scholarly journals Observation and control of maximal Chern numbers in a chiral topological semimetal

Science ◽  
2020 ◽  
Vol 369 (6500) ◽  
pp. 179-183 ◽  
Author(s):  
Niels B. M. Schröter ◽  
Samuel Stolz ◽  
Kaustuv Manna ◽  
Fernando de Juan ◽  
Maia G. Vergniory ◽  
...  
Keyword(s):  
Topological Invariant ◽  
Chern Number ◽  
Linear Dispersion ◽  
Fermi Arc ◽  
Number Magnitude ◽  
Fermi Arcs ◽  
Chern Numbers ◽  
Topological Semimetals ◽  
Chiral Crystals ◽  
And Control

Topological semimetals feature protected nodal band degeneracies characterized by a topological invariant known as the Chern number (C). Nodal band crossings with linear dispersion are expected to have at most |C|=4, which sets an upper limit to the magnitude of many topological phenomena in these materials. Here, we show that the chiral crystal palladium gallium (PdGa) displays multifold band crossings, which are connected by exactly four surface Fermi arcs, thus proving that they carry the maximal Chern number magnitude of 4. By comparing two enantiomers, we observe a reversal of their Fermi-arc velocities, which demonstrates that the handedness of chiral crystals can be used to control the sign of their Chern numbers.

scholarly journals Observation of a singular Weyl point surrounded by charged nodal walls in PtGa

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
J.-Z. Ma ◽  
Q.-S. Wu ◽  
M. Song ◽  
S.-N. Zhang ◽  
E. B. Guedes ◽  
...  
Keyword(s):  
Density Functional ◽  
Density Functional Theory Calculations ◽  
Photoemission Spectroscopy ◽  
Functional Theory ◽  
Fermi Arc ◽  
Angle Resolved Photoemission Spectroscopy ◽  
Fermi Arcs ◽  
Surface Projection ◽  
Applicable Range ◽  
Opposite Chirality

AbstractConstrained by the Nielsen-Ninomiya no-go theorem, in all so-far experimentally determined Weyl semimetals (WSMs) the Weyl points (WPs) always appear in pairs in the momentum space with no exception. As a consequence, Fermi arcs occur on surfaces which connect the projections of the WPs with opposite chiral charges. However, this situation can be circumvented in the case of unpaired WP, without relevant surface Fermi arc connecting its surface projection, appearing singularly, while its Berry curvature field is absorbed by nontrivial charged nodal walls. Here, combining angle-resolved photoemission spectroscopy with density functional theory calculations, we show experimentally that a singular Weyl point emerges in PtGa at the center of the Brillouin zone (BZ), which is surrounded by closed Weyl nodal walls located at the BZ boundaries and there is no Fermi arc connecting its surface projection. Our results reveal that nontrivial band crossings of different dimensionalities can emerge concomitantly in condensed matter, while their coexistence ensures the net topological charge of different dimensional topological objects to be zero. Our observation extends the applicable range of the original Nielsen-Ninomiya no-go theorem which was derived from zero dimensional paired WPs with opposite chirality.

scholarly journals Measuring Chern numbers in Hofstadter strips

2017 ◽  
Vol 3 (2) ◽  
Author(s):  
Samuel Mugel ◽  
Alexandre Dauphin ◽  
Pietro Massignan ◽  
Leticia Tarruell ◽  
Maciej Lewenstein ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary Conditions ◽  
Chern Number ◽  
Open Boundary ◽  
Topological Invariants ◽  
Transverse Displacement ◽  
Open Boundary Conditions ◽  
Open Questions ◽  
Chern Numbers ◽  
Spatial Dimensions

Topologically non-trivial Hamiltonians with periodic boundary conditions are characterized by strictly quantized invariants. Open questions and fundamental challenges concern their existence, and the possibility of measuring them in systems with open boundary conditions and limited spatial extension. Here, we consider transport in Hofstadter strips, that is, two-dimensional lattices pierced by a uniform magnetic flux which extend over few sites in one of the spatial dimensions. As we show, an atomic wave packet exhibits a transverse displacement under the action of a weak constant force. After one Bloch oscillation, this displacement approaches the quantized Chern number of the periodic system in the limit of vanishing tunneling along the transverse direction. We further demonstrate that this scheme is able to map out the Chern number of ground and excited bands, and we investigate the robustness of the method in presence of both disorder and harmonic trapping. Our results prove that topological invariants can be measured in Hofstadter strips with open boundary conditions and as few as three sites along one direction.

scholarly journals Chern Class Inequalities on Polarized Manifolds and Nef Vector Bundles

