Accidental Degeneracy in the Energy Bands of Crystals

Herring, Conyers

doi:10.1103/physrev.52.365

Cited by 545 publications

(398 citation statements)

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“…When the Hamiltonian has both inversion symmetry and time-reversal symmetry and without the spin-orbit interaction, the accidental degeneracy can occur on a line in the 3D momentum space [69]. The matrix representing the Hamiltonian can become real by unitary transform.…”

Section: Dirac Cone and Electronic Structure In The Zgsmentioning

confidence: 99%

Theoretical study of the zero-gap organic conductor α-(BEDT-TTF)₂I₃

Kobayashi

Katayama

Suzumura

2009

Science and Technology of Advanced Materials

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The quasi-two-dimensional molecular conductor α-(BEDT-TTF) 2 I 3 exhibits anomalous transport phenomena where the temperature dependence of resistivity is weak but the ratio of the Hall coefficient at 10 K to that at room temperature is of the order of 10 4 . These puzzling phenomena were solved by predicting massless Dirac fermions, whose motions are described using the tilted Weyl equation with anisotropic velocity. α-(BEDT-TTF) 2 I 3 is a unique material among several materials with Dirac fermions, i.e. graphene, bismuth, and quantum wells such as HgTe, from the view-points of both the structure and electronic states described as follows. α-(BEDT-TTF) 2 I 3 has the layered structure with highly two-dimensional massless Dirac fermions. The anisotropic velocity and incommensurate momenta of the contact points, ±k 0 , originate from the inequivalency of the BEDT-TTF sites in the unit cell, where ±k 0 moves in the first Brillouin zone with increasing pressure. The massless Dirac fermions exist in the presence of the charge disproportionation and are robust against the increase in pressure. The electron densities on those inequivalent BEDT-TTF sites exhibit anomalous momentum distributions, reflecting the angular dependences of the wave functions around the contact points. Those unique electronic properties affect the spatial oscillations of the electron densities in the vicinity of an impurity. A marked behavior of the Hall coefficient, where the sign of the Hall coefficient reverses sharply but continuously at low temperatures around 5 K, is investigated by treating the interband effects of the magnetic field exactly. It is shown that such behavior is possible by assuming the existence of the extremely small amount of electron doping. The enhancement of the orbital diamagnetism is also expected. The results of the present research shed light on a new aspect of Dirac fermion physics, i.e. the emergence of unique electronic properties owing to the structure of the material.

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Section: Dirac Cone and Electronic Structure In The Zgsmentioning

confidence: 99%

Theoretical study of the zero-gap organic conductor α-(BEDT-TTF)₂I₃

Kobayashi

Katayama

Suzumura

2009

Science and Technology of Advanced Materials

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“…Using first-principles band structure calculations, we predict the ferromagnetic full Heusler compound Co2MnGa as a candidate. Both Hopf link and chain-like bulk band crossings and unconventional topological surface states are identified.Since the discovery of Dirac and Weyl semimetals [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], topological semimetals have emerged as an active frontier in condensed matter physics. Their unique topological properties are predicted to give rise to a wide range of exotic transport and optical phenomena [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”

mentioning

confidence: 99%

“…Therefore, the Z numbers are [0, 1]. In region II, the Z numbers become [0,2]. Following this construction, we obtain the Z numbers of the two VBs at other regions, as labeled by the purple indices in Fig.…”

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confidence: 99%

Topological Hopf and Chain Link Semimetal States and Their Application to Co2MnGa

