Three-component Fermi Research Articles

Universal p -wave tetramers in low-dimensional fermionic systems with three-body interaction

Inspired by the narrow Feshbach resonance in systems with the two-body interaction, we propose a two-channel model of three-component fermions with a three-body interaction that takes into account finite-range effects in low dimensions. Within this model, the p-wave Efimov-like effect in the four-body sector is predicted in fractional dimensions between d=1 and d=2. The impact of the finite-range interaction on the formation of the four-body bound states in d=1 is also discussed in detail. Published by the American Physical Society 2024

Giant Nonlinear Optical Response in Topological Semimetal Molybdenum Phosphide

Nonlinear optical properties are investigated using the static and time-resolved second harmonic generation in the topological material molybdenum phosphide (MoP) with three-component fermions. Giant second harmonic generation signals are detected and the derived χ (2) value is larger than that of the typical electro–optic material. Upon optical excitation, no photoinduced change of the symmetry is detected in MoP, which is quite different from previous observations in several other topological materials.

Probe for bound states of SU(3) fermions and colour deconfinement

Fermionic artificial matter realized with cold atoms grants access to an unprecedented degree of control on sophisticated many-body effects with an enhanced flexibility of the operating conditions. Here, we consider three-component fermions with attractive interactions to study the formation of complex bound states, whose nature goes beyond the standard fermion pairing occurring in quantum materials. Such systems display clear analogies with quark matter. We address the nature of the bound states of a three-component fermionic system in a ring-shaped trap through the persistent current. In this way, we demonstrate that we can distinguish between color superfluid and trionic bound states. By analyzing finite temperature effects, we show how finite temperature can lead to the deconfinement of bound states. For weak interactions, the deconfinement occurs because of scattering states. In this regime, the deconfinement depends on the trade-off between interactions and thermal fluctuations. For strong interactions the features of the persistent current result from the properties of a suitable gas of bound states.

Weak localization in disordered spin-1 chiral fermions

We theoretically investigate the quantum interference theory of magnetotransport of the three-component or spin-1 chiral fermions, which possess two linear Dirac bands and a flat band. For isotropic scalar impurities, the correction of conductivity from the coherent backscatter and non-coherent backscatter contributions cancel out in the intravalley scattering, leading to a weak localization correction to the Drude conductivity from the intervalley scattering. For the anisotropic impurities, the above cancelation is removed, we find the approximative quantum interference conductivity in the weak anisotropy case. The contributions from the chiral anomaly and classical Lorentz force are also discussed. Our work reveals some intriguing and detectable transport signatures of the novel spin-1 chiral fermions.

Cooper triples in attractive three-component fermions: Implication for hadron-quark crossover

We investigate many-body properties of equally populated three-component fermions with attractive three-body contact interaction in one dimension. A diagrammatic approach suggests the possible occurrence of Cooper triples at low temperature, which are three-body counterparts of Cooper pairs with a two-body attraction. We develop a minimal framework that bridges the crossover from tightly-bound trimers to Cooper triples with increasing chemical potential and show how the formation of Cooper triples occurs in the grand-canonical phase diagram. Moreover, we argue that this non-trivial crossover is similar to the hadron-quark crossover proposed in dense matter. A coexistence of medium-induced triples and the underlying Fermi sea at positive chemical potential is analogous to quarkyonic matter consisting of baryonic excitations and the underlying quark Fermi sea. The comparison with the existing quantum Monte Carlo results implies that the emergence of these kinds of three-body states can be a microscopic origin of the peak of the sound velocity along the crossover.

Three-body crossover from a Cooper triple to a bound trimer state in three-component Fermi gases near a triatomic resonance

We theoretically investigate ground-state properties of a three-component Fermi gas with pairwise contact interactions between different components near a triatomic resonance where bound trimers are about to appear. Using variational equations for in-medium two- and three-body cluster states in three dimensions, we elucidate the competition of pair and triple formations due to the Fermi surface effects. We present the ground-state phase diagram that exhibits transition from a Cooper pair to Cooper triple state and crossover from a Cooper triple to tightly bound trimer state at negative scattering lengths. This three-body crossover is analogous to the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation crossover observed in a two-component Fermi gas. We predict that the threshold scattering length $a_{-}$ for three-body states can be shifted towards the weak-coupling side due to the emergence of Cooper triples.

