Kondo effect in a quantum dot coupled to ferromagnetic leads and side-coupled to a nonmagnetic reservoir I. Weymann 1, 2, ∗ and J. Barna´s 1, 3 $^{1}$Department of Physics, Adam Mickiewicz University, 61-614 Pozna´ n, Poland $^{2}$Physics Department, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universit¨ at, Theresienstrasse 37, 80333 Munich, Germany $^{3}$Institute of Molecular Physics, Polish Academy of Sciences, 60-179 Pozna´ n, Poland (Dated: June 9, 2018) Equilibrium transport properties of a single-level quantum dot tunnel-coupled to ferromagnetic leads and exchange-coupled to a side nonmagnetic reservoir are analyzed theoretically in the Kondo regime. The equilibrium spectral functions and conductance through the dot are calculated using the numerical renormalization group (NRG) method. It is shown that in the antiparallel magnetic configuration, the system undergoes a quantum phase transition with increasing exchange coupling J , where the conductance drops from its maximum value to zero. In the parallel configuration, on the other hand, the conductance is generally suppressed due to an effective spin splitting of the dot level caused by the presence of ferromagnetic leads, irrespective of the strength of exchange constant. However, for J ranging from J = 0 up to the corresponding critical value, the Kondo effect and quantum critical behavior can be restored by applying properly tuned compensating magnetic field. PACS numbers: 72.25.-b, 73.63.Kv, 73.23.-b, 73.43.Nq, 85.75.-d Transport through a model single-level quantum dot captures many interesting and important features of transport phenomena in real quantum dots. One of such phenomena, which has been of great interest in the last decade, is the Kondo effect. 1–3 When the dot is occupied by a single electron, virtual transitions between the dot and electron reservoirs (external leads) cause spin fluc- tuations in the dot. As a result, the dot’s spin becomes screened by electrons of the reservoirs, which results in the formation of a non-local spin singlet ground state of the system. Furthermore, a resonance in the density of states appears at the Fermi level, which gives rise to en- hanced transmission through the dot. In experiments, this leads to the well-known zero-bias anomaly, i.e. a peak at zero bias in the differential conductance. 1,2 When the reservoirs are ferromagnetic, the effective exchange field generated by the electrodes may sup- press the Kondo anomaly. 4–9 More specifically, when the dot described by an asymmetric Anderson model is symmetrically coupled to ferromagnetic leads, then the Kondo effect becomes suppressed in the parallel configu- ration, while in the antiparallel configuration the Kondo anomaly survives. However, the Kondo effect in the parallel configuration can be restored, when an exter- nal magnetic field, which compensates the exchange field created by the ferromagnetic leads, is applied. 10,11 This behavior was confirmed in a couple of recent experi- ments. 12–17 The situation becomes more complex and physically richer when the dot is exchange-coupled to an additional reservoir. 18 Such a model captures the essential physics of the so-called two-channel Kondo effect. 19–26 In the two- channel Kondo problem, two separate electron reservoirs (channels) compete with each other to screen the im- As discussed above, both the Kondo effect in a quan- tum dot coupled to ferromagnetic leads and the two- channel Kondo phenomenon were already extensively studied. However, the interplay of leads’ ferromagnetism and two-channel Kondo effect remains to a large extent unexplored. Therefore, in this paper we address the two-channel Kondo problem in the presence of ferromag- netism. In particular, we consider an Anderson quantum dot coupled to ferromagnetic leads and exchange-coupled to a nonmagnetic electron reservoir. Using the numerical renormalization group (NRG) method, we analyze the in- purity’s spin. If the coupling to one of them is larger than to the other one, a usual single-channel Kondo state (spin singlet) is formed between the dot and more strongly coupled reservoir. This results in two compet- ing Kondo ground states of the system, depending on the ratio of coupling strengths to the first and second conduc- tion channels. Interestingly, these two Kondo states are separated by a quantum critical point, where both cou- plings are equal and an exotic two-channel Kondo state is formed, which cannot be described within the Lan- dau Fermi-liquid theory. Very recently, the two-channel Kondo effect has been explored experimentally in quan- tum dots. 27 The experimental setup consisted of a small quantum dot coupled to external leads and to a large Coulomb-blockaded island. While the electrons could tunnel between the dot and the leads, only virtual tun- neling processes between the dot and the island were al- lowed, resulting in an exchange coupling. By tuning the exchange coupling, it was possible to study the quantum phase transition between the two ground states of the system and analyze transport behavior in the non-Fermi liquid regime. 27 Theoretically, such a two-channel setup can be modelled for example by a quantum dot which is tunnel-coupled to external leads and exchange-coupled to another electron reservoir. 28–30 I. INTRODUCTION arXiv:1001.2475v1 [cond-mat.mes-hall] 14 Jan 2010