et al. 2017

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Topological semimetals can be classified by the connectivity and dimensionality of the band crossing in momentum space. The band crossings of a Dirac, Weyl, or an unconventional fermion semimetal are zero-dimensional (0D) points, whereas the band crossings of a nodal-line semimetal are one-dimensional (1D) closed loops. Here we propose that the presence of perpendicular crystalline mirror planes can protect three-dimensional (3D) band crossings characterized by nontrivial links such as a Hopf link or a coupled-chain, giving rise to a variety of new types of topological semimetals. We show that the nontrivial winding number protects topological surface states distinct from those in previously known topological semimetals with a vanishing spin-orbit interaction. We also show that these nontrivial links can be engineered by tuning the mirror eigenvalues associated with the perpendicular mirror planes. Using first-principles band structure calculations, we predict the ferromagnetic full Heusler compound Co2MnGa as a candidate. Both Hopf link and chain-like bulk band crossings and unconventional topological surface states are identified.Since the discovery of Dirac and Weyl semimetals [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], topological semimetals have emerged as an active frontier in condensed matter physics. Their unique topological properties are predicted to give rise to a wide range of exotic transport and optical phenomena [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. By considering various rotational and mirror symmetries in both symmorphic and non-symmorphic contexts, researchers have predicted nodal-line semimetals [38] [48][49][50]. Despite this diversity, topological semimetals can be further classified and characterized by the dimensionality of their band crossings in the bulk Brillouin zone (BZ). In a Dirac/Weyl semimetal or an unconventional (higher-fold degenerate) fermion semimetal [41,[43][44][45][46], the conduction and valence bands cross at discrete points in the BZ. Therefore, the dimension of their band crossings is 0D. In a nodal-line semimetal [38], the conduction and valence bands touch along a closed loop, thus the dimension of its band crossing is 1D. In this letter, we propose a number of previously unidentified topological semimetals and identify a candidate material class for the experimental realization. They feature 3D band crossings characterized by nontrivial links such as a Hopf link or a coupled-chain enabled by perpendicular mirror planes. The Hopf link, which consists of two rings that pass through the center of each other, represents the simplest topologically nontrivial link. While originally studied in mathematics and other areas, recently, researchers have applied this concept into topological physics in order to construct novel topological insulators and superconductors [52][53][54], although the role of Hopf link is distinctly different from what is considered here. Here we apply this idea in metals and show that the c...

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“…2 Essential clues to the paradoxical symmetry properties of the HO state can be lent from the theory of symmetryprotected quantum spin Hall 18 and topological phases 19,20 of matter which have been shown in recent years to arise from spin-orbit coupling (SOC) entanglement in the single-electron wavefunction. Another interesting analogy can be made with the theory of Weyl semimetals, originally refereed as 'accidental degeneracy in bands' 21 , in which multiple relativistic Dirac points are scattered in the momentum space (and thus termed 'semimetal') owing to a broken crystal symmetry, but they remain topologically protected via other subjective symmetry invariance. 22 These compelling physical concepts led us to propose and formulate an electronic interaction induced spin-orbit density wave (SODW) as an emergent phase of matter which stabilizes in SOC systems via broken translational but invariant time-reversal symmetry.…”

Section: Introductionmentioning

confidence: 99%

“…21,37 The blue to red color map has no special significance here. (e) Static susceptibility in the 2D q space, affirming a paramount FS instability peak at Q.…”

Section: Introductionmentioning

confidence: 99%

Imprints of spin-orbit density wave in the hidden-order state of URu2Si2

Das

2014

Phys. Rev. B

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The mysterious second order quantum phase transition, commonly attributed to the 'hidden-order' (HO) state, in heavy-fermion metal URu2Si2 exhibits a number of paradoxical electronic and magnetic properties which cannot be associated with any conventional order parameter. We characterize and reconcile these exotic properties of the HO state based on a spin-orbit density wave order (SODW), constructed on the basis of a realistic density-functional theory (DFT) band structure. We quantify the nature of the gapped electronic and magnetic excitation spectrum, in agreement with measurements, while the magnetic moment is calculated to be zero owing to the spin-orbit coupling induced time-reversal invariance. Furthermore, a new collective mode in the spin-1 excitation spectrum is predicted to localize at zero momentum transfer in the HO state which can be visualized, for example, by electron spin resonance (ESR) at zero magnetic field or polarized inelastic neutron scattering measurements. The results demonstrate that the concomitant broken and invariant symmetries protected SODW order not only provides insights into numerous nontrivial hidden-order phenomena, but also offers a parallel laboratory to the formation of a topologically protected quantum state beyond the quantum spin-Hall state and Weyl semimetals.

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Accidental Degeneracy in the Energy Bands of Crystals

Cited by 545 publications

References 5 publications

Theoretical study of the zero-gap organic conductor α-(BEDT-TTF)₂I₃

Theoretical study of the zero-gap organic conductor α-(BEDT-TTF)₂I₃

Topological Hopf and Chain Link Semimetal States and Their Application to Co2MnGa

Imprints of spin-orbit density wave in the hidden-order state of URu2Si2

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Accidental Degeneracy in the Energy Bands of Crystals

Cited by 545 publications

References 5 publications

Theoretical study of the zero-gap organic conductor α-(BEDT-TTF)2I3

Theoretical study of the zero-gap organic conductor α-(BEDT-TTF)2I3

Topological Hopf and Chain Link Semimetal States and Their Application to Co2MnGa

Imprints of spin-orbit density wave in the hidden-order state of URu2Si2

Contact Info

Product

Resources

About

Theoretical study of the zero-gap organic conductor α-(BEDT-TTF)₂I₃

Theoretical study of the zero-gap organic conductor α-(BEDT-TTF)₂I₃