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Physical review. B./Physical review. B

Orbital selective order and Z3 Potts nematicity from a non-Fermi liquid

YuZheng Xie, Andrew Hardy, Arun Paramekanti

Published Oct 23, 2024• 1 citation
Publisher

Abstract

Electronic liquid crystals are ubiquitous in strongly correlated matter, and often seen in multiorbital materials exhibiting non-Fermi-liquid transport. The authors propose here and analyze a three-orbital Sachdev-Ye-Kitaev model that hosts a uniform solution corresponding to a \ensuremath{\mathbb{Z}}${}_{3}$ Potts nematic. In the atomic limit, this model displays an orbital-selective non-Fermi liquid down to $T$=0. On the triangular and cubic lattice, this evolves into a nematic with highly anisotropic transport, reminiscent of dynamical mean field theory studies of multiorbital Hubbard models.

DOI
10.1103/physrevb.110.165158

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Electronic liquid crystals are ubiquitous in strongly correlated matter, and often seen in multiorbital materials exhibiting non-Fermi-liquid transport. The authors propose here and analyze a three-orbital Sachdev-Ye-Kitaev model that hosts a uniform solution corresponding to a \ensuremath{\mathbb{Z}}3{}_{3}3​ Potts nematic. In the atomic limit, this model displays an orbital-selective non-Fermi liquid down to TTT=0. On the triangular and cubic lattice, this evolves into a nematic with highly anisotropic transport, reminiscent of dynamical mean field theory studies of multiorbital Hubbard models.
Orbital selective order and Z3\mathbb{Z}_3Z3​ Potts nematicity from a non-Fermi liquid
Motivated by systems where a high temperature non-Fermi liquid gives way to low temperature Z3\mathbb{Z}_3Z3​ Potts nematic order, we studied a three-orbital Sachdev-Ye-Kitaev (SYK) model in the large-NNN limit. In the single-site limit, this model exhibits a spontaneous orbital-selective transition which preserves average particle-hole symmetry, with two orbitals becoming insulators while the third orbital remains a non-Fermi liquid down to zero temperature. We extend this study to lattice models of three-orbital SYK dots, exploring uniform symmetry broken states on the triangular and cubic lattices. At high temperature, these lattice models exhibit an isotropic non-Fermi liquid metal phase. On the three-dimensional (3D) cubic lattice, the low temperature uniform Z3\mathbb{Z}_3Z3​ nematic state corresponds to an orbital selective layered state which preserves particle-hole symmetry at small hopping and spontaneously breaks the particle-hole symmetry at large hopping. Over a wide range of temperature, the transport in this layered state shows metallic in-plane resistivity but insulating out-of-plane resistivity. On the 2D triangular lattice, the low temperature state with uniform orbital order is also a correlated Z3\mathbb{Z}_3Z3​ nematic with orbital-selective transport but it remains metallic in both principal directions. We discuss a Landau theory with Z3\mathbb{Z}_3Z3​ clock terms which captures salient features of the phase diagram and nematic order in all these models. We also present results on the approximate wavevector dependent orbital susceptibility of the isotropic non-Fermi liquid states.
We study a class of multiorbital models based on those proposed by Venderbos et al. [Phys. Rev. B 98, 235160 (2018)] which exhibit an interplay of topology, interactions, and fermion incoherence. In the noninteracting limit, these models exhibit trivial and Chern insulator phases with Chern number $C\ensuremath{\ge}1$ bands as determined by the relative angular momentum of the participating orbitals. These quantum anomalous Hall insulator phases are separated by topological transitions protected by crystalline rotation symmetry, featuring Dirac or quadratic band-touching points. Here we study the impact of Sachdev-Ye-Kitaev (SYK) type interactions on these lattice models. Given the random interactions, these models display average symmetries upon disorder averaging, including a charge conjugation symmetry, so they behave as interacting models in topological class D\mathbf{D}D enriched by crystalline rotation symmetry. The phase diagram of this model features a non-Fermi liquid at high temperature and an exciton condensate with nematic transport at low temperature. We present results from the free energy, spectral functions, and the anomalous Hall resistivity as a function of temperature and tuning parameters. Our results are broadly relevant to correlated topological matter in multiorbital systems, and may also be viewed, with a suitable particle hole transformation, as an exploration of strong interaction effects on mean-field topological superconductors.
