Precise Quantization of the Anomalous Hall Effect near Zero Magnetic Field

Abstract

We report a nearly ideal quantum anomalous Hall effect in a three-dimensional topological insulator thin film with ferromagnetic doping. Near zero applied magnetic field we measure exact quantization in Hall resistance to within a part per 10,000 and longitudinal resistivity under 1 Ω per square, with chiral edge transport explicitly confirmed by non-local measurements. Deviations from this behavior are found to be caused by thermally-activated carriers, which can be eliminated by taking advantage of an unexpected magnetocaloric effect.PACS numbers: 73.43.Fj, 75.45.+j, 75.50.Pp The discovery of the quantum Hall effect (QHE) [1,2] led to a new understanding of electronic behavior in which topology plays a central role [3,4]. Initially, the critical experimental observation was the precise quantization of the Hall resistance to integer divisions of h/e 2 , where h is Planck's constant and e is the electron charge. This quantization, immune to sample-specific disorder, now forms the basis for a metrological standard [5]. A complementary feature-zero longitudinal resistance, reflecting resistanceless transport along sample edges-could also have technological applications, were it not for the demanding environmental requirements for achieving the QHE: a large magnetic field to break timereversal symmetry (TRS) and, in most cases, cryogenic temperatures. Ideas for producing a similar phenomenology without an external magnetic field have long been considered [6], often involving the interplay of symmetry and topology in new material systems.In the past decade, topological insulators (TIs) have emerged as a promising approach.In both twodimensional [7][8][9] and three-dimensional [10][11][12][13][14] forms, conduction in TIs is restricted to topologically-protected boundary states. In the 3D case, the presence of ferromagnetic exchange can break TRS, opening a gap in the otherwise Dirac-like surface states [15][16][17]. But topology adds a twist: even a uniformly magnetized sample will have, relative to the normal vector of the surface, a domain boundary where the magnetization switches from inward to outward. Along this line the gap should close, restoring conduction [16]. In a thin film geometry in which the easy axis of the magnetism is out-of-plane, confinement along the sample side wall should ensure conduction is one-dimensional while the surface gradient of the magnetism restricts it to only one direction, leading to ballistic, chiral transport. In a Hall bar geometry, this would be observed as the quantum anomalous Hall effect (QAHE), with a zero longitudinal resistance and a transverse resistance quantized to h/ne 2 , where n is typically ±1 but can in principle be a higher integer given sufficiently strong exchange [18].Experimental realization of the QAHE has been swift. Doping films of the ternary TI family (Bi,Sb) 2 Te 3 with Mn or Cr was found to produce robust out-of-plane ferromagnetism and a large anomalous Hall effect in transport [19][20][21]. Further growth optimization and chemical potential man...

Characterizing the structure of topological insulator thin films

“…The ability to place the chemical potential at the Dirac point, along with out-of plane ferromagnetism being possible by Cr or V doping, make this one of the most promising compounds for exotic effects such as the quantum anomalous Hall effect. [16][17][18][19] (Bi, Sb) 2 Te 3 shares the same twinning problems as Bi 2 Se 3 but similarly, growth on InP (111)A strongly favors one orientation (Fig. 2(a)).…”

Quantum Anomalous Hall Effect

“…All these observations confirm the existence of the QAH effect in this system. This experimental breakthrough has immediately aroused great interest of researchers in this field and was soon reproduced by several other experimental groups [29][30][31][32][33][34][35]. Nevertheless, for the first experiment of the QAH effect, a relatively large residual longitudinal resistance (around 2.5kΩ) always remains and the corresponding Hall conductance is around 0.987e 2 /h at zero magnetic field.…”

“…In particular, the Hall conductance is quantized to ± e 2 h at zero external magnetic field. Since then this QAH state has been firmly verified in more and more works [29][30][31][32][33][34][35], in both Cr doped and V doped (Bi, Sb) 2 Te 3 films. An overview on the QAH effect is provided in Ref.…”

Advances in Quantum Mechanics

“…If Φ and Ψ are related by the gauge transformation U as in (4), their connection matrices A Φ and A Φ are linked by the equation 3 A Φ = U −1 A Ψ U − iU −1 dU. 3 An easy way to realize this is the following. The connection matrices A Ψ µ (k) and A Φ µ (k) satisfy…”