情況.在雜質(zhì)點(diǎn)上,當(dāng)VS=-0.13 eV時(shí),僅能在ω+4.2 meV處觀察到一個(gè)雜質(zhì)共振峰.隨著|VS|的增大,峰的位置逐漸向零能移動(dòng),局域態(tài)密度值逐漸減小并趨于零,在負(fù)能側(cè)始終沒(méi)有共振峰出現(xiàn).在最近鄰點(diǎn)上,|VS|<1.0 eV時(shí),在正、負(fù)能側(cè)均觀察不到明顯的雜質(zhì)共振峰,當(dāng)VS=-1.0 eV時(shí),其局域態(tài)密度中存在一個(gè)共振峰,位于ω-2.8 meV處.在次近鄰點(diǎn)上,當(dāng)VS=-0.13 eV時(shí),可以在ω-4.2 meV處觀察到一個(gè)雜質(zhì)共振峰,共振峰的位置隨|VS|的變化趨勢(shì)與雜質(zhì)點(diǎn)相同,當(dāng)VS=-1.0 eV時(shí),其局域態(tài)密度中存在2個(gè)共振峰,分別出現(xiàn)在ω-3.8 meV和ω-2.8 meV處.3個(gè)點(diǎn)上的局域態(tài)密度值都隨著|VS|的增大而減小,當(dāng)VS→-時(shí),雜質(zhì)點(diǎn)上的局域態(tài)密度趨于零.

圖2(a)和4(a)中都給出了VS=0時(shí)的局域態(tài)密度,通過(guò)對(duì)比可以明顯地看出,與排斥勢(shì)相比,吸引勢(shì)時(shí)雜質(zhì)共振峰的高度更低、峰出現(xiàn)的位置更加靠近能隙邊緣,吸引勢(shì)對(duì)局域態(tài)密度有較小的影響.當(dāng)VS>0.13 eV時(shí),局域態(tài)密度中較小能隙Δ2依然能夠被清晰地觀察到,但較大能隙Δ的相干峰則完全消失,如圖2,非磁性雜質(zhì)對(duì)較大能隙Δ有較強(qiáng)的抑制作用.當(dāng)|VS|<0.11 eV時(shí),無(wú)論對(duì)于排斥勢(shì)還是吸引勢(shì),在3個(gè)點(diǎn)上的局域態(tài)密度中均未觀察到明顯的隙內(nèi)束縛態(tài).

圖 4 吸引勢(shì)(VS<0)時(shí)雜質(zhì)點(diǎn)、最近鄰點(diǎn)、次近鄰點(diǎn)上的局域態(tài)密度

我們也計(jì)算了雜質(zhì)勢(shì)取幺正極限(VS→)時(shí)的情況,如圖5所示.當(dāng)VS→時(shí),雜質(zhì)點(diǎn)上的局域態(tài)密度趨于零,最近鄰點(diǎn)和次近鄰點(diǎn)上的局域態(tài)密度的變化趨勢(shì)相同,較高的峰都出現(xiàn)在負(fù)能側(cè),但次近鄰點(diǎn)上的共振峰高度更高.當(dāng)VS→+和VS→-時(shí),最近鄰點(diǎn)和次近鄰點(diǎn)上的局域態(tài)密度曲線分別重合.在次近鄰點(diǎn)上的局域態(tài)密度中可以明顯地觀察到4個(gè)雜質(zhì)共振峰,分別位于ω±3.6 meV和ω±2.4 meV處.

