Weyl Points in Three-Dimensional Optical Lattices: Synthetic Magnetic Monopoles in Momentum Space

Dubček, Tena; Kennedy, Colin J.; Lü, Ling; Ketterle, Wolfgang; Soljačić, Marin; Buljan, Hrvoje

doi:10.1103/physrevlett.114.225301

Cited by 175 publications

(215 citation statements)

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“…One celebrated example in three dimensions is the zero-dimensional Weyl point [7][8][9][10][11][12][13][14][15][16][17][18] described by the Weyl Hamiltonian, which has been long sought-after in particle physics but only experimentally observed in condensed matter materials [19][20][21]. Such a Weyl point can be viewed as a magnetic monopole [22] in the momentum space and possesses a quantized Chern number on a surface enclosing the point.…”

mentioning

confidence: 99%

Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas

2017

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Three-dimensional topological Weyl semimetals can generally support a zero-dimensional Weyl point characterized by a quantized Chern number or a one-dimensional Weyl nodal ring (or line) characterized by a quantized Berry phase in the momentum space. Here, in a dissipative system with particle gain and loss, we discover a new type of topological ring, dubbed Weyl exceptional ring consisting of exceptional points at which two eigenstates coalesce. Such a Weyl exceptional ring is characterized by both a quantized Chern number and a quantized Berry phase, which are defined via the Riemann surface. We propose an experimental scheme to realize and measure the Weyl exceptional ring in a dissipative cold atomic gas trapped in an optical lattice.Recently, condensed matter systems have proven to be a powerful platform to study low energy gapless particles by using momentum space band structures to mimic the energy-momentum relation of relativistic particles [1,2] and beyond [3][4][5][6]. One celebrated example in three dimensions is the zero-dimensional Weyl point [7][8][9][10][11][12][13][14][15][16][17][18] described by the Weyl Hamiltonian, which has been long sought-after in particle physics but only experimentally observed in condensed matter materials [19][20][21]. Such a Weyl point can be viewed as a magnetic monopole [22] in the momentum space and possesses a quantized Chern number on a surface enclosing the point. Another example is the one-dimensional Weyl nodal ring [3,[23][24][25], which has no counterpart in particle physics. It can be regarded as the generalization of zero-dimensional Dirac cones in two-dimensional systems, such as in graphene, to three-dimensional systems. Such a nodal ring has a quantized Berry phase over a closed path encircling it but does not possess a nonzero quantized Chern number. This leads to a natural question of whether there exists a topological ring exhibiting both a quantized Chern number and a quantized Berry phase in the momentum space.So far, studies on those gapless states focus on closed and lossless systems. However, particle gain and loss are generally present in natural systems. Such systems can often be described by non-Hermitian Hamiltonians [26][27][28][29], which are widely applied to many different systems [30][31][32][33][34][35][36][37][38][39][40]. Due to the non-Hermiticity, eigenvalues of the Hamiltonian are generically complex unless the PT symmetry [41] is conserved and the imaginary part of energy is associated with either decay or growth. Another intriguing feature of a non-Hermitian system is the existence of exceptional points (EPs) [26][27][28][29] at which two eigenstates coalesce and the Hamiltonian becomes defective, leading to many novel phenomena, such as lossinduced transparency [30], single-mode lasers [36,37], and reversed pump dependence of lasers [33].In this paper, we investigate a system of Weyl points in the presence of a spin-dependent non-Hermitian term and find a Weyl exceptional ring composed of EPs. In stark contrast to a Weyl nodal ...

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confidence: 99%

Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas

2017

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“…Another hallmark of a WSM is the existence of anomalous surface states protected by the bulk band topology, the so-called Fermi arcs [8,9]. The WSM state has been proposed in magnetic systems [8,[10][11][12][13][14][15][16][17][18][19], Dirac semimetals [20][21][22][23][24][25][26][27] under magnetic field [28], as well as photonic crystals [29,30].Recently, non-magnetic transition-metal monopnictides with broken inversion symmetry (the crystal structure and the first Brillouin zone (BZ) of these materials are shown in Fig. 1a-c [35,41] surfaces, the magnetotransport behaviors related to the chiral anomaly effect are distinct among the different compounds.…”

mentioning

confidence: 99%

Distinct Evolutions of Weyl Fermion Quasiparticles and Fermi Arcs with Bulk Band Topology in Weyl Semimetals

Autès

Matt

et al. 2017

Phys. Rev. Lett.

