Physics of arbitrarily doped Kondo lattices: From a commensurate insulator to a heavy Luttinger liquid and a protected helical metal

We study one-dimensional Kondo lattices (KLs) which consist of itinerant electrons interacting with Kondo impurities (KIs)—localized quantum magnetic moments. We focus on KLs with isotropic exchange interaction between electrons and KIs and with a high KI density. The latter determines the principal role of the indirect interaction between KIs for the low-energy physics. Namely, the Kondo physics becomes suppressed and all properties are governed by spin ordering. We present a comprehensive analytical theory of such KLs at an arbitrary doping and predict a variety of regimes with different electronic phases. They range from commensurate insulators (at filling factors 1/2, 1/4, and 3/4) to metals with strongly interacting conduction electrons (close to these three special cases) to an exotic phase of a helical metal. The helical metals can provide a unique platform for realization of an emergent protection of ballistic transport in quantum wires. We compare our theory with previously obtained numerical results and discuss possible experiments where the theory could be tested.

Figure 1

Upper panel: a cartoon illustrating the weak and the moderate coupling regimes of the phase diagram obtained numerically for 1D KL in Ref. [19]. The two shaded regions are ferromagnetic phases. The region called “Polaronic Liquid” corresponds to the large Fermi surface whose volume incorporates both conduction and localized electrons. The Kondo effect is suppressed in all regions. The orange box marks the range of parameters considered in the present paper. Central and lower panels: phase diagrams of 1D KL obtained for small $J_K/E_F$; see explanations in Sec. 5.

Figure 2

(a),(b) Ground state of fermions $\tilde{R},\tilde{L}$ with zero chemical potential (green region) before and after opening the gap at the level of $\mu$. (c),(d)Ground state of the fermions for the case of a finite positive chemical potential. The red regions mark the states between the gap and the chemical potential which can form Tomonaga-Luttinger liquid. Panel (e) exemplifies a coexistence of the gapped (black lines) and the gapless (orange and blue lines) helical fermions.

Figure 3

The spin response of the KL close to the special commensurate fillings. The main response is at frequencies higher than the spin gap and coming from the vicinity of the commensurate wave vector (e.g., $\pi /\xi$ for half filling). The spin response of TLL is shifted to the region of wave vectors between 0 and $2k_F^{*}$.