The magnetoresistance and Hall coefficient of a doped graphene layer are investigated in the presence of a tilted magnetic field. We consider a graphene layer assembled by either another graphene layer or by a two-dimensional electron gas (2DEG) layer and with the interlayer electron-electron interaction modeled within the random phase approximation. Our calculated magnetoresistances show different interlayer screening effects between decoupled graphene-graphene and graphene-2DEG systems. We also analyze the dependence of dielectric materials as well as the distance between the layers on magnetoresistances. The angle dependence of the Hall coefficient is studied and we show that a quite large Hall resistivity occurs in the graphene layer.
We study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in the presence of spin polarized two-dimensional Dirac fermions. We show that an externally applied spin polarization along the $z$ axis mediates an anisotropic interaction which corresponds to an $XXZ$ model interaction between two magnetic moments. For undoped graphene, while the $x$ part of interaction keeps its constant ferromagnetic sign, its $z$ part oscillates with the distance $R$ of magnetic impurities. A finite doping causes both parts of the interaction to oscillate with $R$. We explore a beating pattern of oscillations of the RKKY interaction along armchair and zigzag lattice directions, which occurs for some certain values of the chemical potential. The two characteristic periods of the beating are determined by inverse of the difference and the sum of the chemical potential and the spin polarization.
We study time-reversal-invariant topological superconductivity in topological insulator (TI) thin films including both intra- and inter-surface pairing. We find a nontrivial topology for multiple different configurations. For intra-surface pairing a $\pi$-phase difference between the intra-surface pairing states is required. We show that in this case the resulting topological phase is highly tunable by both an applied electric field and varied chemical potential. For spin-singlet inter-surface pairing, a sign-changing tunnel coupling present in many TI thin films is needed, and again, the topology can be tuned by electric field or doping. Notably, we find that the required inter-surface pairing strength for achieving nontrivial topology can still be subdominant compared to the intra-surface pairing. Finally, for spin-triplet inter-surface pairing we prove that the superconducting state is always topological nontrivial. We show that thin films of Cu-doped Bi$_2$Se$_3$ will likely host such spin-triplet inter-surface pairing. Taken together, these results show that time-reversal-invariant topological superconductivity is common in superconducting TI thin films and that the topological phase and its Kramers pair of Majorana edge modes is highly tunable with an applied electric field and varied chemical potential.
Magnetic Weyl semimetals (WSMs) have been presumed to be immune to proximity-induced spin-singlet superconducting pairing due to a chirality blockade of the regular Andreev reflection. In this work, we study all possible superconducting pairing induced in a WSM sandwiched between two conventional superconductors in a Josephson junction setup. We confirm that, while conventional intraorbital $s\ensuremath{-}\mathrm{wave}$ pairing is present on the surface of the WSM, it cannot propagate into the bulk due to the chirality blockade. However, interorbital $s\ensuremath{-}\mathrm{wave}$ pairing, with both even-frequency spin-singlet and odd-frequency mixed-spin-triplet symmetry, propagates into the bulk of the WSM, as do several $p\ensuremath{-}\mathrm{wave}$ symmetries. To demonstrate the importance of these finite interorbital and $p\ensuremath{-}\mathrm{wave}$ pair amplitudes in an experimental setup, we calculate the Josephson current and find a finite and even increasing current when the chirality blockade effect for the conventional intraorbital pairing is enhanced.
The Meissner effect is one of the defining properties of superconductivity, with a conventional superconductor completely repelling an external magnetic field. In contrast to this diamagnetic behavior, odd-frequency superconducting pairing has often been seen to produce a paramagnetic Meissner effect, which instead makes the superconductor unstable due to the attraction of magnetic field. In this paper, we study how both even- and odd-frequency superconducting pairing contributes to the Meissner effect in a generic two-orbital superconductor with a tunable odd-frequency pairing component. By dividing the contributions to the Meissner effect into intra- and interband processes, we find that the odd-frequency pairing actually generates both dia- and paramagnetic Meissner responses, determined by the normal-state band structure. More specifically, for materials with two electronlike (holelike) low-energy bands, we find that the odd-frequency interband contribution is paramagnetic but nearly canceled by a diamagnetic odd-frequency intraband contribution. Combined with a diamagnetic even-frequency contribution, such superconductors thus always display a large diamagnetic Meissner response to an external magnetic field, even in the presence of large odd-frequency pairing. For materials with an inverted, or topological, band structure, we find the odd-frequency interband contribution to instead be diamagnetic and even the dominating contribution to the Meissner effect in the near-metallic regime. Taken together, our results show that odd-frequency pairing in multiorbital superconductors does not generate a destabilizing paramagnetic Meissner effect and can even generate a diamagnetic response in topological materials.
