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Physical Review B

Momentum-resolved tunneling between a Luttinger liquid and a two-dimensional electron gas

S. A. Grigera, A. J. Schofield, Silvio Rabello, Qimiao Si A

Published Jun 18, 2004• 8 citations
Publisher

Abstract

We consider momentum resolved tunneling between a Luttinger liquid and a two-dimensional electron gas as a function of transverse magnetic field. We include the effects of an anomalous exponent and Zeeman splitting on both the Luttinger liquid and the two-dimensional electron gas. We show that there are six dispersing features that should be observed in magneto-tunneling, in contrast with the four features that would be seen in a noninteracting one-dimensional electron gas. The strength of these features varies with the anomalous exponent, being most pronounced when ${\ensuremath{\gamma}}_{\ensuremath{\rho}}=0$. We argue that this measurement provides an important experimental signature of spin-charge separation.

DOI
10.1103/physrevb.69.245109

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We consider momentum resolved tunneling between a Luttinger liquid and a two-dimensional electron gas as a function of transverse magnetic field. We include the effects of an anomalous exponent and Zeeman splitting on both the Luttinger liquid and the two-dimensional electron gas. We show that there are six dispersing features that should be observed in magneto-tunneling, in contrast with the four features that would be seen in a noninteracting one-dimensional electron gas. The strength of these features varies with the anomalous exponent, being most pronounced when \ensuremathγ\ensuremathρ=0{\ensuremath{\gamma}}_{\ensuremath{\rho}}=0\ensuremathγ\ensuremathρ​=0. We argue that this measurement provides an important experimental signature of spin-charge separation.
We consider momentum resolved tunneling between a Luttinger liquid and a two dimensional electron gas as a function of transverse magnetic field. We include the effects of an anomalous exponent and Zeeman splitting on both the Luttinger liquid and the two dimensional electron gas. We show that there are six dispersing features that should be observed in magneto-tunneling, in contrast with the four features that would be seen in a non-interacting one dimensional electron gas. The strength of these features varies with the anomalous exponent, being most pronounced when γρ=0γ_ρ=0γρ​=0. We argue that this measurement provides an important experimental signature of spin-charge separation.
We study tunneling between two nearby cleaved edge quantum wires in a perpendicular magnetic field. Due to Coulomb forces between electrons, the wires form a strongly-interacting pair of Luttinger liquids. We calculate the low-temperature differential tunneling conductance, in which singular features map out the dispersion relations of the fractionalized quasiparticles of the system. The velocities of several such spin-charge separated excitations can be explicitly observed. Moreover, the proposed measurement directly demonstrates the splintering of the tunneling electrons into a multi-particle continuum of these quasiparticles, carrying separately charge from spin. A variety of corrections to the simple Luttinger model are also discussed.
Tunneling density of states (DOS) in Luttinger liquid has a dip at zero energy, commonly known as the zero-bias anomaly. In the presence of a magnetic field, in addition to the zero-bias anomaly, the DOS develops two peaks separated from the origin by the Zeeman energy. We show that these finite-bias anomalies are characterized by a power-law behavior of the DOS and the differential conductance, and find the corresponding exponents at arbitrary strength of the electron-electron interaction. The developed theory is applicable to various kinds of quantum wires, including carbon nanotubes.
The theoretical model of the short-range interacting Luttinger liquid predicts a power-law scaling of the density of states and the momentum distribution function around the Fermi surface, which can be readily tested through tunneling experiments. However, some physical systems have long-range interaction, most notably the Coulomb interaction, leading to significantly different behaviors from the short-range interacting system. In this paper, we revisit the tunneling theory for the one-dimensional electrons interacting via the long-range Coulomb force. We show that even though in a small dynamic range of temperature and bias voltage, the tunneling conductance may appear to have a power-law decay similar to short-range interacting systems, the effective exponent is scale-dependent and slowly increases with decreasing energy. This factor may lead to the sample-to-sample variation in the measured tunneling exponents. We also discuss the crossover to a free Fermi gas at high energy and the effect of the finite size. Our work demonstrates that experimental tunneling measurements in one-dimensional electron systems should be interpreted with great caution when the system is a Coulomb Luttinger liquid.
Luttinger liquids occupy a notable place in physics as one of the most understood classes of quantum many-body systems. The experimental mission of measuring its main prediction, power laws in observable quantities, has already produced a body of exponents in different semiconductor and metallic structures. Here, we combine tunneling spectroscopy with density-dependent transport measurements in the same quantum wires over more than two orders of magnitude in temperature to very low electron temperatures down to ∼40 mK. This reveals that, when the second 1D subband becomes populated, the temperature dependence splits into two ranges with different exponents in the power-law dependence of the conductance, both dominated by the finite-size effect of the end-tunneling process. This result demonstrates the importance of measuring the Luttinger parameters as well as the number of modes independently through spectroscopy in addition to the transport exponent in the characterization of Luttinger liquids. This opens a pathway to unambiguous interpretation of the exponents observed in quantum wires.