Condensation of Cooper triples

The condensation of Cooper pairs, originating from the Fermi-surface instability due to a weakly attractive interaction between two fermions, opened a new frontier for exploring many-body physics in interdisciplinary contexts. In this work, we discuss the possible condensation of Cooper triples, which are three-body counterparts of Cooper pairs for three-component fermions with a three-body attraction. Although each composite trimer-like state obeys the Fermi-Dirac statistics, its aggregate can form a condensate at zero center-of-mass momentum in the presence of the internal degrees of freedom associated with the relative momenta of constituent particles of momenta close to the Fermi surface. Such condensation can be regarded as bosonization in infinite-component fermions. We propose a variational wave function for the condensate of Cooper triples in analogy with the Bardeen-Cooper-Schrieffer ground state and obtain the ground-state energy.

SU(3) spin-orbit coupled fermions in an optical lattice

We propose a scheme to realize the SU(3) spin–orbit coupled three-component fermions in an one-dimensional optical lattice. The topological properties of the single-particle Hamiltonian are studied by calculating the Berry phase, winding number and edge state. We also investigate the effects of the interaction on the ground-state topology of the system, and characterize the interaction-induced topological phase transitions, using a state-of-the-art density-matrix renormalization-group numerical method. Finally, we show the typical features of the emerging quantum phases, and map out the many-body phase diagram between the interaction and the Zeeman field. Our results establish a way for exploring novel quantum physics induced by the SOC with SU(N) symmetry.

Virial coefficients of trapped and untrapped three-component fermions with three-body forces in arbitrary spatial dimensions

Using a coarse temporal lattice approximation, we calculate the first few terms of the virial expansion of a three-species fermion system with a three-body contact interaction in $d$ spatial dimensions, both in homogeneous space as well as in a harmonic trapping potential of frequency $\omega$. Using the three-body problem to renormalize, we report analytic results for the change in the fourth- and fifth-order virial coefficients $\Delta b_4$ and $\Delta b_5$ as functions of $\Delta b_3$. Additionally, we argue that in the $\omega \to 0$ limit the relationship $b_n^\text{T} = n^{-d/2} b_n$ holds between the trapped (T) and homogeneous coefficients for arbitrary temperature and coupling strength (not merely in scale-invariant regimes). Finally, we point out an exact, universal (coupling- and frequency-independent) relationship between $\Delta b_3^\text{T}$ in 1D with three-body forces and $\Delta b_2^\text{T}$ in 2D with two-body forces.

Fermiology of ZrTe with triply degenerate nodes and highly anisotropic magnetization

We report the first experimental results of the magnetoresistance, Hall effect, and quantum Shubnikov-de Haas oscillations on single crystals of ZrTe, which was recently predicted to be a new type of topological semimetal hosting both triply degenerate crossing points and Weyl fermion state. The analysis of Hall effect and quantum oscillations indicate that ZrTe is a multiband system with low carrier density, high carrier mobility, small cross-sectional area of Fermi surface, and light cyclotron effective mass, as observed in many topological semimetals. Meanwhile, the angular dependence of the magnetoresistance and the quantum-oscillation frequencies further suggest that ZrTe possesses a three-dimensional Fermi surface that is rather complex. Our results provide a new platform to realize exotic quantum phenomena related to the new three-component fermions distinct from Dirac and Weyl fermions.

Time-reversal symmetry breaking Abelian chiral spin liquid in Mott phases of three-component fermions on the triangular lattice

