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arXiv:2209.04404

Spin-selective insulators

Jereson Silva-Valencia

Published Sep 9, 2022• 0 citations
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Abstract

Spin-selective insulators emerge in systems composed of fermions with two internal degrees of freedom and another carrier, which could be fermionic or bosonic. These insulators are characterized by a gapless state for one kind of fermion and an insulator state for the other, with the latter satisfying a commensurability relation that involves the other carrier. We review the different scenarios where these unique insulators arise, focusing on Bose-Fermi mixtures, the most recent and promising scenario for observing these insulators in cold atom setups.

DOI
10.48550/arxiv.2209.04404

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Spin-selective insulators emerge in systems composed of fermions with two internal degrees of freedom and another carrier, which could be fermionic or bosonic. These insulators are characterized by a gapless state for one kind of fermion and an insulator state for the other, with the latter satisfying a commensurability relation that involves the other carrier. We review the different scenarios where these unique insulators arise, focusing on Bose-Fermi mixtures, the most recent and promising scenario for observing these insulators in cold atom setups.
We investigate an imbalanced mixture composed of two-color fermions and scalar bosons in the hard-core limit, considering repulsive and attractive interspecies and intraspecies interactions. The interplay between commensurability, repulsive interactions, and imbalance generates three insulating phases: a mixed Mott state and two spin-selective insulators characterized by the commensurability relations ${\ensuremath{\rho}}_{B}+{\ensuremath{\rho}}_{F}^{\ensuremath{\uparrow},(\ensuremath{\downarrow})}=1$. For an attractive coupling between fermions and bosons, we found the relations ${\ensuremath{\rho}}_{B}\ensuremath{-}{\ensuremath{\rho}}_{F}^{\ensuremath{\uparrow},(\ensuremath{\downarrow})}=0$ for the spin-selective insulators. State-of-the-art cold-atom setups constitute ideal platforms to implement these unveiled insulating states and verify their commensurability relations.
We study a one-dimensional mixture of two-color fermions and scalar bosons at the hardcore limit, focusing on the effect that the intraspecies next-neighbor interactions have on the zero-temperature ground state of the system for different fillings of each carrier. Exploring the problem’s parameters, we observed that the nearest-neighbor interaction could favor or harm the well-known mixed Mott and spin-selective Mott insulators. We also found the emergence of three unusual insulating states with charge density wave (CDW) structures in which the orders of the carriers are out of phase between each other. For instance, the immiscible CDW appears only at half-filling bosonic density, whereas the mixed CDW state is characterized by equal densities of bosons and fermions. Finally, the spin-selective CDW couples the bosons and only one kind of fermions. Appropriate order parameters were proposed for each phase to obtain the critical parameters for the corresponding superfluid-insulator transition. Our results can inspire or contribute to understanding experiments in cold-atom setups with long-range interactions or recent reports involving quasiparticles in semiconductor heterostructures.
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A mixture of ultracold bosons and fermions placed in an optical lattice constitutes a novel kind of quantum gas, and leads to phenomena, which so far has been discussed neither in atomic physics, nor in condensed matter physics. We discuss the phase diagram at low temperatures, and in the limit of strong atom-atom interactions, and predict the existence of quantum phases that involve pairing of fermions with one or more bosons, or, respectively, bosonic holes. The resulting composite fermions may form, depending on the system parameters, a normal Fermi liquid, a density wave, a superfluid liquid, or an insulator with fermionic domains. We discuss the feasibility for observing such phases in current experiments.
Recent theoretical and experimental progress on studying one-dimensional systems of bosonic, fermionic, and Bose-Fermi mixtures of a few ultracold atoms confined in traps is reviewed in the broad context of mesoscopic quantum physics. We pay special attention to limiting cases of very strong or very weak interactions and transitions between them. For bosonic mixtures, we describe the developments in systems of three and four atoms as well as different extensions to larger numbers of particles. We also briefly review progress in the case of spinor Bose gases of a few atoms. For fermionic mixtures, we discuss a special role of spin and present a detailed discussion of the two- and three-atom cases. We discuss the advantages and disadvantages of different computation methods applied to systems with intermediate interactions. In the case of very strong repulsion, close to the infinite limit, we discuss approaches based on effective spin chain descriptions. We also report on recent studies on higher-spin mixtures and inter-component attractive forces. For both statistics, we pay particular attention to impurity problems and mass imbalance cases. Finally, we describe the recent advances on trapped Bose-Fermi mixtures, which allow for a theoretical combination of previous concepts, well illustrating the importance of quantum statistics and inter-particle interactions. Lastly, we report on fundamental questions related to the subject which we believe will inspire further theoretical developments and experimental verification.
The topic of the present lecture notes are two-species quantum mixtures composed of a deeply degenerate Fermi gas and a second component, the latter being fermionic or bosonic. A key ingredient is the possibility to tune the sss-wave interaction between the different species by means of magnetically controlled Feshbach resonances, which allow us to investigate regimes of strong interactions. In two case studies, we review our experiments on mixtures of 6^66Li fermions with fermionic 40^{40}40K or bosonic 41^{41}41K atoms and on mixtures of fermionic 161^{161}161Dy with 40^{40}40K atoms. We cover various topics of fermionic quantum many-body physics, ranging from impurity physics and quasiparticles over phase separation to the formation of ultracold molecules and progress towards novel superfluids.