Fermionic quantum matter in atomic gases and solid state systems
Final Report Abstract
With this research programme we studied how fermionic degrees of matter influence the macroscopic properties of systems composed of many particles. The effects are inherently quantum mechanical and lead to novel quantum phases of matter at low temperatures. We investigated the two experimentally important platforms of spin-orbit coupled superconductors and ultracold quantum gases. Although these platforms comprise systems at very different temperatures – typical transition temperatures for superconductors are in the Kelvin regime, whereas ultracold gases are at nano-Kelvin temperatures – many similarities could be identified, but also some striking differences. The central lines of research during the funding period have been: (1) Superconductivity in quadratic band touching Luttinger semimetals (2) Tensorial magnetism in quadratic band touching Luttinger semimetals (3) Quasi-long range order in trapped two-dimensional Bose gases (4) High-temperature pairing in the normal phase of a two-dimensional Fermi gas. Whereas the first two directions addressed the physics of spin-orbit coupled electronic materials such as half-Heusler superconductors or Pyrochlore Iridates, the third and fourth projects aimed at understanding the pairing of neutral Lithium fermionic atoms to form a superfluid state at ultracold temperatures. In electronic materials which contain heavy elements, the relativistic quantum mechanical effect of strong spin-orbit coupling can result in a quadratic band touching point in the electronic band structure. The nature of fermionic excitations at such a band touching point is fundamentally different from electronic degrees of freedom in conventional materials. In particular, the fermions can carry an effective spin of 3/2, in contrast to the spin of 1/2 of ordinary electrons. In (1) we identified how superconductivity manifests in such Luttinger semimetals: Local pairing instabilities can either induce a quantum phase transition into an s-wave superconducting state, where the system at its quantum critical point comprises a non-Fermi liquid with unusual scaling of physical observables, or there can be a transition into a state with complex tensor order. The second possibility constitutes a new paradigm for superconductivity, describing Cooper pairs having a spin of 2. In (2) we identified which ordering tendencies are possible in Luttinger semimetals and found that anisotropy can induce non-Fermi liquid behavior and tensorial magnetism. The phenomenon of Cooper pairing in superconductors can be simulated by neutral ultracold Fermi gases that form a superfluid at low temperatures. In particular, twodimensional gases serve as models for layered materials. A recently measured surprisingly large scaling exponent of a two-dimensional fermionic superfluid could be explained by trap effects in (3). In order to address the question whether a two-dimensional Fermi gas above its transition temperature is a Fermi liquid or possesses a pseudogap, we performed radiofrequency spectroscopy of an ultracold Lithium gas in (4). We identified pairing in the BCS-BEC crossover regime at temperatures as high as three times the critical temperature. Consequently, a description of this regime by a Fermi liquid model is necessarily insufficient.
Publications
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Quasi-long-range order in trapped two-dimensional Bose gases. Phys. Rev. A 94, 011602(R) (2016), Rapid Communication
I Boettcher, M Holzmann
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Anisotropy induces non-Fermi-liquid behavior and nematic magnetic order in threedimensional Luttinger semimetals. Phys. Rev. B 95, 075149 (2017)
I Boettcher, IF Herbut
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High temperature pairing in a strongly interacting two-dimensional Fermi gas. Science 359, 452 (2018)
PA Murthy, M Neidig, R Klemt, L Bayha, I Boettcher, T Enss, M Holten, G Zürn, PM Preiss, S Jochim
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Unconventional Superconductivity in Luttinger Semimetals: Theory of Complex Tensor Order and the Emergence of the Uniaxial Nematic State. Phys. Rev. Lett. 120, 057002 (2018)
I Boettcher, IF Herbut
