Quantum Anomalous Hall Insulator of Composite Fermions

Abstract

We show that a weak hexagonal periodic potential could transform a two-dimensional electron gas with an even-denominator magnetic filling factor to a quantum anomalous Hall insulator of composite fermions, giving rise to fractionally quantized Hall effect. The system provides a realization of the Haldane honeycomb-net model, albeit in a composite fermion system. We further propose a trial wave function for the state, and numerically evaluate its relative stability against the competing Hofstadter state. Possible sets of experimental parameters are proposed.PACS numbers: 71.70.Di,71.10.Pm,61.48.Gh It was long predicted that a magnetic insulator could exhibit a nonzero quantized Hall conductance in the absence of an external magnetic field, known as the quantum anomalous Hall insulator (QAHI) [1]. Searching for QAHI in real or artificial materials has been the focus of intensive recent theoretical investigations [2][3][4][5][6][7]. Experimentally, it is demonstrated recently that a Cr-doped (Bi,Sb) 2 Te 3 thin film could be the first QAHI ever realized [8]. As a next logical development of theory, the possibility of finding a QAHI exhibiting the fractional quantum Hall effect in the presence of strong electronelectron interaction is extensively discussed in the context of the flat Chern band insulator [9][10][11][12][13], which is yet to be materialized.In this Letter, we propose a new class of QAHI that exhibits the fractional quantum Hall effect, i.e., quantum anomalous Hall insulator of composite fermions (CF-QAHI). The composite fermion (CF), which is defined as an electron binding with two or even number of quantized vortices, is not only the key theoretical apparatus for describing the extremely complex fractional quantum Hall states, but also a physical entity with well defined charge, spin, and statistics [14][15][16]. In particular, a two-dimensional electron gas (2DEG) with an evendenominator magnetic filling factor behaves just like a fermi liquid of CFs at the zero effective magnetic field, with the external magnetic field fully compensated by the quantized vortices bound in CFs [17][18][19][20][21][22]. Moreover, it was experimentally demonstrated that the picture of CFs is valid even in the presence of superstructures such as anti-dot arrays [20] and periodic potentials [23][24][25]. An interesting possibility naturally arises: a carefully designed superstructure could transform the CF fermi liquid to a CF band insulator with nontrivial topology [26]. We call the resulting insulator as a CF-QAHI.We show that this is indeed possible. We investigate the effect of a weak hexagonal periodic potential superimposed on a spinless 2DEG system at an even-denominator magnetic filling factor ν M = 1/2p. By employing the CF-mean field theory, we show that band gaps can be opened when the strength of the periodic potential exceeds a critical value. More importantly, a staggered effective magnetic field B * experienced by CFs emerges from the locally incomplete compensation of the external magnetic field, makin...

Density-Functional Theory of the Fractional Quantum Hall Effect

“…We note that our result is modified by the exchange correlation energy of composite fermions (through the parameter a); in contrast, Ref. 37 does not include the exchange correlation energy. Also, the large change in ∆ν (note |∆ν| > 0.5 is not physically acceptable) suggests that the potential is not weak.…”

“…This is not surprising because, as stressed by Karlhede et al 32 , the energetics of spin textures at the edge is closely related to that of skyrmions 34 , and calculations have shown that skyrmions at 1/3 become viable only at very low Zeeman energies 35 . We note that the ChernSimons mean field theory of composite fermions 7,36 has also been used to treat the effect of an external periodic potential on the state in the vicinity of half filling 37,38 ; see SM for a comparison with our approach.…”

Chern insulator in a ferromagnetic two-dimensional electron system with Dresselhaus spin–orbit coupling

“…It is the so-called quantum anomalous Hall (QAH) effect, also known as Chern insulators. QAH systems have been intensively studied for their fruitful physics and promising applications in future technology [1][2][3][4][5][6][7][8][9][10][11][12]. They attract the attention of researchers because of the topologically nontrivial chiral edge states in the absence of external magnetic field, which is important to the development of next-generation electronic devices.…”

Coulomb drag in topological insulator films

“…Hybrid struc-tures such as TI/superconductor junctions have been fabricated [39,40], which are expected to give rise to topological superconductivity and Majorana fermions [41,42]. Transport experiments and theoretical work have mostly focused on longitudinal [43][44][45][46][47][48] and Hall transport properties [37,[49][50][51], thermoelectric response [52][53][54] and weak antilocalization [55][56][57][58], all essentially single-particle phenomena. The interplay of strong spin-orbit coupling and electron-electron interactions in TIs is at present not completely understood [59][60][61][62][63][64][65][66].…”