2020 ◽  
Author(s):  
Ping Li ◽  
Fangyang Zheng
Keyword(s):  
Chern Class ◽  
Vector Bundles ◽  
Euler Number ◽  
Type Inequality ◽  
Chern Number ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Bisectional Curvature ◽  
Chern Numbers ◽  
Nef Vector Bundles

Abstract This article is concerned with Chern class and Chern number inequalities on polarized manifolds and nef vector bundles. For a polarized pair $(M,L)$ with $L$ very ample, our 1st main result is a family of sharp Chern class inequalities. Among them the 1st one is a variant of a classical result and the equality case of the 2nd one is a characterization of hypersurfaces. The 2nd main result is a Chern number inequality on it, which includes a reverse Miyaoka–Yau-type inequality. The 3rd main result is that the Chern numbers of a nef vector bundle over a compact Kähler manifold are bounded below by the Euler number. As an application, we classify compact Kähler manifolds with nonnegative bisectional curvature whose Chern numbers are all positive. A conjecture related to the Euler number of compact Kähler manifolds with nonpositive bisectional curvature is proposed, which can be regarded as a complex analogue to the Hopf conjecture.

scholarly journals Nonsaturating large magnetoresistance in semimetals

2018 ◽  
Vol 115 (42) ◽  
pp. 10570-10575 ◽  
Author(s):  
Ian A. Leahy ◽  
Yu-Ping Lin ◽  
Peter E. Siegfried ◽  
Andrew C. Treglia ◽  
Justin C. W. Song ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Magnetic Susceptibility ◽  
Transport Properties ◽  
Applied Magnetic Field ◽  
Charge Compensation ◽  
Linear Dispersion ◽  
Dominant Mechanism ◽  
Temperature Dependences ◽  
Topological Semimetals ◽  
Different Origins

The rapidly expanding class of quantum materials known as topological semimetals (TSMs) displays unique transport properties, including a striking dependence of resistivity on applied magnetic field, that are of great interest for both scientific and technological reasons. So far, many possible sources of extraordinarily large nonsaturating magnetoresistance have been proposed. However, experimental signatures that can identify or discern the dominant mechanism and connect to available theories are scarce. Here we present the magnetic susceptibility (χ), the tangent of the Hall angle (tan⁡θH), along with magnetoresistance in four different nonmagnetic semimetals with high mobilities, NbP, TaP, NbSb2, and TaSb2, all of which exhibit nonsaturating large magnetoresistance (MR). We find that the distinctly different temperature dependences, χ(T), and the values of tan⁡θH in phosphides and antimonates serve as empirical criteria to sort the MR from different origins: NbP and TaP are uncompensated semimetals with linear dispersion, in which the nonsaturating magnetoresistance arises due to guiding center motion, while NbSb2 and TaSb2 are compensated semimetals, with a magnetoresistance emerging from nearly perfect charge compensation of two quadratic bands. Our results illustrate how a combination of magnetotransport and susceptibility measurements may be used to categorize the increasingly ubiquitous nonsaturating large magnetoresistance in TSMs.

scholarly journals Emergence of topological superconductivity in doped topological Dirac semimetals under symmetry-lowering lattice distortions

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Sangmo Cheon ◽  
Ki Hoon Lee ◽  
Suk Bum Chung ◽  
Bohm-Jung Yang
Keyword(s):  
Bound States ◽  
Unconventional Superconductivity ◽  
Zero Bias ◽  
Dirac Semimetal ◽  
Orbital Electron ◽  
Lattice Distortions ◽  
Topological Semimetals ◽  
Superconducting Pairing ◽  
And Control ◽  
Topological Superconductivity

AbstractRecently, unconventional superconductivity having a zero-bias conductance peak is reported in doped topological Dirac semimetal (DSM) with lattice distortion. Motivated by the experiments, we theoretically study the possible symmetry-lowering lattice distortions and their effects on the emergence of unconventional superconductivity in doped topological DSM. We find four types of symmetry-lowering lattice distortions that reproduce the crystal symmetries relevant to experiments from the group-theoretical analysis. Considering inter-orbital and intra-orbital electron density-density interactions, we calculate superconducting phase diagrams. We find that the lattice distortions can induce unconventional superconductivity hosting gapless surface Andreev bound states (SABS). Depending on the lattice distortions and superconducting pairing interactions, the unconventional inversion-odd-parity superconductivity can be either topological nodal superconductivity hosting a flat SABS or topological crystalline superconductivity hosting a gapless SABS. Remarkably, the lattice distortions increase the superconducting critical temperature, which is consistent with the experiments. Our work opens a pathway to explore and control pressure-induced topological superconductivity in doped topological semimetals.

scholarly journals Chiral Majorana Edge Modes and Vortex MajoranaZero Modes in Superconducting Antiferromagnetic TopologicalInsulator

