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arXiv:2001.00075 · Physical review. B./Physical review. B

Bound states in two-dimensional Fermi systems with quadratic band touching

Flávio L. N. Santos, M. A. Caracanhas, Maria C. O. Aguiar, Rodrigo G. Pereira

Published Apr 16, 2020• 1 citation
arXivHTMLPDF

Abstract

The formation of bound states between mobile impurity particles and fermionic atoms has been demonstrated in spin-polarized Fermi gases with attractive interspecies interaction. We investigate bound states of mobile impurities immersed in a two-dimensional system with a symmetry-protected quadratic band touching. In addition to the standard $s$-wave interaction, we consider an anisotropic dipolar exchange interaction that locally breaks point group symmetries. Using a weak-coupling renormalization group approach and a ladder approximation for the impurity-fermion propagator, we establish that the number of bound states can be controlled by varying the anisotropy of the exchange interaction. Our results show that the degeneracy and momentum dependence of the binding energies reflect some distinctive properties of the quadratic band touching.

DOI
10.1103/physrevb.101.155120

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The formation of bound states between mobile impurity particles and fermionic atoms has been demonstrated in spin-polarized Fermi gases with attractive interspecies interaction. We investigate bound states of mobile impurities immersed in a two-dimensional system with a symmetry-protected quadratic band touching. In addition to the standard sss-wave interaction, we consider an anisotropic dipolar exchange interaction that locally breaks point group symmetries. Using a weak-coupling renormalization group approach and a ladder approximation for the impurity-fermion propagator, we establish that the number of bound states can be controlled by varying the anisotropy of the exchange interaction. Our results show that the degeneracy and momentum dependence of the binding energies reflect some distinctive properties of the quadratic band touching.
We investigate the impacts of combination of fermion-fermion interactions and impurity scatterings on the low-energy stabilities of two-dimensional asymmetric materials with a quadratic band-crossing point by virtue of the renormalization group that allows us to treat distinct sorts of physical ingredients on the same footing. The coupled flow evolutions of all interaction parameters which carry the central physical information are derived by taking into account one-loop corrections. Several intriguing results are manifestly extracted from these entangled evolutions. At first, we realize that the quadratic band touching structure is particularly robust once the fermionic couplings flow toward the Gaussian fixed point. Otherwise, it can either be stable or broken down against the impurity scattering in the vicinity of nontrivial fixed points. In addition, we figure out two parameters $\ensuremath{\eta}$ and $\ensuremath{\lambda}$ that measure rotational and particle-hole asymmetries are closely energy dependent and exhibit considerably abundant behaviors depending upon the fates of fermion-fermion couplings and different types of impurities. Incidentally, as both $\ensuremath{\eta}$ and $\ensuremath{\lambda}$ can be remarkably increased or heavily reduced in the low-energy regime, an asymmetric system under certain restricted conditions exhibits an interesting phenomenon in which transitions either from rotational or particle-hole asymmetry to symmetric situation would be activated.
In this essay we study two-dimensional electronic systems that exhibit quadratic band touching (QBT) in their low energy dispersion. A lattice realization is shown to introduce the emergence of a QBT in the framework of the tight binding approximation. We then make a continuum limit, which allows for a more general approach on the level of low energy Hamiltonians. The basic concepts and the applied methods are introduced via a simplified problem, a system of spinless fermions. We use a renormalization group (RG) approach to examine the effects of short-range electron-electron interactions. Once it is found that the system is unstable toward ordered phases, we use the mean field approximation to investigate how the phases compete energetically. We then introduce the spin degree of freedom of the electrons and follow analogous calculations using the RG approach. A number of ordered phases are identified, and the flow equations of the susceptibilities are calculated. We find a symmetry of the action that is larger than what we start with and emerges under some plausible conditions.
Mobile impurities in cold atomic gases constitute a new platform for investigating polaron physics. Here we show that when impurity atoms interact with a two-dimensional Fermi gas with quadratic band touching, the polaron picture may either hold or break down depending on the particle-hole asymmetry of the band structure. If the hole band has a smaller effective mass than the particle band, the quasiparticle is stable and its diffusion coefficient varies with temperature as $D(T)\ensuremath{\propto}{ln}^{2}T$. If the hole band has larger mass, the quasiparticle weight vanishes at low energies due to an emergent orthogonality catastrophe. In this case we map the problem onto a set of one-dimensional channels and use conformal field theory techniques to obtain $D(T)\ensuremath{\propto}{T}^{\ensuremath{\nu}}$ with an interaction-dependent exponent $\ensuremath{\nu}$. The different regimes can be detected in the nonequilibrium expansion dynamics of an initially confined impurity.
We carefully study how the fermion-fermion interactions affect the low-energy states of a two-dimensional spin-1/2 fermionic system on the kagomé lattice with a quadratic band crossing point. With the help of the renormalization group approach, we can treat all kinds of fermionic interactions on the same footing and then establish the coupled energy-dependent flows of fermionic interaction parameters via collecting one-loop corrections, from which a number of interesting results are extracted in the low-energy regime. At first, various sorts of fermion-fermion interactions furiously compete with each other and are inevitably attracted by certain fixed point in the parameter space, which clusters into three qualitatively distinct regions relying heavily upon the structure parameters of materials. In addition, we notice that an instability accompanied by some symmetry breaking is triggered around different sorts of fixed points. Computing and comparing susceptibilities of twelve potential candidates indicates that charge density wave always dominates over all other instabilities. Incidently, there exist several subleading ones including the x-current, bond density, and chiral plus s-wave superconductors. Finally, we realize that strong fluctuations nearby the leading instability prefer to suppress density of states and specific heat as well compressibility of quasiparticles in the lowest-energy limit.
Abstract Interaction-driven topological phases significantly enrich the class of topological materials and thus are of great importance. Here, we study the phase diagram of interacting spinless fermions filling the two-dimensional checkerboard lattice with a quadratic band touching (QBT) point. By developing new diagnosis based on the state-of-the-art density-matrix renormalization group and exact diagonalization, we determine accurate quantum phase diagram for such a system at half-filling with three distinct phases. For weak nearest-neighboring interactions, we demonstrate the instability of the QBT towards an interaction-driven spontaneous quantum anomalous Hall (QAH) effect. For strong interactions, the system breaks the rotational symmetry realizing a nematic charge-density-wave (CDW) phase. Interestingly, for intermediate interactions we discover a symmetry-broken bond-ordered critical phase sandwiched in between the QAH and CDW phases, which splits the QBT into two Dirac points driven by interaction. Instead of the direct transition between QAH and CDW phases, our identification of an intermediate phase sheds new light on the theoretical understanding of the interaction-driven phases in QBT systems.
Motivated by recent advances in cold atomic systems, we study the equilibrium and quench properties of two-dimensional fermions with quadratic band touching at the Fermi level, in the presence of infinitely long-range interactions. Unlike when only short-range interactions are present, both nematic and quantum anomalous Hall (QAH) states appear at weak interactions, separated by a narrow coexistence region, whose boundaries mark second- and third-order quantum phase transitions. After an interaction quench, the QAH order exhibits three distinct regions: persistent or damped oscillations and exponential decay to zero. In contrast, the nematic order always reaches a nonzero stationary value through power-law damped oscillations, due to the interplay between the symmetry of the interaction and the specific topology of the quadratic band touching.