We provide numerical evidence in favor of spontaneous chiral symmetry breaking and the concomitant appearance of an Abelian chiral spin liquid for three-component fermions on the triangular lattice described by an SU(3) symmetric Hubbard model with hopping amplitude $-t$ ($t>0$) and on-site interaction $U$. This chiral phase is stabilized in the Mott phase with one particle per site in the presence of a uniform $\pi$-flux per plaquette, and in the Mott phase with two particles per site without any flux. Our approach relies on effective spin models derived in the strong-coupling limit in powers of $t/U$ for general SU$(N)$ and arbitrary uniform charge flux per plaquette, which are subsequently studied using exact diagonalizations and variational Monte Carlo simulations for $N=3$, as well as exact diagonalizations of the SU($3$) Hubbard model on small clusters. Up to third order in $t/U$, and for the time-reversal symmetric cases (flux $0$ or $\pi$), the low-energy description is given by the $J$-$K$ model with Heisenberg coupling $J$ and real ring exchange $K$. The phase diagram in the full $J$-$K$ parameter range contains, apart from three already known, magnetically long-range ordered phases, two previously unreported phases: i) a lattice nematic phase breaking the lattice rotation symmetry and ii) a spontaneous time-reversal and parity symmetry breaking Abelian chiral spin liquid. For the Hubbard model, an investigation that includes higher-order itinerancy effects supports the presence of a phase transition inside the insulating region, occurring at $(t/U)_{\rm c}\approx 0.07$ [$(U/t)_{\rm c} \approx 13$] between the three-sublattice magnetically ordered phase at small $t/U$ and this Abelian chiral spin liquid.

Evidence from transport measurements for YRh6Ge4 being a triply degenerate nodal semimetal

We have investigated magnetotransport properties of YRh6Ge4, which was recently predicted to be a triply degenerate nodal semimetal. We find it exhibits remarkable signatures of a chiral anomaly, manifested by large negative longitudinal magnetoresistance, quadratic field dependence of magnetoconductance and planar Hall effect. Furthermore, we have also observed Shubnikov-de Haas (SdH) quantum oscillations in the magnetoresistivity measurements on this material. The analyses of the SdH data reveal two point-like Fermi surfaces and these pockets are found to host nearly massless fermions. The small size of these Fermi pockets is in a good agreement with the theoretical prediction that the triply degenerate point in YRh6Ge4 is much closer to the Fermi level than previously demonstrated triply degenerate nodal semimetals such as MoP and WC. These results suggest YRh6Ge4 may serve as a model system to probe exotic properties of three-component fermions and understand their underlying physics.

Virial coefficients of trapped and untrapped three-component fermions with three-body forces in arbitrary spatial dimensions

Virial coefficients of trapped and untrapped three-component fermions with three-body forces in arbitrary spatial dimensions

Unconventional superconductivity in the topological semimetal MoP: Evidence from first-principles calculated electron–phonon coupling

Different from Dirac and Weyl fermion, three-component fermions have no analogue in high-energy physics. Recently, this new fermion was experimentally observed in topological semimetal MoP (Nature 546 (2017), 627). Later, MoP is found to be superconducting below 2.5 K at 30 GPa, and the transition temperature increases with the increasing of pressure. The microscopic paring mechanism in MoP is crucial to topological superconductor but so far unexplored. In this work, we investigate the variation of electron–phonon coupling (EPC) and superconducting critical temperature Tc of MoP with pressures by first-principles calculations. On the one hand, the calculated transition temperature Tc is two orders of magnitude smaller than the experimental value. On the other hand, the calculated EPC strength and Tc decrease monotonically with the increasing of pressure, which is in contradiction with the relation established in experiment. Our results demonstrate that the superconductivity in pressurized MoP cannot be explained within the framework of the conventional electron–phonon pairing mechanism.

Virial expansion for a three-component Fermi gas in one dimension: The quantum anomaly correspondence

In this paper we explore the transport properties of three-component Fermi gases confined to one spatial dimension, interacting via a three-body interaction, in the high temperature limit. At the classical level, the three-body interaction is scale invariant in one dimension. However, upon quantization, an anomaly appears which breaks the scale invariance. This is very similar to the physics of two-component fermions in two spatial dimensions, where the two-body interaction is also anomalous. Previous studies have already hinted that the physics of these two systems are intimately related. Here we expand upon those studies by examining the thermodynamic properties of this anomalous one dimensional system in the high temperature limit. We show there is an exact mapping between the traditional two-body anomalous interaction in two dimensions, to that of three-body interaction in one dimension. This result is valid in the high temperature limit, where the thermodynamics can be understood in terms of few-body correlations.

