Abstract
The temperature-induced emergence of Wigner correlations over finite-size effects in a strongly interacting one-dimensional quantum dot is studied in the framework of the spin coherent Luttinger liquid. We demonstrate that, for temperatures comparable with the zero mode spin excitations, Friedel oscillations are suppressed by the thermal fluctuations of higher spin modes. On the other hand, the Wigner oscillations, sensitive to the charge mode only, are stable and become more visible. This behavior has been proved to be robust both in the thermal electron density and in the linear conductance in the presence of a scanning tunnel microscope tip. The latter probe is not directly proportional to the electron density and may confirm the above phenomena with complementary and additional information.
Highlights
Wigner crystallization [1] is among the most striking quantum many body effects
The temperature-induced emergence of Wigner correlations over finitesize effects in a strongly interacting one-dimensional quantum dot are studied in the framework of the spin coherent Luttinger liquid
For temperatures comparable with the zero mode spin excitations, Friedel oscillations are suppressed by the thermal fluctuations of higher spin modes
Summary
Wigner crystallization [1] is among the most striking quantum many body effects. A Wigner crystal can emerge in two and three dimensions when the interaction energy among electrons dominates over the kinetic one [2]. In order to study the density oscillations arising due to the formation of a Wigner molecule, the properties of 1D quantum dots coupled to AFM tips have been explored, [32, 22, 37, 38, 39] a set up proposed [40, 41] for the detection of spin charge separation, [16, 42] another hallmark of one-dimensional electron systems. Wigner oscillations are robust against the increase of temperature, since they are not sensitive to the spin excitations but to the charge ones which lie, in presence of strong interaction, at a much higher excitation energy We prove this behavior by studying the thermal electron density and the linear conductance in the presence of an STM tip. In Appendix Appendix A, we outline the calculation of the tunneling rates
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