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arXiv:2003.06776 · Physical review. B./Physical review. B

Stability of two-dimensional asymmetric materials with a quadratic band crossing point under four-fermion interaction and impurity scattering

Yao-Ming Dong, Ya-Hui Zhai, Dongxing Zheng, Jing Wang

Published Oct 5, 2020• 18 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.102.134204

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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 \ensuremathη\ensuremath{\eta}\ensuremathη and \ensuremathλ\ensuremath{\lambda}\ensuremathλ 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 \ensuremathη\ensuremath{\eta}\ensuremathη and \ensuremathλ\ensuremath{\lambda}\ensuremathλ 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.
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.
Roles of fermion-fermion interactions are carefully studied in governing the low-energy fates of a two-dimensional spin-1/21/21/2 fermionic system on the kagome lattice, which features a quadratic band crossing point touched parabolically by up and down energy bands. In the framework of a renormalization group, we establish the coupled energy-dependent flows of fermionic interaction parameters by treating all kinds of fermionic interactions on the same footing and unbiasedly taking into account their one-loop corrections. Through a compressive analysis of these evolutions that carry the hierarchical information of physics, a number of outlandish behaviors are progressively decoded and addressed manifestly in the low-energy regime. At first, we find that various sorts of fermion-fermion interactions furiously compete and affect each other. With the decrease of energy scale, they are inevitably attracted by certain fixed point in the parameter space which clusters into three qualitatively distinct regions relying heavily upon structure parameters of materials. In addition, the leading instability accompanied by some symmetry breaking is attentively investigated in the proximity of different sorts of fixed points. Computing and comparing susceptibilities of twelve potential candidates indicates that charge density wave always dominates over others. Incidently, there exists several options for subleading ones including the xxx-current, bond density, and chiral plus s-wave superconductors. At last, we examine how physical observables behave nearby the dominant instability. Due to the strong fluctuations neighboring this instability linked to charge density wave, density of states and specific heat as well compressibility of quasiparticles are significantly suppressed, signalling the emergence of non-Fermi liquid behaviors.
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 interplay of Coulomb interactions and short-range-correlated disorder in three-dimensional systems where absent disorder the noninteracting band structure hosts a quadratic band crossing. Though the clean Coulomb problem is believed to host a non-Fermi liquid phase, disorder and Coulomb interactions have the same scaling dimension in a renormalization group (RG) sense, and thus should be treated on an equal footing. We therefore implement a controlled $\ensuremath{\varepsilon}$ expansion and apply it at leading order to derive RG flow equations valid when disorder and interactions are both weak. We find that the non-Fermi liquid fixed point is unstable to disorder, and demonstrate that the problem inevitably flows to strong coupling, outside the regime of applicability of the perturbative RG. An examination of the flow to strong coupling suggests that disorder is asymptotically more important than interactions, so that the low-energy behavior of the system can be described by a noninteracting sigma model in the appropriate symmetry class (which depends on whether exact particle-hole symmetry is imposed on the problem). We close with a discussion of general principles unveiled by our analysis that dictate the interplay of disorder and Coulomb interactions in gapless semiconductors, and of connections to many-body localized systems with long-range interactions.
We analyze the effect of disorder on the weak-coupling instabilities of a quadratic band crossing point (QBCP) in two-dimensional Fermi systems, which, in the clean limit, display interaction-driven topological insulating phases. In the framework of a renormalization group procedure, which treats fermionic interactions and disorder on the same footing, we test all possible instabilities and identify the corresponding ordered phases in the presence of disorder for both single-valley and two-valley QBCP systems. We find that disorder generally suppresses the critical temperature at which the interaction-driven topologically nontrivial order sets in. Strong disorder can also drive a topological phase transition into a topologically trivial insulating state.
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.