Multi-body Correlations in SU(3) Fermi Gases

We investigate strong-coupling effects in a three-component atomic Fermi gas. It is a promising candidate for simulating quantum chromodynamics (QCD), and furthermore, the emergence of various phenomena such as color superfluidity and Efimov effect are anticipated in this system. In this paper, we study the effects of two-body and three-body correlations by means of the many-body $T$-matrix approximation (TMA) as well as the Skorniakov-Ter-Martirosian (STM) equation with medium corrections. We investigate the effects of finite temperature and chemical potential on the trimer binding energy at the superfluid critical point of the unitarity limit.

Long-lived trimers in a quasi-two-dimensional Fermi system

We consider the problem of three distinguishable fermions confined to a quasi-two-dimensional (quasi-2D) geometry, where there is a strong harmonic potential in one direction. We go beyond previous theoretical work and investigate the three-body bound states (trimers) for the case where the two-body short-range interactions between fermions are unequal. Using the scattering parameters from experiments on ultracold $^{6}$Li atoms, we calculate the trimer spectrum throughout the crossover from two to three dimensions. We find that the deepest Efimov trimer in the $^{6}$Li system is unaffected by realistic quasi-2D confinements, while the first excited trimer smoothly evolves from a 3D-like Efimov trimer to an extended 2D-like trimer as the attractive interactions are decreased. We furthermore compute the excited trimer wave function and quantify the stability of the trimer with respect to three-body recombination by determining the probability that three fermions approach each other at short distances. Our results indicate that the lifetime of the trimer can be enhanced by at least an order of magnitude in the quasi-2D geometry, thus opening the door to realizing long-lived trimers in three-component Fermi gases.

Three-component fermions with surface Fermi arcs in tungsten carbide

Topological Dirac and Weyl semimetals not only host quasiparticles analogous to the elementary fermionic particles in high-energy physics, but also have nontrivial band topology manifested by exotic Fermi arcs on the surface. Recent advances suggest new types of topological semimetals, in which spatial symmetries protect gapless electronic excitations without high-energy analogy. Here we observe triply-degenerate nodal points (TPs) near the Fermi level of WC, in which the low-energy quasiparticles are described as three-component fermions distinct from Dirac and Weyl fermions. We further observe the surface states whose constant energy contours are pairs of Fermi arcs connecting the surface projection of the TPs, proving the nontrivial topology of the newly identified semimetal state.

Triply degenerate nodal points and topological phase transitions in NaCu3Te2

Quasiparticle excitations of free electrons in condensed-matter physics, characterized by the dimensionality of the band crossing, can find their elementary-particle analogs in high-energy physics, such as Majorana, Weyl, and Dirac fermions. While crystalline symmetry allows more quasiparticle excitations and exotic fermions to emerge. Using symmetry analysis and {\it ab-initio} calculations, we propose that the 3D honeycomb crystal NaCu$_3$Te$_2$ hosts triply degenerate nodal points (TDNPs) which are perfectly separated from the bulk states. We find a tunable phase transition between TDNPs and a weak TI triggered by a symmetry-allowed perturbation, and we further reveal the crucial role played by the spin-orbital coupling (SOC) for the emergence of the TDNPs in this system. Such topological non-trivial ternary compound not only serves as a perfect candidate for studying three-component fermions, but also provides a beautiful playground for understanding the topological phase transitions between TDNPs, TIs and trivial insulators, which distinguishes this system from other TDNP candidates.

Three-body correlations in a two-dimensional SU(3) Fermi gas

We consider a three-component Fermi gas that has SU(3) symmetry and is confined to two dimensions (2D). For realistic cold atomic gas experiments, we show that the phase diagram of the quasi-2D system can be characterized using two 2D scattering parameters: the scattering length and the effective range. Unlike the case in 3D, we argue that three-body bound states (trimers) in the quasi-2D system can be stable against three-body losses. Using a low-density expansion coupled with a variational approach, we investigate the fate of such trimers in the many-body system as the attractive interactions are decreased (or, conversely, as the density of particles is increased). We find that remnants of trimers can persist in the form of strong three-body correlations in the weak-coupling (high-density) limit.