Carbon nanotubes in electric and magnetic fields

We derive an effective low-energy theory for metallic (armchair and non-armchair) single-wall nanotubes in the presence of an electric field perpendicular to the nanotube axis, and in the presence of magnetic fields, taking into account spin-orbit interactions and screening effects on the basis of a microscopic tight binding model. The interplay between electric field and spin-orbit interaction allows us to tune armchair nanotubes into a helical conductor in both Dirac valleys. Metallic non-armchair nanotubes are gapped by the surface curvature, yet helical conduction modes can be restored in one of the valleys by a magnetic field along the nanotube axis. Furthermore, we discuss electric dipole spin resonance in carbon nanotubes, and find that the Rabi frequency shows a pronounced dependence on the momentum along the nanotube

Helical modes in carbon nanotubes generated by strong electric fields

Helical modes, conducting opposite spins in opposite directions, are shown to exist in metallic armchair nanotubes in an all-electric setup. This is a consequence of the interplay between spin-orbit interaction and strong electric fields. The helical regime can also be obtained in chiral metallic nanotubes by applying an additional magnetic field. In particular, it is possible to obtain helical modes at one of the two Dirac points only, while the other one remains gapped. Starting from a tight-binding model we derive the effective low-energy Hamiltonian and the resulting spectrum

Topological Floquet Phases in Driven Coupled Rashba Nanowires

We consider periodically driven arrays of weakly coupled wires with conduction and valence bands of Rashba type and study the resulting Floquet states. This nonequilibrium system can be tuned into nontrivial phases such as topological insulators, Weyl semimetals, and dispersionless zero-energy edge mode regimes. In the presence of strong electron-electron interactions, we generalize these regimes to the fractional case, where elementary excitations have fractional charges e/m with m being an odd integer

Topological phases of inhomogeneous superconductivity

We theoretically consider the effect of a spatially periodic modulation of the superconducting order parameter on the formation of Majorana fermions induced by a one-dimensional system with magnetic impurities brought into close proximity to an s-wave superconductor. When the magnetic exchange energy is larger than the inter-impurity electron hopping we model the effective system as a chain of coupled Shiba states, while in the opposite regime, the effective system is accurately described by a quantum wire model. Upon including a spatially modulated superconducting pairing, we find, for sufficiently large magnetic exchange energy, that the system is able to support a single pair of Majorana fermions with one Majorana fermion on the left end of the system and one on the right end. When the modulation of superconductivity is large compared to the magnetic exchange energy, the Shiba chain returns to a trivially gapped regime while the quantum wire enters a new topological phase capable of supporting two pairs of Majorana fermions

Chiral and nonchiral edge states in quantum Hall systems with charge density modulation

We consider a system of weakly coupled wires with quantum Hall effect (QHE) and in the presence of a spatially periodic modulation of the chemical potential along the wire, equivalent to a charge density wave (CDW). We investigate the competition between the two effects which both open a gap. We show that by changing the ratio between the amplitudes of the CDW modulation and the tunneling between wires, one can switch between nontopological CDW-dominated phase to topological QHE-dominated phase. Both phases host edge states of chiral and nonchiral nature robust to on-site disorder. However, only in the topological phase, the edge states are immune to disorder in the phase shifts of the CDWs. We provide analytical solutions for filling factor nu = 1 and study numerically effects of disorder as well as present numerical results for higher filling factors

From coupled Rashba electron- and hole-gas layers to three-dimensional topological insulators

We introduce a system of stacked two-dimensional electron-and hole-gas layers with Rashba spin-orbit interaction and show that the tunnel coupling between the layers induces a strong three-dimensional (3D) topological insulator phase. At each of the two-dimensional bulk boundaries we find the spectrum consisting of a single anisotropic Dirac cone, which we show by analytical and numerical calculations. Our setup has a unit cell consisting of four tunnel coupled Rashba layers and presents a synthetic strong 3D topological insulator and is distinguished by its rather high experimental feasibility

Dimensional reduction of the Luttinger-Ward functional for spin-degenerate DD-dimensional electron gases

