The chiral anomaly in real space

The chiral anomaly is based on a non-conserved chiral charge and can happen in Dirac fermion systems under the influence of external electromagnetic fields. In this case, the spectral flow leads to a transfer of right- to left-moving excitations or vice versa. The corresponding transfer of chiral particles happens in momentum space. We here describe an intriguing way to introduce the chiral anomaly into real space. Our system consists of two quantum dots that are formed at the helical edge of a quantum spin Hall insulator on the basis of three magnetic impurities. Such a setup gives rise to fractional charges which we show to be sharp quantum numbers for large barrier strength. Interestingly, it is possible to map the system onto a quantum spin Hall ring in the presence of a flux pierced through the ring where the relative angle between the magnetization directions of the impurities takes the role of the flux. The chiral anomaly in this system is then directly related to the excess occupation of particles in the two quantum dots. This analogy allows us to predict an observable consequence of the chiral anomaly in real space.Comment: 7 pages, 5 figure

Effects of the Vertices on the Topological Bound States in a Quasicrystalline Topological Insulator

The experimental realization of twisted bilayer graphene strongly pushed the inspection of bilayer systems. In this context, it was recently shown that a two layer Haldane model with a thirty degree rotation angle between the layers represents a higher order topological insulator, with zero-dimensional states isolated in energy and localized at the physical vertices of the nanostructure. We show, within a numerical tight binding approach, that the energy of the zero dimensional states strongly depends on the geometrical structure of the vertices. In the most extreme cases, once a specific band gap is considered, these bound states can even disappear just by changing the vertex structure.Comment: 12 pages, 6 figures, published on Symmetr

An exact local mapping from clock-spins to fermions

Clock-spin models are attracting great interest, due to both their rich phase diagram and their connection to parafermions. In this context, we derive an exact local mapping from clock-spin to fermionic partition functions. Such mapping, akin to techniques introduced by Fedotov and Popov for spin $\frac{1}{2}$ chains, grants access to well established numerical tools for the perturbative treatment of fermionic systems in the clock-spin framework. Moreover, in one dimension, it allows to use bosonization to access the low energy properties of clock-spin models. Finally, aside from the direct application in clock-spin models, this new mapping enables the conception of interesting fermionic models, based on the clock-spin counterparts.Comment: 26 pages, 0 figures, Submission to SciPos

Coulomb blockade microscopy of spin density oscillations and fractional charge in quantum spin Hall dots

We evaluate the spin density oscillations arising in quantum spin Hall quantum dots created via two localized magnetic barriers. The combined presence of magnetic barriers and spin-momentum locking, the hallmark of topological insulators, leads to peculiar phenomena: a half-integer charge is trapped in the dot for antiparallel magnetization of the barriers, and oscillations appear in the in-plane spin density, which are enhanced in the presence of electron interactions. Furthermore, we show that the number of these oscillations is determined by the number of particles inside the dot, so that the presence or the absence of the fractional charge can be deduced from the in-plane spin density. We show that when the dot is coupled with a magnetized tip, the spatial shift induced in the chemical potential allows to probe these peculiar features.Comment: 6 pages, 6 figure

Reconstruction-Induced φ0\varphi_0 Josephson Effect in Quantum Spin Hall Constrictions

The simultaneous breaking of time-reversal and inversion symmetry, in connection to superconductivity, leads to transport properties with disrupting scientific and technological potential. Indeed, the anomalous Josephson effect and the superconducting-diode effect hold promises to enlarge the technological applications of superconductors and nanostructures in general. In this context, the system we theoretically analyze is a Josephson junction (JJ) with coupled reconstructed topological channels as a link; such channels are at the edges of a two-dimensional topological insulator (2DTI). We find a robust $\varphi_0$ Josephson effect without requiring the presence of external magnetic fields. Our results, which rely on a fully analytical analysis, are substantiated by means of symmetry arguments: Our system breaks both time-reversal symmetry and inversion symmetry. Moreover, the anomalous current increases as a function of temperature. We interpret this surprising temperature dependence by means of simple qualitative arguments based on Fermi's golden rule.Comment: 13 pages, 3 figure

