Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances

Fukui, Tsuguya; Hatsugai, Yasuhiro; Suzuki, Hiroshi

doi:10.1143/jpsj.74.1674

Cited by 1,244 publications

(1,011 citation statements)

References 18 publications

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“…Time-reversal symmetry dictates that Ω n (−k) = −Ω n (k). Based on the TBH model we derived, the Berry curvature can be readily evaluated 53 . In Fig.…”

Section: B Berry Curvaturementioning

confidence: 99%

Ab initio tight-binding Hamiltonian for transition metal dichalcogenides

et al. 2015

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We present an accurate ab-initio tight-binding hamiltonian for the transition-metal dichalcogenides, MoS2, MoSe2, WS2, WSe2, with a minimal basis (the d orbitals for the metal atoms and p orbitals for the chalcogen atoms) based on a transformation of the Kohn-Sham density function theory (DFT) hamiltonian to a basis of maximally localized Wannier functions (MLWF). The truncated tight-binding hamiltonian (TBH), with only on-site, first and partial second neighbor interactions, including spin-orbit coupling, provides a simple physical picture and the symmetry of the main band-structure features. Interlayer interactions between adjacent layers are modeled by transferable hopping terms between the chalcogen p orbitals. The full-range tight-binding hamiltonian (FTBH) can be reduced to hybrid-orbital k · p effective hamiltonians near the band extrema that captures important low-energy excitations. These ab-initio hamiltonians can serve as the starting point for applications to interacting many-body physics including optical transitions and Berry curvature of bands, of which we give some examples.

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“…Time-reversal symmetry dictates that Ω n (−k) = −Ω n (k). Based on the TBH model we derived, the Berry curvature can be readily evaluated 53 . In Fig.…”

Section: B Berry Curvaturementioning

confidence: 99%

Ab initio tight-binding Hamiltonian for transition metal dichalcogenides

et al. 2015

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“…i) Compute the Z 2 numbers using the integration of both Berry's connection and curvature over half of the Brillouin Zone (BZ). In order to do so, one has to set up a mesh in the k-space and calculate the corresponding quantities on the lattice version of the problem 18,41,42 . Since the calculation involves the Berry's connection, one has to numerically fix the gauge on the half BZ, which is not easy for the realistic wave functions obtained by first principle calculation.…”

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confidence: 99%

Equivalent expression ofZ2topological invariant for band insulators using the non-Abelian Berry connection

et al. 2011

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We introduce a new expression for the Z2 topological invariant of band insulators using nonAbelian Berry's connection. Our expression can identify the topological nature of a general band insulator without any of the gauge fixing problems that plague the concrete implementation of previous invariants. The new expression can be derived from the "partner switching" of the Wannier function center during time reversal pumping and is thus equivalent to the Z2 topological invariant proposed by Kane and Mele. Using the new expression, we have recalculated the Z2 topological index for several topological insulator material systems and obtained consistent results with the previous studies.

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“…It is, therefore, of interest to quantify the topological character of the fully SOC-gapped superlattice, by computing the U (N ) Berry curvature of Kohn-Sham Bloch states. The Berry curvature, Ω(k), is computed directly from the Kohn-Sham Bloch wavefunctions on a discretized k mesh, as [28,29] …”

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confidence: 99%

Single-Spin Dirac Fermion and Chern Insulator Based on Simple Oxides

et al. 2015

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It is highly desirable to combine recent advances in the topological quantum phases with technologically relevant materials. Chromium dioxide (CrO2) is a half-metallic material, widely used in high-end data storage applications. Using first principles calculations, we show via interfacial orbital design that a novel class of half semi-metallic Dirac electronic phase emerges at the interface CrO2 with TiO2 in both thin film and superlattice configurations, with four spin-polarized Dirac points in momentum-space (k-space) band structure. When the spin and orbital degrees of freedom are allowed to couple, the CrO2/TiO2 superlattice becomes a Chern insulator without external fields or additional doping. With topological gaps equivalent to 43 Kelvin and a Chern number 2, the ensuing quantization of Hall conductance to 2e 2 /h will enable potential development of these highly industrialized oxides for applications in topologically high fidelity data storage and energy-efficient electronic and spintronic devices.The defining feature of massless Dirac Fermions [1,2] is the linear energy dispersion, implying that a quasiparticle moves at a constant speed independent of its energy, as governed by relativistic quantum mechanics. The exploration of novel Dirac materials with bulk Dirac or Dirac-Weyl states remains a great challenge in condensed matter and materials physics. [3][4][5][6][7][8][9][10] In particular, there has yet been neither theoretical proposal nor observation of materials systems with Dirac points a single spin species, which may be called a half-semimetal. Half metals are a class of ferromagnetic materials in which the conduction is dominated by one spin component while the other spin is gapped, which stands to enable reduced device size and non-volatile memory. At a rudimentary level, a half semi-metal will harbour the fascinating Dirac physics [1][2][3][4][5][6][7][8][9][10] all with a single spin. And as a not-so-trivial consequence, it may lead to Chern insulators [11][12][13][14] or valleytronics materials [15][16][17][18] when the low-energy excitations turn massive. In particular, a Chern insulator exhibits quantum anomalous Hall (QAH) effect in the absence of external magnetic field. This important fundamental phenomenon was established experimentally recently in magnetically doped topological insulator. [14] A spontaneous half semimetal will lead to a Chern insulator with appropriate spin-orbit coupling (SOC) and symmetry, which is advantageous for it requires no addition of impurity to the system. Precisely controlled growth of heterojunctions of oxides offers a unique avenue for exploring novel interfacial quantum phases, in which the interplay of orbital, charge, spin and lattice degrees of freedom gives rise to remarkably rich chemical, structural, electronic and magnetic varieties. Bulk CrO 2 (structure shown in Fig. 1) is a robust half metal even at elevated temperatures, [19][20][21] and widely used in enterprisegrade data storage. Here, we consider the possibility to fashion the CrO 2 int...

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Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances

Cited by 1,244 publications

References 18 publications

Ab initio tight-binding Hamiltonian for transition metal dichalcogenides

Ab initio tight-binding Hamiltonian for transition metal dichalcogenides

Equivalent expression ofZ2topological invariant for band insulators using the non-Abelian Berry connection

Single-Spin Dirac Fermion and Chern Insulator Based on Simple Oxides

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