Probing Spin-Charge Separation in a Tomonaga-Luttinger Liquid

Abstract

In a one-dimensional (1D) system of interacting electrons, excitations of spin and charge travel at different speeds, according to the theory of a Tomonaga-Luttinger Liquid (TLL) at low energies. However, the clear observation of this spin-charge separation is an ongoing challenge experimentally. We have fabricated an electrostatically-gated 1D system in which we observe spin-charge separation and also the predicted power-law suppression of tunnelling into the 1D system. The spin-charge separation persists even beyond the low-energy regime where the TLL approximation should hold. TLL effects should therefore also be important in similar, but shorter, electrostatically gated wires, where interaction effects are being studied extensively worldwide.The effects of interactions are almost impossible to calculate in a general many-particle system, though they cannot be ignored. However, for a one-dimensional (1D) system, Luttinger, building on an approximation scheme of Tomonaga, constructed a soluble 1D model with infinite linear dispersion and a restricted set of interactions. The solution has 1 arXiv:1002.2782v1 [cond-mat.str-el]

Charge dynamics in half-filled Hubbard chains with finite on-site interaction

“…One motivation for this is that questions about features of the excitation spectrum of 1D systems, such as the persistence of spin-charge separation at high energies, have become relevant with the improvement in the resolution of momentum-resolved experiments. [4][5][6][7][8] In addition, ultracold atoms trapped in optical lattices have emerged as a new means to study coherent dynamics of 1D models, including integrable ones which are not realizable in condensed matter systems. 9 At the same time, significant progress has been achieved in developing analytical [10][11][12][13][14][15][16][17][18][19][20][21][22] and numerical [23][24][25] techniques to study dynamical correlation functions in the high energy regime where conventional Luttinger liquid theory 26,27 does not apply.…”

Separation of neutral and charge modes in one-dimensional chiral edge channels

“…M ost studies of collective excitations in one-dimensional (1D) systems performed so far have focused on nonchiral quantum wires [1][2][3] . In these systems, the collective excitations carrying the charge and the spin propagate at different velocities, leading to the separation of the charge and spin degrees of freedom.…”

“…In these systems, the collective excitations carrying the charge and the spin propagate at different velocities, leading to the separation of the charge and spin degrees of freedom. This spin-charge separation has been probed by measuring the tunnelling spectroscopy of individual electrons between a pair of 1D wires 1 , or alternatively, between a wire and a two-dimensional (2D) electron gas 3 . However, a direct observation of the collective modes is experimentally challenging as the relevant energy scales are too high for usual low-frequency measurements.…”

Spin and Charge Ordering in the Quantum Hall Regime

“…Apart from that, it is a beautiful example of fractionalization in solid state physics, according to which the properties of quasiparticles cannot be understood as a linear combination of its elementary constituents. This general phenomenon has been encountered in different manifestations in recent years, for example as magnetic monopoles in spin ice materials [71][72][73] or as deconfinement of an electron into holon, spinon and orbiton [74][75][76]. Further support for Laughlin's theory comes from exact diagonalization studies [77] and Monte Carlo simulations [78].…”

“…The observation of fractionally charged quasiparticles, for instance, is a beautiful manifestation of fractionalization -a many body phenomenon characterized by the appearance of quasiparticles which cannot be understood as a linear combination of its constituent particles. Similar physics is at play when a single electron decomposes in its fictitious constituents, the spinon, holon and orbiton [74][75][76], or alternatively in the case of magnetic monopoles in spin ice materials [71][72][73]. Another beautiful example of quantum Hall physics is the spontaneous symmetry breaking occurring in the density modulated phases at partially filled Landau levels [3].…”