Quantum phase transitions into Kondo states in bilayer graphene

Abstract

We study a magnetic impurity intercalated in bilayer graphene. A representative configuration generates a hybridization function with strong dependence on the conduction-electron energy, including a full gap with one hard and one soft edge. Shifts of the chemical potential via gating or doping drive the system between non-Kondo (free-moment) and Kondo-screened phases, with strong variation of the Kondo scale. Quantum phase transitions near the soft edge are of KosterlitzThouless type, while others are first order. Near the hard edge, a bound-state singlet appears inside the gap; although of single-particle character, its signatures in scanning tunneling spectroscopy are very similar to those arising from a many-body Kondo resonance.PACS numbers: 72.15. Qm, 73.22.Pr, 75.20.Hr, 64.70.Tg One of the remarkable manifestations of cooperative phenomena in condensed matter is the many-body screening of a magnetic impurity in a nonmagnetic metal. This Kondo effect, well understood in ordinary metals [1], acquires added complexity in cases where the host density of states (DOS) varies strongly with energy E near the chemical potential µ. The pseudogap Kondo problem [2-6] with a DOS ρ(E) ∝ |E − µ| r (realized, for example, for r = 1 in high-temperature superconductors [7]) exhibits a rich phase diagram that depends on the band exponent r, the impurity-host exchange coupling J, and the presence or absence of particle-hole (p-h) symmetry.Similar DOS features can also appear in lowdimensional systems such as graphene [8]. The technologically and conceptually important issue of creating localized magnetic moments in monolayer graphene, and the appearance of the Kondo effect, have been the focus of many recent theoretical [9][10][11][12][13][14][15][16][17][18][19][20] and experimental [21][22][23][24] studies, with controversial results (see [25] for an overview). A more complex DOS appears in bilayer graphene (BLG), a material that can be gapped by gating, and thus has attracted much attention for possible device applications [26]. The variety of microscopic environments for magnetic impurities combined with easy tunability, make BLG highly promising for the study of quantum phase transitions (QPTs) into various Kondo states [27,28].This paper explores such QPTs for a representative configuration of an intercalated spin σ = 1/2 magnetic impurity in BLG. This setup is described by an Anderson impurity model with an energy-dependent hybridization featuring a gap that has one hard and one soft edge. Under variation of the chemical potential µ, the system passes from a free-moment (FM) phase to a Kondo phase featuring a strong µ dependence of the Kondo temperature scale. The QPTs found near the soft hybridization edge are of Kosterlitz-Thouless type, while all other QPTs are first order. We present thermodynamic and spectral properties near these QPTs, and discuss some of their consequences for spectroscopy measurements. For µ near the hard hybridization edge, the FM phase exhibits a singlet bound state inside the gap. This bo...

Kondo effect in graphene with Rashba spin-orbit coupling

“…8 stem from the jump in the hybridization function. The dip or antiresonance in A imp at the location of the hybridization step is reminiscent of behavior found previously in systems with a gapped DOS, 52,[54][55][56][57] where resonances of single-particle character can appear inside the gap due to the jump onset in the hybridization function at the the gap edge.…”

“…Similar features have been predicted before in other situations where the hybridization function exhibits rapid or discontinuous energy dependence. [49][50][51][52][53] In the same range of µ, the impurity spectral function shows anomalies connected to those seen in the thermodynamic quantities. The Kondo peak is asymmetric about ω = 0 and for |µ − 2λ| T K has a sharp dip-like structure, which can be traced back to a similar feature found in the noninteracting limit of the model.…”

“…This distinctive property is associated with the sharp jump in Γ(E), similar to behavior found in other systems where the hybridization function has a strong energy dependence. [49][50][51][52] As χ imp is the impurity contribution to the susceptibility, the negative values mean that the introduction of the magnetic adatom lowers the susceptibility compared to that of an impurity-free graphene layer.…”

Ferromagnetism-induced Kondo effect in graphene with a magnetic impurity

“…In particular, graphene provides a perfect realization of the pseudogap Kondo problem [35][36][37], when local magnetic moments are created in graphene either by adatom deposition [38][39][40] or via point defects [41][42][43][44][45]. The resulting Kondo physics has attracted much research interest in the last decade [46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61]. Graphene can even realize salient Kondo models with multiple screening channels [62][63][64], having the SU (4) symmetry [65], and exhibiting the super-Ohmic dissipation [66].…”

Propriedades Magnéticas, De Transporte E Emergentes Em Sistemas Nanoscópicos Fortemente Correlacionados

“…Alguns autores argumentam que a susceptibilidade magnética da impureza, χ imp , pode ser negativa [82,[117][118][119][120], em particular quando o nível de Fermi está próximo a uma singularidade de Van-Hove para o sistema de uma rede quadrada [119]. Contudo, outros autores defendem que o comportamento observado para χ imp não é físico e que as propriedades magnéticas da impureza devem ser deduzidas da susceptibilidade magnética local, χ loc , [121], sugerindo que o sistema é sempre um líquido de Fermi.…”