PhD Hall-Effect in One-Dimension

When the lateral dimensions of a metallic structure are severely reduced, it becomes one-dimensional. When gold atoms are arranged in rows, they constitute a metal along these lines. When the electronic anisotropy of a solid exceeds an order of mag­nitude, the compound may serve as a model of a quasi-one-dimensional con­ductor. Theory predicts that the physical properties of one-dimensional electron systems are fundamentally different compared to two and three dimensions. Instead like a Fermi-liquid, the electrons behave according to the quantum theory of Tomonaga and Luttinger: The separation of spin and charge excitations, the absence of a Fermi-edge, collective excitations with power-laws in the temperature and frequency-dependent conductivity, are just some of the hallmarks [1,2].

While many predictions have been confirmed experi­mentally, the issue of the Hall effect in quasi-one-dimen­sional quantum systems remains unresolved. With simple Fermi liquids, the Hall effect is supposedly measuring the number of carriers. This changes drastically as soon as interactions are considered [1]. 

In a quasi-one dimensional system, as shown in the Figure, in the absence of hopping between the chains, there would not be any Hall effect. It is completely open, however, how the Hall resistance depends on the perpendicular hopping t_⊥, the temperature T, the magnetic field B and the interactions. One might expect a power law in temperature R_H = R_H⁰ + gT ⁿ, where the deviations from the classical value of the Hall resistance R_H⁰ reflect the Tomonaga-Luttinger-liquid behavior. Confirming or challenging this behavior is crucial; by now no consensus was reach between different groups [3-5].

The task of the present PhD project is the solution of this longstanding puzzle.

[1] Giamarchi, Quantum Physics in One Dimension, Oxford University Press, 2004;
     Chem. Rev. 104, 5037 (2004); C. R. Physique 17, 322 (2016)
[2] Dressel, Naturwissenschaften 90, 337 (2003); 94, 527 (2007)
[3] Mihály et al., Phys. Rev. Lett. 84, 2670 (2005)
[4] Moser et al., Phys. Rev. Lett. 84, 2674 (2000)
[5] Kobayashi, et al. Phys. Rev. Lett. 112, 116805 (2014)