Observation of Dirac Node Formation and Mass Acquisition in a Topological Crystalline Insulator

Okada, Yoshinori; Serbyn, Maksym; Lin, Hsin; Walkup, Daniel; Zhou, Wenwen; Dhital, Chetan; Neupane, Madhab; Xu, Su-Yang; Wang, Yung Jui; Sankar, Raman; Chou, F. C.; Bansil, Arun; Hasan, M. Zahid; Wilson, Stephen D.; Fu, Liang; Madhavan, Vidya

doi:10.1126/science.1239451

Cited by 290 publications

(300 citation statements)

References 25 publications

(37 reference statements)

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“…This prediction was later verified by the direct observation of topological surface states in the ARPES experiments [7][8][9]. Signatures of surface states have also been observed in transport and scanning tunneling microscopy (STM) measurements [10][11][12]. Remarkably, a recent STM experiment on (001) surface states in a magnetic field by Okada et al [11] has found interesting features in the Landau levels that are not expected for a pristine TCI surface but are consistent with a particular type of mirror symmetry breaking due to structural distortion [5].…”

Section: Introductionmentioning

confidence: 53%

Symmetry breaking and Landau quantization in topological crystalline insulators

2014

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In the recently discovered topological crystalline insulators SnTe and Pb 1−x Sn x (Te, Se), crystal symmetry and electronic topology intertwine to create topological surface states with many interesting features including Lifshitz transition, Van-Hove singularity, and fermion mass generation. These surface states are protected by mirror symmetry with respect to the (110) plane. In this work we present a comprehensive study of the effects of different mirror-symmetry-breaking perturbations on the (001) surface band structure. Pristine (001) surface states have four branches of Dirac fermions at low energy. We show that ferroelectric-type structural distortion generates a mass and gaps out some or all of these Dirac points, while strain shifts Dirac points in the Brillouin zone. An in-plane magnetic field leaves the surface state gapless, but introduces asymmetry between Dirac points. Finally, an out-of-plane magnetic field leads to discrete Landau levels. We show that the Landau level spectrum has an unusual pattern of degeneracy and interesting features due to the unique underlying band structure. This suggests that Landau level spectroscopy can detect and distinguish between different mechanisms of symmetry breaking in topological crystalline insulators.

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Section: Introductionmentioning

confidence: 53%

Symmetry breaking and Landau quantization in topological crystalline insulators

2014

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“…A topological crystalline insulator (TCI) is a new symmetry protected topological phase that is protected by crystalline space group symmetries [16][17][18] . The surface states of this novel topological phase are predicted to host many uniquely-new quantum phenomena, including surface spin filtering 19 , strain-induced crystalline symmetry protected Chern currents 20 , correlation physics due to surface electronic singularities 21,22 , none of which are possible in the much studied Z 2 TI 1,2 . The realization of these proposals requires the ability to control a TCI material to be topological or non-topological as a function of various material parameters, and to understand the properties of the protected surface states under all these parameter conditions.…”

Section: Introductionmentioning

confidence: 99%

Topological phase diagram and saddle point singularity in a tunable topological crystalline insulator

Neupane

Sankar

et al. 2015

Phys. Rev. B

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We report the evolution of the surface electronic structure and surface material properties of a topological crystalline insulator (TCI) Pb1−xSnxSe as a function of various material parameters including composition x, temperature T and crystal structure. Our spectroscopic data demonstrate the electronic groundstate condition for the saddle point singularity, the tunability of surface chemical potential, and the surface states' response to circularly polarized light. Our results show that each material parameter can tune the system between trivial and topological phase in a distinct way unlike as seen in Bi2Se3 and related compounds, leading to a rich and unique topological phase diagram. Our systematic studies of the TCI Pb1−xSnxSe are valuable materials guide to realize new topological phenomena.

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“…Pairs of Dirac cones with spin-momentum locking are located near theX points of the surface Brillouin zone, forming a Kramers pair. At low temperatures the surface undergoes a structural transition into a ferroelectric state and one of the mirror symmetries is spontaneously broken [14,15], while the other remains intact. As a result, two of the surface Dirac cones become massive, while the other two remain massless [16] (see inset in Fig.…”

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confidence: 99%

Quantum Nonlinear Hall Effect Induced by Berry Curvature Dipole in Time-Reversal Invariant Materials

2015

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It is well known that a nonvanishing Hall conductivity requires broken time-reversal symmetry. However, in this work, we demonstrate that Hall-like currents can occur in second-order response to external electric fields in a wide class of time-reversal invariant and inversion breaking materials, at both zero and twice the driving frequency. This nonlinear Hall effect has a quantum origin arising from the dipole moment of the Berry curvature in momentum space, which generates a net anomalous velocity when the system is in a current-carrying state. The nonlinear Hall coefficient is a rank-two pseudotensor, whose form is determined by point group symmetry. We discus optimal conditions to observe this effect and propose candidate two-and three-dimensional materials, including topological crystalline insulators, transition metal dichalcogenides, and Weyl semimetals. DOI: 10.1103/PhysRevLett.115.216806 PACS numbers: 73.43.-f, 03.65.Vf, 72.15.-v, 72.20.My Introduction.-The Hall conductivity of an electron system whose Hamiltonian is invariant under time-reversal symmetry is forced to vanish. Crystals with sufficiently low symmetry can have resistivity tensors which are anisotropic, but Onsager's reciprocity relations [1] force the conductivity to be a symmetric tensor in the presence of time-reversal symmetry. Hence, when the electric field is along its principal axes the current and the electric field are collinear, at least to the first order in electric fields. However, this constraint is only about the linear response and does not necessarily enforce the full current to flow collinearly with the local electric field.In this Letter we study a special type of such nonlinear Hall-like currents. We will demonstrate that metals without inversion symmetry can have a nonlinear Hall-like current arising from the Berry curvature in momentum space. The conventional Hall conductivity can be viewed as the zeroorder moment of the Berry curvature over occupied states, namely, as an integral of the Berry curvature within the metal's Fermi surface. The effect we discuss here is determined by a pseudotensorial quantity that measures a first-order moment of the Berry curvature over the occupied states, and hence we call it the Berry curvature dipole. This nonlinear Hall effect has a quantum origin arising from the anomalous velocity of Bloch electrons generated by the Berry curvature [2], but it is not expected to be quantized.In a time-reversal invariant system, the Berry curvature is odd in momentum space, Ω a ðkÞ ¼ −Ω a ð−kÞ, and hence its integral weighed by the equilibrium Fermi distribution is forced to vanish, because Kramers pair states at k and −k are equally occupied. However, the second-order response is determined by the integral of the Berry curvature evaluated in the nonequilibrium distribution of electrons computed to first order in the electric field. Since the

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Observation of Dirac Node Formation and Mass Acquisition in a Topological Crystalline Insulator

Cited by 290 publications

References 25 publications

Symmetry breaking and Landau quantization in topological crystalline insulators

Symmetry breaking and Landau quantization in topological crystalline insulators

Topological phase diagram and saddle point singularity in a tunable topological crystalline insulator

Quantum Nonlinear Hall Effect Induced by Berry Curvature Dipole in Time-Reversal Invariant Materials

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