2021 ◽  
Author(s):  
Beibing Huang ◽  
Xiaosen Yang ◽  
Qinfang Zhang ◽  
Ning Xu
Keyword(s):  
Local Density ◽  
Three Dimensional ◽  
Chern Number ◽  
Theoretic Model ◽  
S Wave ◽  
Topological Stability ◽  
Surface Layers ◽  
New Era ◽  
Vortex Phase ◽  
Chern Numbers

Abstract The antiferromagnetic topological insulator (AFTI) is topologically protected by the combined time-reversal and translational symmetry $\mathcal{T}_c$. In this paper we investigate the effects of the $s$-wave superconducting pairings on the multilayers of AFTI, which breaks $\mathcal{T}_c$ symmetry and can realize quantum anomalous Hall insulator with unit Chern number. For the weakly coupled pairings, the system corresponds to the topological superconductor (TSC) with the Chern number $C=\pm 2$. We answer the following questions whether the local Chern numbers and chiral Majorana edge modes of such a TSC distribute around the surface layers. By the numerical calculations based on a theoretic model of AFTI, we find that when the local Chern numbers are always dominated by the surface layers, the wavefunctions of chiral Majorana edge modes must not localize on the surface layers and show a smooth crossover from spatially occupying all layers to only distributing near the surface layers, similar to the hinge states in a three dimensional second-order topological phases. The latter phase, denoted by the hinged TSC, can be distinguished from the former phase by the measurements of the local density of state. In addition we also study the superconducting vortex phase transition in this system and find that the exchange field in the AFTI not only enlarges the phase space of topological vortex phase but also enhances its topological stability. These conclusions will stimulate the investigations on superconducting effects of AFTI and drive the studies on chiral Majorana edge modes and vortex Majorana zero modes into a new era.

scholarly journals 3D Quantum Hall Effect of Fermi Arcs in Topological Semimetals

2017 ◽  
Vol 119 (13) ◽  
Author(s):  
C. M. Wang ◽  
Hai-Peng Sun ◽  
Hai-Zhou Lu ◽  
X. C. Xie
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Fermi Arcs ◽  
Topological Semimetals

scholarly journals Observation of giant spin-split Fermi-arc with maximal Chern number in the chiral topological semimetal PtGa

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Mengyu Yao ◽  
Kaustuv Manna ◽  
Qun Yang ◽  
Alexander Fedorov ◽  
Vladimir Voroshnin ◽  
...  
Keyword(s):  
Chern Number ◽  
Fermi Arc ◽  
Topological Semimetal

scholarly journals Visualizing weakly bound surface Fermi arcs and their correspondence to bulk Weyl fermions

2016 ◽  
Vol 2 (8) ◽  
pp. e1600709 ◽  
Author(s):  
Rajib Batabyal ◽  
Noam Morali ◽  
Nurit Avraham ◽  
Yan Sun ◽  
Marcus Schmidt ◽  
...  
Keyword(s):  
Wave Function ◽  
Bloch Wave ◽  
Scanning Tunneling ◽  
Tunneling Microscopy ◽  
Weakly Bound ◽  
Fermi Arc ◽  
Fermi Arcs ◽  
Surface Manifestation ◽  
Energy And Momentum ◽  
Spectroscopic Tool

Fermi arcs are the surface manifestation of the topological nature of Weyl semimetals, enforced by the bulk-boundary correspondence with the bulk Weyl nodes. The surface of tantalum arsenide, similar to that of other members of the Weyl semimetal class, hosts nontopological bands that obscure the exploration of this correspondence. We use the spatial structure of the Fermi arc wave function, probed by scanning tunneling microscopy, as a spectroscopic tool to distinguish and characterize the surface Fermi arc bands. We find that, as opposed to nontopological states, the Fermi arc wave function is weakly affected by the surface potential: it spreads rather uniformly within the unit cell and penetrates deeper into the bulk. Fermi arcs reside predominantly on tantalum sites, from which the topological bulk bands are derived. Furthermore, we identify a correspondence between the Fermi arc dispersion and the energy and momentum of the bulk Weyl nodes that classify this material as topological. We obtain these results by introducing an analysis based on the role the Bloch wave function has in shaping quantum electronic interference patterns. It thus carries broader applicability to the study of other electronic systems and other physical processes.

scholarly journals Double Weyl points and Fermi arcs of topological semimetals in non-Abelian gauge potentials

2016 ◽  
Vol 94 (5) ◽  
Author(s):  
L. Lepori ◽  
I. C. Fulga ◽  
A. Trombettoni ◽  
M. Burrello
Keyword(s):  
Abelian Gauge ◽  
Fermi Arcs ◽  
Topological Semimetals
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