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Although any evidence of chiral Weyl fermions as fundamental particles in vacuum is still lacking, recent advances in topological condensed matter physics [1,2] provide a new way of realizing them in Weyl semimetals (WSMs). In an ideal WSM, bands without spin degeneracy cross at pairs of points at the Fermi level, the Weyl nodes, and the corresponding low-energy excitations fulfill the Weyl equation [3,4].As a consequence, the quasiparticles in a WSM show the same exotic behaviors as Weyl fermions, such as the chiral anomaly effect [5][6][7] that can induce a negative longitudinal magneto-resistance (MR). Another hallmark of a WSM is the existence of anomalous surface states protected by the bulk band topology, the so-called Fermi arcs [8,9]. The WSM state has been proposed in magnetic systems [8,[10][11][12][13][14][15][16][17][18][19], Dirac semimetals [20][21][22][23][24][25][26][27] under magnetic field [28], as well as photonic crystals [29,30].Recently, non-magnetic transition-metal monopnictides with broken inversion symmetry (the crystal structure and the first Brillouin zone (BZ) of these materials are shown in Fig. 1a-c [35,41] surfaces, the magnetotransport behaviors related to the chiral anomaly effect are distinct among the different compounds. The negative longitudinal MR, which has a maximum value of -30% at ~6 T in TaAs [42] and as large as -3000% at 9T in TaP without any sign of saturation [43,44], has never been observed in NbP [45,46]. The apparent disagreement between the transport and spectroscopic signatures of WSM raises the questions of whether the observation of topological Fermi arcs is sufficient to identify a WSM phase [38,47], and whether the negative longitudinal MR in transition-metal monopnictides is not induced by the chiral anomaly but rather by the axial anomaly effect, which is not related to the Weyl fermion quasiparticles [48].Here, we present a comparative study of transition-metal monopnictides by Polycrystalline NbP (TaP) was synthesized by a solid-state reaction using elemental niobium (tantalum) and red phosphorus with a minimum purity of 99.99 %. The respective amounts of starting reagents were mixed and pressed into pellets in a Heglove box and annealed in an evacuated quartz ampule at 1050 °C for 60 hours.Laboratory x-ray diffraction measurements, which were done at room temperature using Cu Ka radiation on a Brucker D8 diffractometer, have shown that the obtained crystals are single phase with the tetragonal structure of space group I41/amd (N 141).Clean surfaces for ARPES measurements were obtained by cleaving NbP and TaP samples in a vacuum better than 5 × 10 -11 Torr. Surface-sensitive VUV-ARPES measurements were performed with circular-polarized light at the Surface/Interface Spectroscopy (SIS) beamline at the Swiss Light Source (SLS) with a Scienta R4000.Bulk-sensitive soft X-ray ARPES measurements were performed at the Advanced Resonant Spectroscopies (ADRESS) beamline at SLS [49] using a SPECS analyser, and data were collected using circular-polarized light w...

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“…Moreover the second partition translates in n-fold degeneracy of each subband. In the particular case Φ = π, two sub-bands are obtained, touching in Weyl cones as discussed in [71,72,73]; in this case the system in Eq. (23) is the direct three-dimensional generalization of the square lattice model with π-fluxes in [74].…”

Section: Isotropic Fluxmentioning

confidence: 99%

Abelian Gauge Potentials on Cubic Lattices

Burrello

Lepori

Paganelli

et al. 2017

Advances in Quantum Mechanics

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The study of the dynamics of a quantum particle in a magnetic field is a fascinating subject of perduring interest both in physics and mathematics literature. The quantization of energy levels giving rise to the Landau levels is at the basis of our understanding of integer and fractional quantum Hall effects [1, 2, 3, 4, 5] and its higher-dimensional counterparts and generalizations, including topological insulators [6,7,8]. The use of vector potentials in quantum mechanics is associated in itself to very interesting consequences, such as the purely quantum mechanical interference in the Aharonov-Bohm effect [9]. On the other side, the mathematical formalism for a particle in a magnetic field has been developed and refined along the time, based on the rigorous definition of Schrödinger operators with magnetic fields [10]. An important role is played by the construction of families of observables in the presence of gauge fields relying on the progresses in gauge covariant

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Weyl Points in Three-Dimensional Optical Lattices: Synthetic Magnetic Monopoles in Momentum Space

Cited by 175 publications

References 50 publications

Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas

Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas

Distinct Evolutions of Weyl Fermion Quasiparticles and Fermi Arcs with Bulk Band Topology in Weyl Semimetals

Abelian Gauge Potentials on Cubic Lattices

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