We study the Ruderman-Kittle-Kasuya-Yosida (RKKY) interaction in a monolayer MoS${}_{2}$. We show that the rotation of the itinerant electron spin due to the spin-orbit coupling causes a twisted interaction between two magnetic adatoms, which consists of different RKKY coupling terms: the Heisenberg, Dzyaloshinsky-Moriya, and Ising interactions. We find that the interaction terms are very sensitive to the Fermi energy values and change dramatically from doped to undoped systems. A finite doping causes all parts of the interaction to oscillate with the distance of two magnetic impurities $R$, and the interaction behaves like ${R}^{\ensuremath{-}2}$ for a long distance between two localized spins. We explore a beating pattern of oscillations of the RKKY interaction that occurs for the doped system.
We investigate the optical properties of ultrathin film of a topological insulator in the presence of an in-plane magnetic field. We show that due to the combination of the overlap between the surface states of the two layers and the magnetic field, the optical conductivity can show strong anisotropy. This leads to the effective optical activity of the ultrathin film by influencing the circularly polarized incident light. Intriguingly, for a range of magnetic fields, the reflected and transmitted lights exhibit elliptic character. Even for certain values almost linear polarizations are obtained, indicating that the thin film can act as a polaroid in reflection. All these features are discussed in the context of the time-reversal symmetry breaking as one of the key ingredients for the optical activity.
The possible symmetries of the superconducting pair amplitude is a consequence of the fermionic nature of the Cooper pairs. For spin-$1/2$ systems this leads to the $\mathcal{SPOT}=-1$ classification of superconductivity, where $\mathcal{S}$, $\mathcal{P}$, $\mathcal{O}$, and $\mathcal{T}$ refer to the exchange operators for spin, parity, orbital, and time between the paired electrons. However, this classification no longer holds for higher spin fermions, where each electron also possesses a finite orbital angular momentum strongly coupled with the spin degree of freedom, giving instead a conserved total angular moment. For such systems, we here instead introduce the $\mathcal{JPT}=-1$ classification, where $\mathcal{J}$ is the exchange operator for the $z$-component of the total angular momentum quantum numbers. We then specifically focus on spin-$3/2$ fermion systems and several superconducting cubic half-Heusler compounds that have recently been proposed to be spin-$3/2$ superconductors. By using a generic Hamiltonian suitable for these compounds we calculate the superconducting pair amplitudes and find finite pair amplitudes for all possible symmetries obeying the $\mathcal{JPT}=-1$ classification, including all possible odd-frequency (odd-$\omega$) combinations. Moreover, one of the very interesting properties of spin-$3/2$ superconductors is the possibility of them hosting a Bogoliubov Fermi surface (BFS), where the superconducting energy gap is closed across a finite area. We show that a spin-$3/2$ superconductor with a pair potential satisfying an odd-gap time-reversal product and being non-commuting with the normal-state Hamiltonian hosts both a BFS and has finite odd-$\omega$ pair amplitudes. We then reduce the full spin-$3/2$ Hamiltonian to an effective two-band model and show that odd-$\omega$ pairing is inevitably present in superconductors with a BFS and vice versa.
We investigate the impact of topology on the existence of impurity subgap states in a time-reversal-invariant superconductor with an extended $s$-wave pairing and strong spin-orbit coupling. By simply tuning the chemical potential, we access three distinct phases: topologically trivial $s$-wave, topologically nontrivial ${s}_{\ifmmode\pm\else\textpm\fi{}}$-wave, and nodal superconducting phase. For a single potential impurity, we find subgap impurity bound states in the topological phase, but notably no subgap states in the trivial phase. This is in sharp contrast with the expectation that there would be no subgap state in the presence of potential impurities in $s$-wave superconductors. These subgap impurity states have always finite energies for any strength of the potential scattering and, subsequently, the superconducting gap in the topological ${s}_{\ifmmode\pm\else\textpm\fi{}}$-wave phase survives but is attenuated in the presence of finite disorder. By creating islands of potential impurities, we smoothly connect the single impurity results to topological edge states of impurity islands. On the other hand, magnetic impurities lead to the formation of Yu-Shiba-Rusinov states in both the trivial and topological phases, which even reach zero energy at certain scattering strengths. We thus propose that potential impurities can be a very valuable tool to detect time-reversal-invariant topological superconductivity.
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