Quadratic band touching with long-range interactions in and out of equilibrium

Abstract

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 state 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 non-zero stationary value through power law damped oscillations, due to the interplay of the symmetry of the interaction and the specific topology of the quadratic band touching.

Floquet topological phase transition in two-dimensional quadratic band crossing system*

“…[22] Given this background, we study quadratic band crossing (QBC) fermions in a square optical lattice, which have attracted intensive studies in modern condensed matter physics. [23][24][25][26][27][28] We find that the interplay between the shaking, orbital Zeeman term, and the spin-orbit coupling can lead to the nontrivial topology characterized by the (spin) Chern number of its energy band. By varying the orbital Zeeman term and shaking strength, the quantum spin Hall (QSH) and quantum anomalous Hall (QAH) phase may appear.…”

Search for plasmons in isotropic Luttinger semimetals

“…In contemporary research, three-dimensional (3d) semimetals with a quadratic band-crossing point (QBCP) are being extensively studied [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Distinct from Dirac/Weyl semimetals possessing band-crossings with linear energy dispersions [16], such a bandstructure can be realized in materials like pyrochlore iridates A 2 Ir 2 O 7 (where A is a lanthanide element [17,18]), gray tin (α-Sn) [19,20], and HgTe [21].…”

Tuning topological phase and quantum anomalous Hall effect by interaction in quadratic band touching systems

“…The theoretical prediction of such interaction-driven topological phases [17][18][19][20][21][22][23][24][25], stimulates extensive studies by more rigorously theoretical and numerical methods, including low energy renormalization group approach in C 4 symmetric checkerboard lattice [26][27][28][29] and bilayer graphene [30,31], first-principle calculations in spindependent optical square lattice [32] and halogenated hematite nanosheets [33], and recently the unbiased nu-merical exact diagonalization (ED) diagnosis in both C 4 symmetric checkerboard lattice [34] and C 6 symmetric Kagome lattice [35]. However, the stability of the QAH effect in the presence of weak interaction has not been settled.…”