3 結(jié)果與討論

本文基于一個(gè)鐵基超導(dǎo)體的兩軌道四帶緊束縛模型,詳細(xì)地研究了在具有S±-波配對(duì)對(duì)稱性的鐵基超導(dǎo)體中一個(gè)位于亞晶格A原點(diǎn)處的非磁性雜質(zhì)對(duì)局域態(tài)密度的影響.通過(guò)調(diào)節(jié)非磁性雜質(zhì)勢(shì)VS的大小,詳細(xì)地分析了在不同雜質(zhì)勢(shì)下單個(gè)非磁性雜質(zhì)引起的隙內(nèi)束縛態(tài),獲得了雜質(zhì)共振峰的高度及位置隨雜質(zhì)勢(shì)VS的變化規(guī)律,與Kariyado等[28]基于一個(gè)五軌道模型研究得出的變化規(guī)律定性一致.我們也計(jì)算了雜質(zhì)勢(shì)取幺正極限時(shí)的情況,當(dāng)VS→時(shí),雜質(zhì)點(diǎn)上的局域態(tài)密度趨于零,在最近鄰點(diǎn)和次近鄰點(diǎn)上的局域態(tài)密度中在靠近能隙邊緣處可以觀察到明顯的隙內(nèi)束縛態(tài).本文中發(fā)現(xiàn)當(dāng)雜質(zhì)勢(shì)在一定范圍內(nèi)時(shí),正、負(fù)能側(cè)雜質(zhì)共振峰出現(xiàn)的位置是對(duì)稱的,當(dāng)VS>0.40 eV時(shí),正能側(cè)的雜質(zhì)共振峰分裂為2個(gè)峰,在VS=0.70 eV附近區(qū)間,在次近鄰點(diǎn)上的局域態(tài)密度中可以觀察到4個(gè)雜質(zhì)共振峰,分別位于ω±3.4 meV和ω±2.2 meV處.鐵基超導(dǎo)體中單個(gè)非磁性雜質(zhì)引起的隙內(nèi)束縛態(tài)可以用來(lái)區(qū)分其超導(dǎo)序參量的S-波和S±-波配對(duì)對(duì)稱性,而這樣的隙內(nèi)束縛態(tài)能夠通過(guò)STM/STS實(shí)驗(yàn)描繪的雜質(zhì)點(diǎn)及其鄰近點(diǎn)上的局域態(tài)密度圖像直接觀測(cè).

[1] KAMIHARA Y, WATANABE T, HIRANO M, et al. Iron-based layered superconductor La [O1-xFx] FeAs (x=0.05-0.12) with Tc= 26 K[J]. Am Chem Soc,2008,130(11):3296-3297.

[2] ZHI A R, WEI L, JIE Y, et al. Superconductivity at 55 K in iron-based F-doped layered quaternary compound Sm [O1-xFx] FeAs[J]. Chin Phys Lett,2008,25(6):2215.

[3] CHEN X H, WU T, WU G, et al. Superconductivity at 43 K in SmFeAsO1-xFx[J]. Nature,2008,453(7196):761-762.

[4] CHEN G F, LI Z, WU D, et al. Superconductivity at 41 K and its competition with spin-density-wave instability in layered CeO1-xFxFeAs[J]. Phys Rev Lett,2008,100(24):247002.

[5] WEN H H, MU G, FANG L, et al. Superconductivity at 25 K in hole-doped (La1-xSrx) OFeAs[J]. Euro phys Lett,2008,82(1):17009.

[6] SINGN D J, DU M H. Density functional study of LaFeAsO1-xFx:a low carrier density superconductor near itinerant magnetism[J]. Phys Rev Lett,2008,100(23):237003.

[7] NEKRASOV I A, PCHELKINA Z V, SADOVSKII M V. Electronic structure of prototype AFe2As2and ReOFeAs high-temperature superconductors:a comparison[J]. JETP Lett,2008,88(2):144-149.

[8] LU D H, YI M, MO S K, et al. Electronic structure of the iron-based superconductor LaOFeP[J]. Nature,2008,455(7209):81-84.

[9] LIU C, SAMOLYUK G D, LEE Y, et al. K-doping dependence of the Fermi surface of the iron-arsenic Ba1-xKxFe2As2superconductor using angle-resolved photoemission spectroscopy[J]. Phys Rev Lett,2008,101(17):177005.

