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arXiv:cond-mat/9510125 · Physical review. B, Condensed matter

Generation of spin-polarized currents in Zeeman-split Tomonaga-Luttinger models

T. Kimura, Kazuhiko Kuroki, Hideo Aoki

Published Apr 15, 1996• 42 citations
arXivHTMLPDF

Abstract

In a magnetic field an interacting electron gas in one dimension may be described as a Tomonaga-Luttinger model comprising two components with different Fermi velocities due to the Zeeman splitting. This destroys the spin-charge separation, and even the quantities such as the density-density correlation involve the spins. Specifically, we have shown that the ratio of the up-spin and down-spin conductivities in a dirty system diverges at low temperatures like an inverse power of the temperature, resulting in a spin-polarized current. In finite, clean systems the conductance becomes different for up and down spins as another manifestation of the electron-electron interaction. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevb.53.9572

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In a magnetic field an interacting electron gas in one dimension may be described as a Tomonaga-Luttinger model comprising two components with different Fermi velocities due to the Zeeman splitting. This destroys the spin-charge separation, and even the quantities such as the density-density correlation involve the spins. Specifically, we have shown that the ratio of the up-spin and down-spin conductivities in a dirty system diverges at low temperatures like an inverse power of the temperature, resulting in a spin-polarized current. In finite, clean systems the conductance becomes different for up and down spins as another manifestation of the electron-electron interaction. \textcopyright{} 1996 The American Physical Society.
Interacting electron systems in one dimension with spin-split Fermi points are studied theoretically with the aid of the Tomonaga-Luttinger bosonization. The spin splitting of the systems considered is classified into three categories: (i) the momentum-dependent spin splitting without the time-reversal symmetry, (ii) the momentum-dependent spin splitting with the time-reversal symmetry, and (iii) the momentum-independent spin splitting. Calculating analytically the current-current correlation functions in the three cases, the critical exponents of the optical Fermi-edge singularity (FES) are obtained by using the forward-scattering Tomonaga-Luttinger model. The phase diagrams for the sign of the FES exponent are drawn to clarify the relation between the shape of optical edge spectra and the electron-electron or the electron-hole interactions. Response to circularly polarized incident light is also revealed. In the case of the momentum-dependent spin splitting, the power-law divergence of the edge spectra is possible even for repulsive electron-hole interactions. This is in striking contrast to the FES in spin-degenerate (no spin splitting) electron systems. The FES in a spin-split chiral Luttinger liquid is also discussed. \textcopyright{} 1996 The American Physical Society.
We investigate spin-charge mixing effect on resonant tunneling in spin-polarized Tomonaga-Luttinger liquid with double impurities. The mixing arises from Fermi velocity difference between two spin species due to Zeeman effect. Zero bias conductance is calculated as a function of gate voltage Vg{V}_{g}Vg​, gate magnetic field Bg{B}_{g}Bg​, temperature, and magnetic field applied to the system. Mixing effect is shown to cause rotation of the lattice pattern of the conductance peaks in (Vg,Bg)({V}_{g},{B}_{g})(Vg​,Bg​) plane, which can be observed in experiments. At low temperatures, the contour shapes are classified into three types, reflecting the fact that effective barrier potential is renormalized towards ``perfect reflection,'' ``perfect transmission,'' and magnetic field induced ``spin-filtering,'' respectively.
A system of one-dimensional electrons interacting via a short-range potential described by Hubbard model is considered in the regime of strong coupling using the Bethe ansatz approach. We study its momentum distribution function at zero temperature and find one additional singularity at the 3kF3{k}_{\mathrm{F}}3kF​ point. We identify that the second singularity is of the same Luttinger liquid type as the low-energy one at kF{k}_{\mathrm{F}}kF​. By calculating the spectral function simultaneously, we show that the second Luttinger liquid at 3kF3{k}_{\mathrm{F}}3kF​ is formed by charge modes only, unlike the known one around kF{k}_{\mathrm{F}}kF​ consisting of both spin and charge modes. This result reveals the ability of the spin-charge separation effect to split the Fermi point of free electrons into two, demonstrating its robustness beyond the low-energy limit of Luttinger liquid where it was originally found.
Conductivity of a coupled two-channel dirty Tomonaga-Luttinger model is calculated from the Mori formalism. We find that the conductivity becomes enhanced as the interchannel interaction is turned on even when the interaction is repulsive. This effect is opposite to those from the 2KF{\mathit{K}}_{\mathit{F}}KF​ charge-fluctuation coupling in systems with the channel separation 1/kF{\mathit{k}}_{\mathit{F}}kF​, and is considered to come from the suppressed charge-density-wave fluctuations.
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 tunneling 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.
Abstract It has been shown (Yang and You 2011 Chin. Phys. Lett. 28 020503 ) that at zero temperature the ground state of the one-dimensional (1D) w -component Fermi gas coincides with that of the spinless Bose gas in the limit . This behavior was experimentally evidenced through quasi-1D tightly trapping ultracold 173 Yb atoms in a recent paper (Pagano et al 2014 Nat. Phys. 10 198 ). However, understanding of low-temperature behavior of Fermi gases with a repulsive interaction requires spin-charge separated conformal field theories of an effective Tomonaga–Luttinger liquid and an antiferromagnetic SU ( w ) Heisenberg spin chain. Here we analytically derive universal thermodynamics of 1D strongly repulsive fermionic gases with SU ( w ) symmetry via the Yang–Yang thermodynamic Bethe ansatz method. The analytical free energy and magnetic properties of the systems at low temperature in a weak magnetic field are obtained through the Wiener–Hopf method. In particular, the free energy essentially manifests the spin-charge separated conformal field theories for high-symmetry systems with arbitrary repulsive interaction strength. We also find that the sound velocity of the Fermi gases in the large w limit coincides with that for the spinless Bose gas, whereas the spin velocity vanishes quickly as w becomes large. This indicates strong suppression of the Fermi exclusion statistics by the commutativity feature among the w -component fermions with different spin states in the Tomonaga–Luttinger liquid phase. Moreover, the equations of state and critical behavior of physical quantities at finite temperature are analytically derived in terms of the polylogarithm functions in the quantum critical region.