Spinor Research Articles

Tunneling between two systems of interacting chiral fermions

Tunneling between two systems of interacting chiral fermions

Trace Anomaly Redefined in a Convention Leading to the Pontryagin Resolution

It is sought a fundamental reason for the then fore contradictory or randomly correct outcomes. As due the dilemma borne out from the multiple methods for the Pontryagin Chiral Fermions density anomalies resolutions and their either zero or imaginary results. Such is based on extracting the unitarity from a unity-scale diffeomorphic transformation. The same result can be found independently while is being linked to a generalization of the Wick rotation and as a result of an orbital-wise Pfaffian differential satisfying Gravity.

Dark torsion oscillations and bounces induced by Barbero-Immirzi and quantum correction on Einstein-Cartan gravity with very light inflatons

In this paper we present several examples of how to constrain loop quantum gravity Barbero-Immirzi (BI) parameter, either by using quantum corrections in Nieh–Yan (NY) modified Einstein-Cartan (EC) gravity with the Holst term. The reason why we introduce some extra terms in the actions, is that even when one adds both NY and Holst terms, being topological terms, they do not contribute to the dynamics of the problem and to the equations of motion (EOM). Examples run from quantum corrections and torsion mass in the dark universe with very light inflaton approximation to bouncing cosmologies in NY gravity. This follows similar model from Tukhashvili and Steinhardt (2023) of a bouncing cosmology induced by torsion condensates in EC gravity. The Lagrangian in this paper, is shown to be expressed in terms of NY polynomial form. The quantum one-loop correction is taken in NY Lagrangian as the inverse of BI parameter. This has been recently appeared in He et al. (2024) quantum corrections in Einstein-Cartan-Nieh–Yan one loop quantum gravity in Starobinsky inflation. We show that to have a cosmological NY dark universe one needs a real BI parameter. Inflation Hubble scale of the order of O(100eV) and very light inflaton of mass ∼10−12TeV are used due to its relation with dark matter. The very light mass character of inflatons and much heavier torsion are responsible to induced cosmological bounce in dark universe. When one introduces the quantum correction parameter b as second-order in front of the NY topological term in squared and introduce the NY term back into the ECH gravity, the EC gravity limit where BI parameter β→∞, yields a chiral fermion density ρ5. This result lies very close to the upper bound in the range of 0≤β≤1.185, previously obtained by Panza et al. Analysis of fermionic currents shows that Holst term can be eliminated by choosing β=0.288. Massive torsion oscillates in Einstein-Cartan gravity in the BI limit of β→∞.

Higher rank chiral fermions in three-dimensional Weyl semimetals

Higher rank chiral fermions in three-dimensional Weyl semimetals

Higher order gaps in the renormalized band structure of doubly aligned hBN/bilayer graphene moiré superlattice

This paper presents our findings on the recursive band gap engineering of chiral fermions in bilayer graphene doubly aligned with hBN. Using two interfering moiré potentials, we generate a supermoiré pattern that renormalizes the electronic bands of the pristine bilayer graphene, resulting in higher order fractal gaps even at very low energies. These Bragg gaps can be mapped using a unique linear combination of periodic areas within the system. To validate our findings, we use electronic transport measurements to identify the position of these gaps as a function of the carrier density. We establish their agreement with the predicted carrier densities and corresponding quantum numbers obtained using the continuum model. Our study provides strong evidence of the quantization of the momentum-space area of quasi-Brillouin zones in a minimally incommensurate lattice. It fills important gaps in the understanding of band structure engineering of Dirac fermions with a doubly periodic superlattice spinor potential.

Trace Anomaly Redefined in a Convention Leading to the Pontryagin Resolution

It is sought a fundamental reason for the then fore contradictory or randomly correct outcomes. As due the dilemma borne out from the multiple methods for the Pontryagin Chiral Fermions density anomalies resolutions and their either zero or imaginary results. Such is based on extracting the unitarity from a unity-scale diffeomorphic transformation, which is resulted from being a regularization of\(\ \gamma^{0}\).

Majorana chain and Ising model - (non-invertible) translations, anomalies, and emanant symmetries

We study the symmetries of closed Majorana chains in 1+1d, including the translation, fermion parity, spatial parity, and time-reversal symmetries. The algebra of the symmetry operators is realized projectively on the Hilbert space, signaling anomalies on the lattice, and constraining the long-distance behavior. In the special case of the free Hamiltonian (and small deformations thereof), the continuum limit is the 1+1d free Majorana CFT. Its continuum chiral fermion parity (-1)^{F_L}(−1)FL emanates from the lattice translation symmetry. We find a lattice precursor of its mod 8 ’t Hooft anomaly. Using a Jordan-Wigner transformation, we sum over the spin structures of the lattice model (a procedure known as the GSO projection), while carefully tracking the global symmetries. In the resulting bosonic model of Ising spins, the Majorana translation operator leads to a non-invertible lattice translation symmetry at the critical point. The non-invertible Kramers-Wannier duality operator of the continuum Ising CFT emanates from this non-invertible lattice translation of the transverse-field Ising model.