We consider an isotropic spin-degenerate interacting uniform $D$-dimensional electron gas (DDEG) with $D > 1$ within the Luttinger-Ward (LW) formalism. We derive the asymptotically exact semiclassical/infrared limit of the LW functional at large distances, $r \gg \lambda_F$, and large times, $\tau \gg 1/E_F$, where $\lambda_F$ and $E_F$ are the Fermi wavelength and the Fermi energy, respectively. The LW functional is represented by skeleton diagrams, each skeleton diagram consists of appropriately connected dressed fermion loops. First, we prove that every $D$-dimensional skeleton diagram consisting of a single fermion loop is reduced to a one-dimensional (1D) fermion loop with the same diagrammatic structure, which justifies the name dimensional reduction. This statement, combined with the fermion loop cancellation theorem (FLCT), agrees with results of multidimensional bosonization. Here we show that the backscattering and the spectral curvature, both explicitly violate the FLCT and both are irrelevant for a 1DEG, become relevant at $D > 1$ and $D > 2$, respectively. The reason for this is a strong infrared divergence of the skeleton diagrams containing multiple fermion loops at $D > 1$. These diagrams, which are omitted within the multidimensional bosonization approaches, account for the non-collinear scattering processes. Thus, the dimensional reduction provides the framework to go beyond predictions of the multidimensional bosonization. A simple diagrammatic structure of the reduced LW functional is another advantage of our approach. The dimensional reduction technique is also applicable to the thermodynamic potential and various approximations, from perturbation theory to self-consistent approaches.Comment: 15 pages, 4 figure

Entangling Spins in Double Quantum Dots and Majorana Bound States

We study the coupling between a singlet-triplet qubit realized in a double quantum dot to a topological qubit realized by spatially well-separated Majorana bound states. We demonstrate that the singlet-triplet qubit can be leveraged for readout of the topological qubit and for supplementing the gate operations that cannot be performed by braiding of Majorana bound states. Furthermore, we extend our setup to a network of singlet-triplet and topological hybrid qubits that paves the way to scalable fault-tolerant quantum computing

RKKY interaction in one-dimensional flat band lattices

We study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two classical magnetic impurities in one-dimensional lattice models with flat bands. As two representative examples, we pick the stub lattice and the diamond lattice at half filling. We first calculate the exact RKKY interaction numerically and then compare our data to results obtained via different analytical techniques. In both our examples, we find that the RKKY interaction exhibits peculiar features that can directly be traced back to the presence of a flat band. Importantly, these features are not captured by the conventional RKKY approximation based on non-degenerate perturbation theory. Instead, we find that degenerate perturbation theory correctly reproduces our exact results if there is an energy gap between the flat and the dispersive bands, while a non-perturbative approach becomes necessary in the absence of a gap

From Andreev to Majorana bound states in hybrid superconductor-semiconductor nanowires

Electronic excitations above the ground state must overcome an energy gap in superconductors with spatially-homogeneous s-wave pairing. In contrast, inhomogeneous superconductors such as those with magnetic impurities or weak links, or heterojunctions containing normal metals or quantum dots, can host subgap electronic excitations that are generically known as Andreev bound states (ABSs). With the advent of topological superconductivity, a new kind of ABS with exotic qualities, known as Majorana bound state (MBS), has been discovered. We review the main properties of ABSs and MBSs, and the state-of-the-art techniques for their detection. We focus on hybrid superconductor-semiconductor nanowires, possibly coupled to quantum dots, as one of the most flexible and promising experimental platforms. We discuss how the combined effect of spin-orbit coupling and Zeeman field in these wires triggers the transition from ABSs into MBSs. We show theoretical progress beyond minimal models in understanding experiments, including the possibility of different types of robust zero modes that may emerge without a band-topological transition. We examine the role of spatial non-locality, a special property of MBS wavefunctions that, together with non-Abelian braiding, is the key to realizing topological quantum computation.Comment: Review. 23 pages, 8 figures, 1 table. Shareable published version by Springer Nature at https://rdcu.be/b7DWT (free to read but not to download