[10] ZABOLOTNYY V B, INOSOV D S, EVTUSHINSKY D V, et al. (π,π) Electronic order in iron arsenide superconductors[J]. Nature,2009,457(7229):569-72.

[11] TERASHIMA K, SEKIBA Y, BOWEN J H, et al. Fermi surface nesting induced strong pairing in iron-based superconductors[J]. Proceedings of the National Academy of Sciences,2009,106(18):7330-7333.

[12] SEKIBA Y, SATO T, NAKAYAMA K, et al. Electronic structure of heavily electron-doped BaFe1.7Co0.3As2studied by angle-resolved photoemission[J].New Physics,2009,11(2):025020.

[13] KUROKI K, ONARI S, ARITA R, et al. Unconventional pairing originating from the disconnected Fermi surfaces of superconducting LaFeAsO1-xFx[J]. Phys Rev Lett,2008,101(8):087004.

[14] MAZIN I I, SINGH D J, JOHANNES M D, et al. Unconventional superconductivity with a sign reversal in the order parameter of LaFeAsO1-xFx[J]. Phys Rev Lett,2008,101(5):057003.

[15] TSAI W F, YAO D X, BERNEVIG B A, et al. Properties of Josephson junctions involving the cos(kx)·cos(ky) pairing state in iron pnictides[J]. Phys Rev,2009,B80(1):012511.

[16] NOMURA T. Perturbation theory of high-Tc superconductivity in iron pnictides[J].Physical Society of Japan,2009,78(3):034716.

[17] GHAEMI P, WANG F, VISHWANATH A. Andreev bound states as a phase-sensitive probe of the pairing symmetry of the iron pnictide superconductors[J]. Phys Rev Lett,2009,102(15):157002.

[18] HANAGURI T, NIITAKA S, KUROKI K, et al. Unconventional s-wave superconductivity in Fe (Se,Te)[J]. Science,2010,328(5977):474-476.

[19] DING H, RICHARD P, NAKAYAMA K, et al. Observation of Fermi-surface-dependent nodeless superconducting gaps in Ba0.6K0.4Fe2As2[J]. Euro Phys Lett,2008,83(4):47001.

[20] NAKAYAMA K, SATO T, RICHARD P, et al. Superconducting gap symmetry of Ba0.6K0.4Fe2As2studied by angle-resolved photoemission spectroscopy[J]. Euro Phys Lett,2009,85(6):67002.

[21] HASHIMOTO K, SHIBAUCHI T, KATO T, et al. Microwave penetration depth and quasiparticle conductivity of PrFeAsO1-ysingle crystals:evidence for a full-gap superconductor[J]. Phys Rev Lett,2009,102(1):017002.

[22] EVTUSHINSKY D V, INOSOV D S, ZZBOLOTNYY V B, et al. Momentum dependence of the superconducting gap in Ba1-xKxFe2As2[J]. Phys Rev,2009,B79(5):054517.

[23] WANG X P, QIAN T, RICHARD P, et al. Strong nodeless pairing on separate electron Fermi surface sheets in (Tl,K) Fe1.78Se2probed by ARPES[J]. Euro Phys Lett,2011,93(5):57001.

[24] KONDO T, SANTANDER-SYRO A F, COPIE O, et al. Momentum dependence of the superconducting gap in NdFeAsO0.9F0.1single crystals measured by angle resolved photoemission spectroscopy[J]. Phys Rev Lett,2008,101(14):147003.

[25] KONTANI H, ONARI S. Orbital-fluctuation-mediated superconductivity in iron pnictides: analysis of the five-orbital Hubbard-Holstein model[J]. Phys Rev Lett,2010,104(15):157001.

[26] BALATSKY A V, VEKHTER I, ZHU J X. Impurity-induced states in conventional and unconventional superconductors[J]. Reviews of Modern Physics,2006,78(2):373.

[27] ZHANG D. Nonmagnetic impurity resonances as a signature of sign-reversal pairing in FeAs-based superconductors[J]. Phys Rev Lett,2009,103(18):186402.