Torsional constitutive relations at finite temperature

The general form of the linear torsional constitutive relations at finite temperature of the chiral current, energy-momentum tensor, and spin energy potential are computed for a chiral fermion fluid minimally coupled to geometric torsion and with nonzero chiral chemical potential. The corresponding transport coefficients are explicitly calculated in terms of the energy and number densities evaluated at vanishing torsion. A microscopic calculation of these constitutive relations in some particular backgrounds is also presented, confirming the general structure found.

Trace anomaly Redefined in a Convention Leading to the Pontryagin Resolution

It is sought a fundamental reasoning for the then fore contradictory or randomly correct outcomes. As due the dilemma borne out from the multiple methods for the Pontryagin Chiral Fermions density anomalies resolutions and their either zero or imaginary results. Such is based on extracting the unitarity from a unity-scale diffeomorphic transformation, which resulted in the being of a \(\gamma^{0}\) regularization.

Trace Anomaly Redefined in a Convention Leading to the Pontryagin Resolution

It is sought a fundamental reason for the then contradictory or randomly correct outcomes, as due to the dilemma borne out from the multiple methods for the Pontryagin Chiral Fermions density anomalies resolutions and their either zero or imaginary results. Such is based on extracting the unitarity from a unity-scale diffeomorphic transformation, which resulted in the being of a\(\ \gamma^{0}\) regularization.

Anomalous Hall Transport by Optically Injected Isospin Degree of Freedom in Dirac Semimetal Thin Film.

Chirality of massless fermions emerging in condensed matter is a key to understand their characteristic behavior as well as to exploit their functionality. However, the chiral nature of massless fermions in Dirac semimetals has remained elusive, due to equivalent occupation of carriers with the opposite chirality in thermal equilibrium. Here, we show that the isospin degree of freedom, which labels the chirality of massless carriers from a crystallographic point of view, can be injected by circularly polarized light. Terahertz Faraday rotation spectroscopy successfully detects the anomalous Hall conductivity by a light-induced isospin polarization in a three-dimensional Dirac semimetal, Cd3As2. Spectral analysis of the Hall conductivity reveals a long scattering time and a long decay time, which are characteristic of the isospin. The long-lived, robust, and reversible character of the isospin promises a potential application of Dirac semimetals in future information technology.

Closing in on new chiral leptons at the LHC

We study the phenomenological viability of chiral extensions of the Standard Model, with new chiral fermions acquiring their mass through interactions with a single Higgs. We examine constraints from electroweak precision tests, Higgs physics and direct searches at the LHC. Our analysis indicates that purely chiral scenarios are perturbatively excluded by the combination of Higgs coupling measurements and LHC direct searches. However, allowing for a partial contribution from vector-like masses opens up the parameter space and non-decoupled exotic leptons could account for the observed 2σ deviation in h → Zγ. This scenario will be further tested in the high-luminosity phase of the LHC.

Chiral Dirac Fermion in a Collinear Antiferromagnet

In a Dirac semimetal, the massless Dirac fermion has zero chirality, leading to surface states connected adiabatically to a topologically trivial surface state as well as vanishing anomalous Hall effect. Recently, it is predicted that in the nonrelativistic limit of certain collinear antiferromagnets, there exists a type of chiral “Dirac-like” fermion, whose dispersion manifests four-fold degenerate crossing points formed by spin-degenerate linear bands, with topologically protected Fermi arcs. Such an unconventional chiral fermion, protected by a hidden SU(2) symmetry in the hierarchy of an enhanced crystallographic group, namely spin space group, is not experimentally verified yet. Here, by angle-resolved photoemission spectroscopy measurements, we reveal the surface origin of the electron pocket at the Fermi surface in collinear antiferromagnet CoNb3S6. Combining with neutron diffraction and first-principles calculations, we suggest a multidomain collinear antiferromagnetic configuration, rendering the the existence of the Fermi-arc surface states induced by chiral Dirac-like fermions. Our work provides spectral evidence of the chiral Dirac-like fermion caused by particular spin symmetry in CoNb3S6, paving an avenue for exploring new emergent phenomena in antiferromagnets with unconventional quasiparticle excitations.

Chiral fermion anomaly as a memory effect

Chiral fermion anomaly as a memory effect

High-pressure induced Weyl semimetal phase in 2D Tellurium

Relativistic Weyl fermion quasiparticles in Weyl semimetal bring the electron’s chirality degree of freedom into the electrical transport and give rise to exotic phenomena. A topological phase transition from a topological trivial phase to a topological non-trivial phase offers a route to control electronic devices through its topological properties. Here, we report the Weyl semimetal phase in hydrothermally grown two-dimensional Tellurium (2D Te) induced by high hydrostatic pressure (up to 2.47 GPa). The unique chiral crystal structure gives rise to chiral fermions with different topological chiral charges ({{C}}=-{{1}},+{{1}},{{and}}-{{2}}). The highly tunable chemical potential in 2D Te provides comprehensive information for understanding the pressure-dependent electron band structure. The pressure-induced insulator-to-metal transition, two-carrier transport, and the non-trivial π Berry phase shift in quantum oscillations are observed in the 2D Te Weyl semimetal phase. Our work demonstrates the pressure-induced bandgap closing in the inversion asymmetric narrow bandgap semiconductor 2D Te.

