scholarly journals Chiral symmetry and fermion doubling in the zero-mode Landau levels of massless Dirac fermions with disorder

2013 ◽  
Author(s):  
Tohru Kawarabayashi ◽  
Takahiro Honda ◽  
Hideo Aoki ◽  
Yasuhiro Hatsugai
Keyword(s):  
Chiral Symmetry ◽  
Zero Mode ◽  
Landau Levels ◽  
Dirac Fermions

scholarly journals Emergent chiral symmetry in a three-dimensional interacting Dirac liquid

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
András L. Szabó ◽  
Bitan Roy
Keyword(s):  
Fixed Points ◽  
Chiral Symmetry ◽  
Rotational Symmetry ◽  
Three Dimensional ◽  
Spatial Dimension ◽  
Dirac Fermions ◽  
Electronic Interactions ◽  
Emergent Phenomena ◽  
Ordered Phases ◽  
The Stability

Abstract We compute the effects of strong Hubbardlike local electronic interactions on three-dimensional four-component massless Dirac fermions, which in a noninteracting system possess a microscopic global U(1) ⊗ SU(2) chiral symmetry. A concrete lattice realization of such chiral Dirac excitations is presented, and the role of electron-electron interactions is studied by performing a field theoretic renormalization group (RG) analysis, controlled by a small parameter ϵ with ϵ = d−1, about the lower-critical one spatial dimension. Besides the noninteracting Gaussian fixed point, the system supports four quantum critical and four bicritical points at nonvanishing interaction couplings ∼ ϵ. Even though the chiral symmetry is absent in the interacting model, it gets restored (either partially or fully) at various RG fixed points as emergent phenomena. A representative cut of the global phase diagram displays a confluence of scalar and pseudoscalar excitonic and superconducting (such as the s-wave and p-wave) mass ordered phases, manifesting restoration of (a) chiral U(1) symmetry between two excitonic masses for repulsive interactions and (b) pseudospin SU(2) symmetry between scalar or pseudoscalar excitonic and superconducting masses for attractive interactions. Finally, we perturbatively study the effects of weak rotational symmetry breaking on the stability of various RG fixed points.

scholarly journals Majorana zero modes in impurity-assisted vortex of LiFeAs superconductor

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Lingyuan Kong ◽  
Lu Cao ◽  
Shiyu Zhu ◽  
Michał Papaj ◽  
Guangyang Dai ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Zero Mode ◽  
Scanning Tunneling ◽  
Homogeneous Material ◽  
Dirac Fermions ◽  
Tunneling Microscopy ◽  
Zero Modes ◽  
Topological Quantum ◽  
One Step ◽  
Topological Quantum Computation

AbstractThe iron-based superconductor is emerging as a promising platform for Majorana zero mode, which can be used to implement topological quantum computation. One of the most significant advances of this platform is the appearance of large vortex level spacing that strongly protects Majorana zero mode from other low-lying quasiparticles. Despite the advantages in the context of physics research, the inhomogeneity of various aspects hampers the practical construction of topological qubits in the compounds studied so far. Here we show that the stoichiometric superconductor LiFeAs is a good candidate to overcome this obstacle. By using scanning tunneling microscopy, we discover that the Majorana zero modes, which are absent on the natural clean surface, can appear in vortices influenced by native impurities. Our detailed analysis reveals a new mechanism for the emergence of those Majorana zero modes, i.e. native tuning of bulk Dirac fermions. The discovery of Majorana zero modes in this homogeneous material, with a promise of tunability, offers an ideal material platform for manipulating and braiding Majorana zero modes, pushing one step forward towards topological quantum computation.

scholarly journals Boundary states for chiral symmetries in two dimensions

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Philip Boyle Smith ◽  
David Tong
Keyword(s):  
Boundary Conditions ◽  
Ground State ◽  
Zero Mode ◽  
Central Charge ◽  
Two Dimensions ◽  
Dirac Fermions ◽  
Chiral Symmetries ◽  
Boundary States ◽  
Ground State Degeneracy ◽  
Left And Right

Abstract We study boundary states for Dirac fermions in d = 1 + 1 dimensions that preserve Abelian chiral symmetries, meaning that the left- and right-moving fermions carry different charges. We derive simple expressions, in terms of the fermion charge assignments, for the boundary central charge and for the ground state degeneracy of the system when two different boundary conditions are imposed at either end of an interval. We show that all such boundary states fall into one of two classes, related to SPT phases supported by (−1)F , which are characterised by the existence of an unpaired Majorana zero mode.

scholarly journals Magnetoinfrared Spectroscopy of Landau Levels and Zeeman Splitting of Three-Dimensional Massless Dirac Fermions inZrTe5

2015 ◽  
Vol 115 (17) ◽  
Author(s):  
R. Y. Chen ◽  
Z. G. Chen ◽  
X.-Y. Song ◽  
J. A. Schneeloch ◽  
G. D. Gu ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Zeeman Splitting ◽  
Landau Levels ◽  
Dirac Fermions

scholarly journals Asymptotically Safe Gravity-Fermion Systems on Curved Backgrounds

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 306
Author(s):  
Jesse Daas ◽  
Wouter Oosters ◽  
Frank Saueressig ◽  
Jian Wang
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Chiral Symmetry ◽  
Chiral Symmetry Breaking ◽  
Background Field ◽  
High Energy ◽  
Dirac Fermions ◽  
Dynamical Mechanism ◽  
Asymptotic Safety ◽  
Set Up

We set up a consistent background field formalism for studying the renormalization group (RG) flow of gravity coupled to Nf Dirac fermions on maximally symmetric backgrounds. Based on Wetterich’s equation, we perform a detailed study of the resulting fixed point structure in a projection including the Einstein–Hilbert action, the fermion anomalous dimension, and a specific coupling of the fermion bilinears to the spacetime curvature. The latter constitutes a mass-type term that breaks chiral symmetry explicitly. Our analysis identified two infinite families of interacting RG fixed points, which are viable candidates to provide a high-energy completion through the asymptotic safety mechanism. The fixed points exist for all values of Nf outside of a small window situated at low values Nf and become weakly coupled in the large Nf-limit. Symmetry-wise, they correspond to “quasi-chiral” and “non-chiral” fixed points. The former come with enhanced predictive power, fixing one of the couplings via the asymptotic safety condition. Moreover, the interplay of the fixed points allows for cross-overs from the non-chiral to the chiral fixed point, giving a dynamical mechanism for restoring the symmetry approximately at intermediate scales. Our discussion of chiral symmetry breaking effects provides strong indications that the topology of spacetime plays a crucial role when analyzing whether quantum gravity admits light chiral fermions.

MAGNETO-SPECTROSCOPY OF EPITAXIAL GRAPHENE

2007 ◽  
Vol 21 (08n09) ◽  
pp. 1145-1154 ◽  
Author(s):  
M. L. SADOWSKI ◽  
G. MARTINEZ ◽  
M. POTEMSKI ◽  
C. BERGER ◽  
W. A. DE HEER
Keyword(s):  
Magnetic Field ◽  
Cyclotron Resonance ◽  
Far Infrared ◽  
Theoretical Models ◽  
Epitaxial Graphene ◽  
Landau Levels ◽  
Perpendicular Magnetic Field ◽  
Dirac Fermions ◽  
Optical Transitions ◽  
Interband Transitions

We present a far infrared investigation of the optical transitions in epitaxial graphene subjected to a perpendicular magnetic field. Cyclotron-resonance-like transitions between adjacent electron Landau levels are observed, as well as interband transitions. The results are discussed in terms of existing theoretical models of Dirac fermions in graphene, and the relevant optical selection rules.

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