screening，kohnanomaly，friedeloscillation，andrkkyinteractioninbilayergraphene-外文文献(编辑修改稿)

screening，kohnanomaly，friedeloscillation，andrkkyinteractioninbilayergraphene-外文文献(编辑修改稿)内容摘要：

0skC0C0sk0C211C0cos2C182: (10)C5intra(C5inter) indicates the polarization due to intraband(interband) transition. After angular integration over thedirection of q, we haveC5intra240。 q222。 188。 gm2C25ZkF0dkk3C20k2C0jk2C0q2j254。 240。 2k2C0q2222。 2qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiq2C04k2p C18240。 qC02k222。 C21。 (11)C5inter240。 q222。 188。 gm2C25Z1kFdkk3189。 C0k2C0jk2C0q2j254。 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4k4254。 q4qC138:(12)ThenC5intra240。 q222。 N0188。 8:1C0q22k2Fif q C20 kF。 q22k2FC02logqkFif kFq2kF。 q22k2FC02logqkFC0f240。 q222。 if q2kF。 (13)C5inter240。 q222。 N0188。 8:C01254。 q22k2F254。 g240。 q222。 if q C20 kF。 C0q22k2F254。 2logq254。 g240。 q222。 if qkF。 (14)withf240。 q222。 188。 2k2F254。 q22k2Fqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiq2C04k2Fq254。 logqC0ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiq2C04k2Fqq254。 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiq2C04k2Fq。 g240。 q222。 188。 12k2Fffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4k4F254。 q4qC0logC20k2F254。 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffik4F254。 q4=4q2k2FC21:(15)Finally, we have the extrinsic BLG static polarizability asC5240。 q222。 188。 N0189。 g240。 q222。 C0f240。 q222。 C18240。 qC02kF222。 C138: (16)Equation (16) with Eq. (15) is the basic result obtained inthis Letter, giving the doped BLG polarizabilityanalytically.In Fig. 1, we show the calculated static polarizabilityas a function of the wave vector. Figures 1(a) and 1(b)show the calculated intraband and interband polarizabilities, respectively, with those of single layer graphene forparison. Figure 1(c) shows total polarizability of bilayer graphene. At q 188。 0, we have C5intra240。 0222。 188。 N0andC5inter240。 0222。 188。 0, which follow also from the pressibilitysum rule C5240。 q 188。 0222。 188。 Rd189。 C0df240。 C15222。 =dC138N240。 q222。 . For smallPRL 101, 156802 (2020)PHYSICAL REVIEW LETTERSweek ending10 OCTOBER 20201568022q, C5intra240。 q222。 decreases as 1C0q2=2k2F, and C5inter240。 q222。 increases as q2=2k2F. This behavior es from the overlapfactor Fss0 in Eq. (3). For SLG, intraband (interband)polarizability decreases (increases) linearly as q increases,and these two effects exactly cancel out up to q 188。 2kF,which gives rise to the total static polarizability beingconstant for q2kFas in the 2DEG. However, for BLG,the cancellation of two polarizability functions is not exactespecially for qkFbecause of the enhanced backscattering, so the total polarizability increases as q approaches2kF, which means screening increases as q increases. ThusBLG, in spite of being a 2D system, does not have aconstant ThomasFermi screening up to q 188。 2kFas existsin SLG and 2DEG.A qualitative difference between SLG and BLG polarizability functions is at q 188。 2kF. Because of the suppression of 2kFbackward scattering in SLG, the totalpolarizability as well as its first derivative are continuous.In BLG, however, the large angle scattering is enhanceddue to chirality [., the overlap factor Fss0 in Eq. (3)],whichgivesrisetothesingularbehaviorofpolarizabilityatq 188。 2kF. Even though the BLG polarizability is continuous at q 188。 2kF, it has a sharp cusp and its derivative isdiscontinuous at 2kF, diverging as q approaches 2kF。 .,as q ! 2kF, dC5240。 q222。 =dq / 1=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiq2C04k2Fq. This behavior isexactly the same as that of the regular 2DEG, which alsohas a cusp at q 188。 2kFin addition to being constant in the0 C20 q C20 2kFregion. Note that in SLG this nonanalyticbehavior of polarizability occurs in the second derivative:d2C5240。 q222。 =dq2/ 1=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiq2C04k2Fq.In the large momentum transfer regime q2kF, theBLG polarizability approaches a constant value (intrinsicpolarizability C50), ., C5240。 q222。 !N0log4, because the interband tr。