Monopole-like orbital-momentum locking and the induced orbital transport in topological chiral semimetals.

The interplay between chirality and topology nurtures many exotic electronic properties. For instance, topological chiral semimetals display multifold chiral fermions that manifest nontrivial topological charge and spin texture. They are an ideal playground for exploring chirality-driven exotic physical phenomena. In this work, we reveal a monopole-like orbital-momentum locking texture on the three-dimensional Fermi surfaces of topological chiral semimetals with B20 structures (e.g., RhSi and PdGa). This orbital texture enables a large orbital Hall effect (OHE) and a giant orbital magnetoelectric (OME) effect in the presence of current flow. Different enantiomers exhibit the same OHE which can be converted to the spin Hall effect by spin-orbit coupling in materials. In contrast, the OME effect is chirality-dependent and much larger than its spin counterpart. Our work reveals the crucial role of orbital texture for understanding OHE and OME effects in topological chiral semimetals and paves the path for applications in orbitronics, spintronics, and enantiomer recognition.

Plane vortex pairs, colorful structures and low-lying Dirac modes

In this paper, we investigate the influence of topological charges on nonstable zero and near-zero modes of the single uni-color plane vortex pairs. We combine the uni-color plane vortices with the spherical vortex and also construct the plane vortex pairs with two colorful vortices. The stability of zero and near-zero modes is analyzed where various boundary conditions for the fermions are checked. In addition, plane vortex pairs may show the role of the topological charges for changing the chirality of fermions. The results clearly indicate characteristic properties for spontaneous chiral symmetry breaking.

The universal one-loop effective action with gravity

We complete the so-called Universal One-Loop Effective Action (UOLEA) with effects of gravity and provide a systematic approach to incorporate higher dimensional operators in curved spacetime. The functional determinant stemming from the path integral is computed using the Covariant Derivative Expansion (CDE), in a momentum representation that does not rely on a specific choice of coordinate to be defined, as it often is. This efficient approach manifests an interesting novelty as it allows to integrate out chiral fermions in curved spacetime in a direct manner leading to new operators involving the curvature, and provides a new alternative to the use of Feynman diagrams in that regard. The method presented would very well fit in a code that performs CDE, offering the possibility to integrate out at one-loop fields on a curved spacetime background, including spin-2 fields, like the graviton. Eventually these results should provide an interesting way to study low energy effects of UV completions of gravity.

Synthetic complex Weyl superconductors, chiral Josephson effect and synthetic half-vortices

We show that the most generic form of spin-singlet superconducting order parameter for chiral fermions in systems with broken time reversal symmetry and inversion symmetry is of the Delta _s+igamma ^5Delta _5 where Delta _s is the usual order parameter and Delta _5 is the pseudo-scalar order parameter. After factoring out the U(1) phase e^{iphi }, this form of superconductivity admits yet additional complex structure in the plane of (Delta _s,Delta _5). The polar angle chi in this plane, which we call the chiral angle, can be controlled by the external flux bias. We present a synthetic setup based on stacking of topological insulators (TIs) and superconductors (SCs). Alternatively flux biasing the superconductors with a fluxes pm Phi leads to Delta _5=Delta _0 sin (chi ), where Delta _0 is the superconducting order parameter of the SC layers, and the chiral angle chi ={2pi }Phi /Phi _0 is directly given by the flux Phi in units of the flux quantum Phi _0=h/(2e). This can be used as a building block to construct a two-dimensional Josephson array. In this setup chi will be a background field defining a pseudoscalar Delta _5 that can be tuned to desired configuration. While in a uniform background field Delta _5 the dynamics of phi is given by standard XY model and its associated vortices, a staggered background pm Delta _5 (or equivalently chi and chi +pi in alternating lattice sites) creates a new set of minima for the phi field that will support half-vortex excitations. An isolated single engineered “half-vortex” in the chi field in an otherwise uniform background will bind a phi -half-vortex. This is similar to the way a p-wave superconducting vortex core binds a Majorana fermion.

Topological Circular Dichroism in Chiral Multifold Semimetals.

Uncovering the physical contents of the nontrivial topology of quantum states is a critical problem in condensed matter physics. Here, we study the topological circular dichroism in chiral semimetals using linear response theory and first-principles calculations. We show that, when the low-energy spectrum respects emergent SO(3) rotational symmetry, topological circular dichroism is forbidden for Weyl fermions, and thus is unique to chiral multifold fermions. This is a result of the selection rule that is imposed by the emergent symmetry under the combination of particle-hole conjugation and spatial inversion. Using first-principles calculations, we predict that topological circular dichroism occurs in CoSi for photon energy below about 0.2eV. Our Letter demonstrates the existence of a response property of unconventional fermions that is fundamentally different from the response of Dirac and Weyl fermions, motivating further study to uncover other unique responses.