[28] KARIYADO T, OGATA M. Single-impurity problem in iron-pnictide superconductors[J]. J Phys Society Jpn,2010,79(8):1154-1174.

[29] TSAI W F, ZHANG Y Y, FANG C, et al. Impurity-induced bound states in iron-based superconductors with s-wave coskx·coskypairing symmetry[J]. Phys Rev,2009,B80(6):064513.

[30] ZHANG D. In-gap bound states induced by interstitial Fe impurities in iron-based superconductors[J]. Physica C:Superconductivity and Its Applications,2015,519:43-46.

[31] HUANG H, ZHANG D, ZHOU T, et al. Domain walls in normal and superconducting states of iron pnictides[J]. Phys Rev,2011,B83(13):134517.

[32] LI B, LI J, BASSLER K E, et al. Magnetic domain walls induced by twin boundaries in low doped Fe-pnictides[J].New Physics,2013,15(10):103018.

[33] LAPLACE Y, BOBROFF J, RULLIER-ALBENQUE F, et al. Atomic coexistence of superconductivity and incommensurate magnetic order in the pnictide Ba (Fe1-xCox) 2As2[J]. Phys Rev,2009,B80(14):140501.

[34] ZHOU T, ZHANG D, TING C S. Spin-density wave and asymmetry of coherence peaks in iron pnictide superconductors from a two-orbital model[J]. Phys Rev,2010,B81(5):052506.

[35] GAO Y, HUANG H X, CHEN C, et al. Model of vortex states in hole-doped iron-pnictide superconductors[J]. Phys Rev Lett,2011,106(2):027004.

[36] SHAN L, WANG Y L, SHEN B, et al. Observation of ordered vortices with Andreev bound states in Ba0.6K0.4Fe2As2[J]. Nature Physics,2011,7(4):325-331.

[37] GROTHE S, CHI S, DOSANJH P, et al. Bound states of defects in superconducting LiFeAs studied by scanning tunneling spectroscopy[J]. Phys Rev,2012,B86(17):174503.

In-gap Bound States Induced by a Nonmagnetic Impurity in Iron-based Superconductors

LIU Zhihai1, LIU Jiangshan1, MA Jianming1, ZHENG Tiejun2, ZHANG Degang1

(1.CollegeofPhysicsandElectronicEngineering,SichuanNormalUniversity,Chengdu610101,Sichuan;2.DepartmentofFundamentalEducation,ChengduTextileCollege,Chengdu611731,Sichuan)

In-gap bound states induced by a nonmagnetic impurity can be used to distinguish the S-wave and S±-wave pairing symmetry in iron-based superconductors. Based on a two-orbit four-band tight binding model, the effect of single nonmagnetic impurity effects on the local density of states in iron-based superconductors with the S±-wave symmetry is studied. The dependence of the intensities and positions of the impurity resonance peaks and the strength of impurity potential was obtained. The resonance peaks at positive and negative energies are symmetric in a certain range of the impurity potential. The impurity resonance peak at positive energy splits into two peaks whenVS>0.40 eV. An impurity withVS=0.70 eV induces four impurity resonance peaks on the next-nearest-neighbor site atω=±3.4 meV andω=2.2 meV, respectively. Such in-gap bound states could be observed by scanning tunneling microscopy experiments.

iron-based superconductors; superconducting order parameter; nonmagnetic impurity; in-gap bound states

2016-09-27

四川省“千人計(jì)劃”資助項(xiàng)目(34125003)

*通信作者簡(jiǎn)介：張德剛(1962—)，男，教授，主要從事超導(dǎo)理論、自旋電子學(xué)和統(tǒng)計(jì)模型精確解的研究，E-mail：degangzhang@yahoo.com

O48

A

1001-8395(2017)05-0666-09

10.3969/j.issn.1001-8395.2017.05.018

(編輯 鄭月蓉)