As in between liquid and crystal phases lies a nematic liquid crystal, which breaks rotation with preservation of translation symmetry, there is a nematic superfluid phase bridging a superfluid and a supersolid. The nematic order also emerges in interacting electrons and has been found to largely intertwine with multiorbital correlation in high-temperature superconductivity, where Ising nematicity arises from a four-fold rotation symmetry C_{4} broken down to C_{2}. Here, we report an observation of a three-state (Z_{3}) quantum nematic order, dubbed "Potts-nematicity", in a system of cold atoms loaded in an excited band of a hexagonal optical lattice described by an sp^{2}-orbital hybridized model. This Potts-nematic quantum state spontaneously breaks a three-fold rotation symmetry of the lattice, qualitatively distinct from the Ising nematicity. Our field theory analysis shows that the Potts-nematic order is stabilized by intricate renormalization effects enabled by strong interorbital mixing present in the hexagonal lattice. This discovery paves a way to investigate quantum vestigial orders in multiorbital atomic superfluids.
We study the phase diagram of the asymmetric Hubbard model (AHM), which is characterized by different values of the hopping for the two spin projections of a fermion or, equivalently, two different orbitals. This model is expected to provide a good description of a mass-imbalanced cold fermionic mixture in a 3D optical lattice. We use the dynamical mean-field theory to study various physical properties of this system. In particular, we show how orbital-selective physics, observed in multiorbital strongly correlated electron systems, can be realized in such a simple model. We find that the density distribution is a good probe of this orbital-selective crossover from a Fermi-liquid to a non-Fermi-liquid state. Below an ordering temperature To{T}_{o}To​, which is a function of both the interaction and hopping asymmetry, the system exhibits staggered long-range orbital order. Apart from the special case of the symmetric limit, i.e., Hubbard model, where there is no hopping asymmetry, this orbital order is accompanied by a true charge density wave order for all values of the hopping asymmetry. We calculate the order parameters and various physical quantities including the thermodynamics in both the ordered and disordered phases. We find that the formation of the charge density wave is signaled by an abrupt increase in the sublattice double occupancies. Finally, we propose a new method, entropic chromatography, for cooling fermionic atoms in optical lattices, by exploiting the properties of the AHM. To establish this cooling strategy on a firmer basis, we also discuss the variations in temperature induced by the adiabatic tuning of interactions and hopping parameters.
Power-law spectra and asymptotic ω/T\omega/Tω/T scaling in the orbital-selective Mott phase of a three-orbital Hubbard model
Quantum materials whose properties lie beyond the celebrated Landau Fermi-liquid paradigm have been observed for decades across diverse material platforms. Finding microscopic lattice models for metallic states that exhibit such peculiar behavior remains a major theoretical challenge, as these features often originate from strong quantum fluctuations in strongly interacting electron systems. Here we investigate a three-orbital Hubbard model at a high-symmetry point that hosts a transition from a metallic to an orbital-selective Mott (OSM) phase. Employing single-site dynamical mean-field theory combined with full-density-matrix numerical renormalization group, we chart the T T – U U phase diagram and obtain high-resolution real-frequency dynamics. In the OSM regime we find asymptotically scale-invariant (power-law) single-particle spectra and asymptotic \omega/T ω / T scaling in both charge and spin channels, spanning several decades in frequency and temperature.
Some of the most interesting phenomena in condensed matter occur in high-temperature superconductors and heavy fermions, and arise from a parent non-Fermi-liquid background. Although the non-Fermi-liquid phase has metallic character, it is very different from typical metals in that the electronic excitations are not particlelike (no quasiparticles), and this has lead to these phases eluding a clear theoretical description. Here, the authors develop a model that provides a route to describe non-Fermi liquids realized in condensed matter systems. Building on the zero-dimensional Sachdev-Ye-Kitaev model that is inspired by connections between a non-Fermi liquid and black holes, the authors construct a model in a lattice system where the bands touch to give a divergent density of states (Lifshitz point). The resulting non-Fermi-liquid phases exhibit intriguing properties such as scaling symmetry, nontrivial power-law dependence of entropy on temperature, and fast information scrambling with rate linear in temperature, as well as dynamical transitions to more conventional phases with well-defined quasiparticles.