Charge and spin density in the helical Luttinger liquid

Abstract

-The weakly interacting helical Luttinger liquid, due to spin momentum locking, is characterized by extremely peculiar local observables: we show that the density-density correlation functions do not exhibit signatures of Friedel and Wigner oscillations, and that spin-spin correlation functions, which are strongly anisotropic, witness the formation of a planar spin wave. Moreover, we demonstrate that the most relevant scattering potentials involving a localized impurity are not able to modify the electron density, while only magnetic impurities can pin the planar spin density wave. editor's choice Copyright c EPLA, 2016Introduction. -One-dimensional gapless quantum systems are characterized by a peculiar behavior: if (arbitrarily weak) inter-particle interaction is present, the low-energy excitations have a collective nature and are described by the Luttinger liquid theory [1][2][3]. Experimental evidence of the validity of the Luttinger liquid theory in fermionic systems has been achieved in a number of different devices, ranging from carbon nanotubes [4,5] and quantum wires [6,7], to Bechgaard salts [8] and edges of quantum Hall bars [9][10][11]. Exotic behaviors related to the Luttinger liquid, like spin charge separation [12] and charge fractionalization [13,14], have also been observed. Moreover, the Luttinger liquid picture is able to capture the low-energy properties of gapless one-dimensional bosonic [15] and spin systems [16]. In addition to its wide range of applicability, the Luttinger liquid picture has another important technical advantage: its Hamiltonian describes a collection of free bosons, and the fundamental field operators (right and left movers) of the theory can also be expressed by means of the creation and annihilation operators of such bosons, so that the correlation functions can very often be calculated analytically [2]. As a direct consequence of its wide range of validity, the relation between the fundamental field operators of the Luttinger liquid and the observables do depend on the system under consideration. Even though the thermodynamics of all the Luttinger liquid pictures of various systems is

Indirect exchange interaction between magnetic impurities in one-dimensional gapped helical states

“…For non-interacting case K = 1 while 0 < K < 1 (K > 1) corresponds to repulsive (attractive) electronic interactions. Also, we have assumed that the interactions are weak enough to ignore backscattering potential [76,77]. Note, however, that it has been shown that elastic spin-flip backscattering can be occurred by coupling of electrons to nuclear spins through the hyperfine interaction causing a significant edge resistance at low enough temperatures [56].…”