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]
We calculate the out-of-plane thermopower in a quasi-two-dimensional system and argue that this quantity is an effective probe of the asymmetry of the single-particle spectral function. We find that the temperature and doping dependence of the out-of-plane thermopower in Bi 2 ͑Sr, La͒ 2 CaCu 2 O 8+␦ single crystals is broadly consistent with the behavior of the spectral function determined from angle resolved photoemission spectroscopy and tunneling experiments. We also investigate the relationship between out-of-plane thermopower and entropy in a quasi-two-dimensional material. We present experimental evidence that at moderate temperatures, there is a qualitative correspondence between the out-of-plane thermopower in Bi 2 ͑Sr, La͒ 2 CaCu 2 O 8+␦ and the entropy obtained from specific-heat measurements. Finally, we argue that the derivative of the entropy with respect to particle number may be the more appropriate quantity to compare with the thermopower rather than the entropy per particle.
We present the results of non-linear tunnelling spectroscopy between an array of independent quantum wires and an adjacent two-dimensional electron gas (2DEG) in a double-quantum-well structure. The two layers are separately contacted using a surface-gate scheme, and the wires are all very regular, with dimensions chosen carefully so that there is minimal modulation of the 2DEG by the gates defining the wires. We have mapped the dispersion spectrum of the 1D wires down to the depletion of the last 1D subband by measuring the conductance G as a function of the in-plane magnetic field B, the interlayer bias V dc and the wire gate voltage. There is a strong suppression of tunnelling at zero bias, with temperature and dc-bias dependences consistent with power laws, as expected for a Tomonaga-Luttinger Liquid caused by electron-electron interactions in the wires. In addition, the current peaks fit the free-electron model quite well, but with just one 1D subband there is extra structure that may indicate interactions. adjacent low-disorder 2D layer depends on the overlap between the spectral functions of the two systems, which is varied by using an in-plane magnetic field B perpendicular to the wires to offset the two in k-space; a bias V dc between the layers is used to investigate the energy dependence. In a non-interacting system, peaks in the conductance G follow the 1D and 2D subbands. In contrast, for a TLL, there should be two features, for spin and charge, instead of one for a non-interacting 1D subband. [6,7] We have previously used ion-beam lithography to make separate contact to two such layers of electrons, for investigating arrays of 1D wires [8] and antidots [9], but here we adopt a simpler technique that uses just
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