screeningkohnanomalyfriedeloscillationandrkkyinteractioninbilayergraphene-外文文獻(xiàn)-全文預(yù)覽
【正文】 ture Phys. 2, 177(2020)。 J. Nilsson, . Castro Neto, . Peres, andF. Guinea, Phys. Rev. B 73, 214418 (2020)。kFr222。r222。 formally scales as 1=r3, itsmagnitude does not converge], which means that intrinsicSLG is susceptible to ferromagic ordering in the presence of magic impurities [16,17] due to the divergentRKKY coupling.In doped (or gated) BLG, the oscillatory term in RKKYinteraction is restored due to the singularity of polarizability at q 188。r222。q222。r222。, where J is the exchange coupling01234q/k01Π(q)/NF0SLGBLG01234q/k01Π(q)/NF0SLGBLG01234q/k012Π(q)/NF0SLGBLG2D(a) (b)(c)FIG. 1 (color online). Calculated (a) intraband, (b) interband,and (c) total static polarizability of bilayer graphene. For parison, the single layer polarizabilities are shown. In (c), wealso show the regular 2D static polarizability (dashed line).PRL 101, 156802 (2020)PHYSICAL REVIEW LETTERSweek ending10 OCTOBER 20201568023constant. The RKKY interaction between two localizedmoments via the conduction electrons may then be writtenin the following form: HRKKY240。s240。r222。q222。q222。 2kF. It is obvious from Fig. 1(c), andfrom the discussion above based on our analytical resultsfor C15240。2kFr222。=2C138, which is similar to the2DEG except for the additional constant C (C 188。???5pC0log189。240。2kF254。 at q 188。 for SLG and C15240。q !1222。q222。 .,as q ! 2kF, dC5240。 2kFas existsin SLG and 2DEG.A qualitative difference between SLG and BLG polarizability functions is at q 188。 decreases as 1C0q2=2k2F, and C5inter240。=dC138N240。188。188。0222。C18240。g240。q4=4q2k2FC21:(15)Finally, we have the extrinsic BLG static polarizability asC5240。188。logqC0???????????????????q2C04k2Fqq254。q222。g240。q222。N0188。q222。N0188。C0k2C0jk2C0q2j254。 (11)C5inter240。2k2C0q2222。q222。cos2C182(9)andC5inter240。, whereC5intra240。q222。.Then we can rewrite Eq. (1)asC5240。 1 and f254。188。q222。e2g=vF222。C25=8222。1254。2C25vF222。188。C24eqs=C20240。 and N0240。qsr222。eC20rC0eC20C25qs2189。 (6)where qTFis the 2D ThomasFermi screening wave vector[11]: qTF188。188。N0log4。=jk254。 (4)where cosC18 188。2C25222。, whereC50240。 1. Since the conduction band is empty, the polarization is induced by thevirtual interband transition of electrons from the valenceto the conduction band. The polarizability due to the interband transition bees C5240。 1=kBT and C22 thechemical potential.PRL 101, 156802 (2020)PHYSICAL REVIEW LETTERSweek ending10 OCTOBER 202000319007=08=101(15)=156802(4) 1568021 C211 2020 The American Physical SocietyFirst, we consider intrinsic (., undoped or ungated,with n and EFboth being zero) BLG where the conductionband is empty and the valence band fully occupied at T 188。expfC12240。1254。k。q, s。k0222。q222。q222。C61denote the band index. Using the Hamiltonian of Eq. (1),we theoretically obtain the screening function of BLG bycalculating the polarizability and the dielectric functionwithin the RPA.The static dielectric function can be written asC15240。 sk2=2m, where C18k188。eikr240。 (1)where m 188。2240。 matrix form and isgiven by (we use 188。Screening, Kohn Anomaly, Friedel Oscillation, and RKKY Interaction in Bilayer Graphene. Hwang and S. Das SarmaCondensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 207424111, USA(Received 18 April 2020。2C22222。kxC0iky222。20 !。, C131is the interlayer tunneling amplitude, and vFis the SLG Fermi velocity. The wavefunction of Eq. (1) can be written as csk188。=???2p, and the corresponding energy is givenby C15sk188。 and s 188。1C02C25e2C20qC5240。thepolarizability. The static BLG polarizability is given by thebare bubble diagramC5240。k。 k254。 sk2=2m, and Fss0240。240。189。1C138C01, with C12 188。 0 and fC0k188。q222。g2Zd2k240。k0
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