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Register a new userLightwave Terahertz Quantum Manipulation of Non-equilibrium Superconductor Phases and their Collective Modes
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We present a gauge-invariant density matrix description of non-equilibrium superconductor (SC) states with spatial and temporal correlations driven by intense terahertz (THz) lightwaves. We derive superconductor Bloch--Maxwell equations of motion that extend Anderson pseudo-spin models to include the Cooper pair center-of-mass motion and electromagnetic propagation effects. We thus describe quantum control of dynamical phases, collective modes, quasi-particle coherence, and high nonlinearities during cycles of carrier wave oscillations, which relate to our recent experiments. Coherent photogeneration of a nonlinear supercurrent with dc component via condensate acceleration by an effective lightwave field dynamically breaks the equilibrium inversion symmetry. Experimental signatures include high harmonic light emission at equilibrium-symmetry-forbidden frequencies, Rabi--Higgs collective modes and quasi-particle coherence, and non-equilibrium moving condensate states tuned by few-cycle THz fields. We use such lightwaves as an oscillating accelerating force that drives strong nonlinearities and anisotropic quasi-particle populations to control and amplify different classes of collective modes, e.g., damped oscillations, persistent oscillations, and overdamped dynamics via Rabi flopping. Recent phase-coherent nonlinear spectroscopy experiments can be modeled by solving the full nonlinear quantum dynamics including self-consistent light--matter coupling.
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We theoretically study the low energy electromagnetic response of BCS type superconductors focusing on propagating collective modes that are observable with THz near field optics. The interesting frequency and momentum range is $omega < 2Delta$ and $q < 1/xi$ where $Delta$ is the gap and $xi$ is the coherence length. We show that it is possible to observe the superfluid plasmons, amplitude (Higgs) modes, Bardasis-Schrieffer modes and Carlson-Goldman modes using THz near field technique, although none of these modes couple linearly to far field radiation. Coupling of THz near field radiation to the amplitude mode requires particle-hole symmetry breaking while coupling to the Bardasis-Schrieffer mode does not and is typically stronger. For parameters appropriate to layered superconductors of current interest, the Carlson-Goldman mode appears in the near field reflection coefficient as a weak feature in the sub-THz frequency range. In a system of two superconducting layers with nanometer scale separation, an acoustic phase mode appears as the antisymmetric density fluctuation mode of the system. This mode produces well defined resonance peaks in the near-field THz response and has strong anticrossings with the Bardasis-Schrieffer and amplitude modes, enhancing their response. In a slab consisting of many layers of quasi-two dimensional superconductors, realized for example in samples of high T$_c$ cuprate compounds, many branches of propagating Josephson plasmon modes are found to couple to the THz near field radiation.
Noncollinear magnetism opens exciting possibilities to generate topological superconductivity. Here, we focus on helical and cycloidal magnetic textures in magnet-superconductor hybrid structures in a background magnetic field. We demonstrate that this system can enter a topological phase which can be understood as a set of parallel topological wires. We explore and confirm this idea in depth with three different approaches: a continuum model, a tight-binding model based on the magnetic unit cell, and exact diagonalization on a finite two-dimensional lattice. The key signature of this topological state is the presence of Majorana bound states at certain disclination defects in the magnetic texture. Based on the $C_2$ symmetry imposed by the helical or cycloidal texture, we employ the theory of topological crystalline superconductors with rotation invariants to obtain the Majorana parity at disclinations. Furthermore, we consider a 90-degree helimagnet domain wall, which is formed by a string of alternating disclinations. We discuss how the resulting chain of disclination bound states hybridizes into two chiral modes with different velocities. We suggest that hybrid systems of chiral magnets and superconductors are capable of hosting Majorana modes in various spatial configurations with potentially far less nano-engineering than in, e.g., semiconductor wires.
Collective modes in two dimensional topological superconductors are studied by an extended random phase approximation theory while considering the influence of vector field of light. In two situations, the s-wave superconductors without spin-orbit-coupling (SOC), and the hybrid semiconductor and s-wave superconductor layers with strong SOC, we get the analytical results for longitudinal modes which are found to be indeed gapless. Further more, the effective modes volumes can be calculated, the electric and magnetic fields can be expressed as the creation and annihilation operators of such modes. So, one can study the interaction of them with other quasi-particles through fields.
We study Majorana zero energy modes (MZEM) that occur in a s-wave superconducting surface, at the ends of a ferromagnetic (FM) chain of adatoms, in the presence of Rashba spin-orbit interaction (SOI) considering both non self-consistent and self-consistent superconducting order. We find that in the self-consistent solution the average superconducting gap function over the adatom sites has a discontinuous drop with increasing exchange interaction at the same critical value where the topological phase transition occurs. We also study the MZEM for both treatments of superconducting order and find that the decay length is a linear function of the exchange coupling strength, chemical potential and superconducting order. For wider FM chains the MZEM occur at smaller exchange couplings and the slope of the decay length as a function of exchange coupling grows with chain width. Thus we suggest experimental detection of different delocalization of MZEM in chains of varying widths. We discuss similarities and differences between the MZEM for the two treatments of the superconducting order.
In physical systems, coupling to the environment gives rise to dissipation and decoherence. For nanoscopic materials this may be a determining factor of their physical behavior. However, even for macroscopic many-body systems, if the strength of this coupling is sufficiently strong, their ground state properties and phase diagram may be severely modified. Also dissipation is essential to allow a system in the presence of a time dependent perturbation to attain a steady, time independent state. In this case, the non-equilibrium phase diagram depends on the intensity of the perturbation and on the strength of the coupling of the system to the outside world. In this paper, we investigate the effects of both, dissipation and time dependent external sources in the phase diagram of a many-body system at zero and finite temperatures. For concreteness we consider the specific case of a superconducting layer under the action of an electric field and coupled to a metallic substrate. The former arises from a time dependent vector potential minimally coupled to the electrons in the layer. We introduce a Keldysh approach that allows to obtain the time dependence of the superconducting order parameter in an adiabatic regime. We study the phase diagram of this system as a function of the electric field, the coupling to the metallic substrate and temperature.
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