Effects of the Vertices on the Topological Bound States in a Quasicrystalline Topological Insulator

The experimental realization of twisted bilayer graphene strongly pushed the inspection of bilayer systems. In this context, it was recently shown that a two layer Haldane model with a thirty degree rotation angle between the layers represents a higher order topological insulator, with zero-dimensional states isolated in energy and localized at the physical vertices of the nanostructure. We show, within a numerical tight binding approach, that the energy of the zero dimensional states strongly depends on the geometrical structure of the vertices. In the most extreme cases, once a specific band gap is considered, these bound states can even disappear just by changing the vertex structure

An exact local mapping from clock-spins to fermions

Clock-spin models are attracting great interest, due to both their rich phase diagram and their connection to parafermions. In this context, we derive an exact local mapping from clock-spin to fermionic partition functions. Such mapping, akin to techniques introduced by Fedotov and Popov for spin $\frac{1}{2}$ chains, grants access to well established numerical tools for the perturbative treatment of fermionic systems in the clock-spin framework. Moreover, in one dimension, it allows to use bosonization to access the low energy properties of clock-spin models. Finally, aside from the direct application in clock-spin models, this new mapping enables the conception of interesting fermionic models, based on the clock-spin counterparts

New Directions in the Physics of One-dimensional Electron Systems

This volume is devoted to the latest developments in the physics of electrons in one-dimensional condensed matter systems. Particular attention is devoted to spin-orbit coupling and its consequences, that range from topological edge and bound states to the identification of possible host systems for odd frequency superconductivity. The possibility of using the methods of one-dimensional physics to describe higher dimensional correlated system is also addressed. The non-equilibrium properties are then inspected under different points of view: Generating states on demand, using such states for caloritronics, mimicking non-equilibrium properties on one-dimensional systems with quantum circuits. Our hope is that this volume could be beneficial and entertaining to both specialists and non-specialists in field

Parity-Dependent Quantum Phase Transition in the Quantum Ising Chain in a Transverse Field

Phase transitions—both classical and quantum types—are the perfect playground for appreciating universality at work. Indeed, the fine details become unimportant and a classification in very few universality classes is possible. Very recently, a striking deviation from this picture has been discovered: some antiferromagnetic spin chains with competing interactions show a different set of phase transitions depending on the parity of number of spins in the chain. The aim of this article is to demonstrate that the same behavior also characterizes the most simple quantum spin chain: the Ising model in a transverse field. By means of an exact solution based on a Wigner–Jordan transformation, we show that a first-order quantum phase transition appears at the zero applied field in the odd spin case, while it is not present in the even case. A hint of a possible physical interpretation is given by the combination of two facts: at the point of the phase transition, the degeneracy of the ground state in the even and the odd case substantially differs, being respectively 2 and 2N, with N being the number of spins; the spin of the most favorable kink shows changes at that point

Parity-Dependent Quantum Phase Transition in the Quantum Ising Chain in a Transverse Field

Phase transitions—both classical and quantum types—are the perfect playground for appreciating universality at work. Indeed, the fine details become unimportant and a classification in very few universality classes is possible. Very recently, a striking deviation from this picture has been discovered: some antiferromagnetic spin chains with competing interactions show a different set of phase transitions depending on the parity of number of spins in the chain. The aim of this article is to demonstrate that the same behavior also characterizes the most simple quantum spin chain: the Ising model in a transverse field. By means of an exact solution based on a Wigner–Jordan transformation, we show that a first-order quantum phase transition appears at the zero applied field in the odd spin case, while it is not present in the even case. A hint of a possible physical interpretation is given by the combination of two facts: at the point of the phase transition, the degeneracy of the ground state in the even and the odd case substantially differs, being respectively 2 and 2N, with N being the number of spins; the spin of the most favorable kink shows changes at that point