Fate of interaction-driven topological insulators under disorder

Abstract

We analyze the effect of disorder on the weak-coupling instabilities of quadratic band crossing point (QBCP) in two-dimensional Fermi systems, which, in the clean limit, display interactiondriven 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 non-trivial order sets in. Strong disorder can also cause a topological phase transition into a topologically trivial insulating state.PACS numbers: 73.43. Nq, 71.55.Jv, 11.30.Qc The study of topological phases of matter is one of the most active research areas in contemporary condensed matter physics. The explanation of the quantum Hall effect in terms of the topological properties of the Landau levels [1,2] in the 1980's triggered an intense research effort in the theoretical prediction [3][4][5] and the experimental discovery [6,7] of a plethora of different topologically non-trivial quantum phases. In two-dimensional (2D) insulating systems only two distinct topological non-trivial phases can be realized according to the well-established classification of topological insulators and superconductors [8,9] : (i) the quantum anomalous Hall state (QAH) [3] with a time-reversal symmetry-broken ground state and topologically protected chiral edge states and (ii) the time-reversal invariant quantum spin Hall (QSH) state [4,5], which possesses helical edge states with counterpropagating electrons of opposite spins.In recent years, attention has gradually shifted from non-interacting topological states of matter towards interaction-driven topological phases:many-particle quantum ground-states in which chiral orbital currents or spin-orbit couplings are spontaneously generated by electronic correlations. These states of matter possess both conventional order, characterized by an order parameter and a broken symmetry, and protected edge states associated with a topological quantum number. Interactiondriven QAH and QSH phases were first conceived in the context of 2D honeycomb lattice Dirac fermions [10] assuming sufficiently strong electronic repulsions although more recent analytical and numerical works question the proposal for this particular model [11][12][13][14].On the contrary, it has been proposed that 2D systems with a quadratic band crossing point (QBCP) are unstable to electronic correlation because of the finite density of states at the Fermi level leading to the possibility of The relationship between fixed points QAH and QAH-II is provided in the inset figure of Fig. 2(a).weak-coupling interaction-driven topological insulating phases [15][16][17]. And, indeed, QAH and QSH phases generated by electronic repulsions occur both in the checkerboard lattice model [15,18], and in two-valley QB...

Instability of QBC systems to Topological Anderson Insulating phases

“…The latter phases are TAI as it is possible to reach them by increasing disorder from a topologically trivial phase, at fixed B. For large enough disorder, all topological phases are suppressed, in agreement with one-loop RG calculations [25].…”

“…The fate of interaction induced topological insulating phases in the presence of disorder has been examined in Refs. [25,26] within the one-loop RG approach. The suppression of topological phases under increasing disorder and possible transition to trivial phases was predicted.…”

Topological superconducting transition driven by time-reversal-symmetry breaking

“…The parameters u i go to infinity at different speeds. Their relative importance [16,17,30] can be distinguished by re-scaling all the parameters with respect to one of them (no sign change). Here, we choose to analyze the energy-dependence of the ratios u i /u 2 .…”

“…T -symmetry breaking (T SB) drives the system into a distinct SC phase. This transition is characterized by the simultaneous changes of both symmetry and topology, at which * E-mail address: jing wang@tju.edu.cn the conventional symmetry-breaking is a crucial ingredient in reconstructing the band structure and leading to topological changes [15][16][17]. A schematic phase diagram is presented in Fig.…”

Renormalization group study of systems with quadratic band touching

“…Some studies such as Refs. [34,35] have focused on the effects of disorder on the stability of the quadratic band crossing point in the presence of interactions.…”