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While the vast majority of known physical realizations of the Tomonaga-Luttinger liquid (TLL) have repulsive interactions defined with the dimensionless interaction parameter $K_{rm c}<1$, we here report that Rb$_2$Mo$_3$As$_3$ is in the opposite TLL regime of attractive interactions. This is concluded from a TLL-characteristic power-law temperature dependence of the $^{87}$Rb spin-lattice relaxation rates over broad temperature range yielding the TLL interaction parameter for charge collective modes $K_{rm c}=1.4$. The TLL of the one-dimensional band can be traced almost down to $T_{rm c} = 10.4 $~K, where the bulk superconducting state is stabilized by the presence of a three-dimensional band and characterized by the $^{87}$Rb temperature independent Knight shift and the absence of Hebel-Slichter coherence peak in the relaxation rates. The small superconducting gap measured in high magnetic fields reflects either the importance of the vortex core relaxation or the uniqueness of the superconducting state stemming from the attractive interactions defining the precursor TLL.
We present NMR measurements of a strong-leg spin-1/2 Heisenberg antiferromagnetic ladder compound (C7H10N)2CuBr4 under magnetic fields up to 15 T in the temperature range from 1.2 K down to 50 mK. From the splitting of NMR lines we determine the phas
In this work we derive a new scheme to calculate Tomonaga-Luttinger liquid (TLL) parameters and holon (charge modes) velocities in a quasi-1D material that consists of two-leg ladders coupled through Coulomb interactions. Firstly, we obtain an analyt
We study both noncentrosymmetric and time-reversal breaking Weyl semimetal systems under a strong magnetic field with the Coulomb interaction. The three-dimensional bulk system is reduced to many mutually interacting quasi-one-dimensional wires. Each
We present two methods to determine whether the interactions in a Tomonaga-Luttinger liquid (TLL) state of a spin-$1/2$ Heisenberg antiferromagnetic ladder are attractive or repulsive. The first method combines two bulk measurements, of magnetization
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 sep