Dynamical perturbations modify the states of classical systems in surprising ways and give rise to important applications in science and technology. For example, Floquet engineering exploits the possibility of band formation in the frequency domain when a strong, periodic variation is imposed on parameters such as spring constants. We describe here Kapitza engineering, where a drive field oscillating at a frequency much higher than the characteristic frequencies for the linear response of a system changes the potential energy surface so much that maxima found at equilibrium become local minima, in precise analogy to the celebrated Kapitza pendulum where the unstable inverted configuration, with the mass above rather than below the fulcrum, actually becomes stable. Our starting point is a quantum field theory of the Ginzburg-Devonshire type, suitable for many condensed matter systems, including particularly ferroelectrics and quantum paralectrics. We show that an off-resonance oscillatory electric field generated by a laser-driven terahertz source can induce ferroelectric order in the quantum-critical limit. Heating effects are estimated to be manageable using pulsed radiation; "hidden"radiation-induced order can persist to low temperatures without further pumping due to stabilization by strain. We estimate the Ginzburg-Devonshire free-energy coefficients in SrTiO3 using density-functional theory and the stochastic self-consistent harmonic approximation accelerated by a machine-learned force field. Although we find that SrTiO3 is not an optimal choice for Kapitza stabilization, we show that scanning for further candidate materials can be performed at the computationally convenient density-functional theory level. We suggest second harmonic generation, soft-mode spectroscopy, and x-ray diffraction experiments to characterize the induced order.

Superconductivity and magnetism are competing effects that can coexist in certain regimes. Their co-existence leads to unexpected new behaviors that include the onset of exotic electron pair mechanisms and topological phases. In this work, we study the properties of a Josephson junction between two spin-split superconductors. The spin-splitting in the superconductors can arise from either the coupling to a ferromagnetic material or an external magnetic field. The properties of the junction are dominated by the Andreev bound states that are also split. One of these states can cross the superconductor’s Fermi level, leading to a ground-state transition characterized by a suppressed supercurrent. We interpret the supercurrent blockade as coming from a dominance of p-wave pairing close to the junction, where the electrons are at both sides. To support this interpretation, we analyze the different pairing channels and show that p-wave pairing is favored in the case where the magnetization of the two superconductors is parallel and suppressed in the anti-parallel case. We also analyze the noise spectrum that shows signatures of the ground-state transition in the form of an elevated zero-frequency noise.

Josephson junctions have broad applications in metrology, quantum information processing, and remote sensing. For these applications, the electronic noise is a limiting factor. In this work we study the thermal noise in narrow Josephson junctions using a tight-binding Hamiltonian. For a junction longer than the superconducting coherence length, several self-consistent gap profiles appear close to a phase difference π. They correspond to two stable solutions with an approximately constant phase gradient over the thin superconductor connected by a 2π phase slip, and a solitonic branch. The current noise power spectrum has pronounced peaks at the transition frequencies between the different states in each branch. We find that the noise is reduced in the gradient branches in comparison to the zero-length junction limit. In contrast, the solitonic branch exhibits an enhanced noise and a reduced current due to the pinning of the lowest excitation energy to close to zero energy.

The most promising mechanisms for the formation of Majorana bound states (MBSs) in condensed matter systems involve one-dimensional systems [such as semiconductor nanowires, magnetic chains, and quantum spin Hall insulator (QSHI) edges] proximitized to superconducting materials. The choice between each of these options involves tradeoffs between several factors such as reproducibility of results, system tunability, and robustness of the resulting MBS. In this paper, we propose that a combination of two of these systems, namely, a magnetic chain deposited on a QSHI edge in contact with a superconducting surface, offers a better choice of tunability and MBS robustness compared to magnetic chain deposited on bulk. We study how the QSHI edge interacts with the magnetic chain, and see how the topological phase is affected by edge proximity. We show that MBSs near the edge can be realized with lower chemical potential and Zeeman field than the ones inside the bulk, independently of the chain's magnetic order (ferromagnetic or spiral order). Different magnetic orderings in the chain modify the overall phase diagram, even suppressing the boundless topological phase found in the bulk for chains located at the QSHI edge. Moreover, we quantify the quality of MBSs by calculating the Majorana polarization (MP) for different configurations. For chains located at the edge, the MP is close to its maximum value already for short chains. For chains located away from the edge, longer chains are needed to attain the same quality as chains located at the edge. The MP also oscillates in phase with the in-gap states, which is relatively unexpected as peaks in the energy spectrum correspond to stronger overlap of MBSs.

We demonstrate that SrTiO3 can be a platform for observing the bulk odd-frequency superconducting state owing to its multiorbital/multiband nature. We consider a three-orbital tight-binding model for SrTiO3 in the vicinity of a ferroelectric critical point. Assuming an intraorbital spin-singlet s-wave superconducting order parameter, it is shown that the odd-frequency pair correlations are generated due to the intrinsic LS coupling which leads to local orbital mixing. Furthermore, we show the existence of additional odd-frequency pair correlations in the ferroelectric phase, which is induced by an odd-parity orbital hybridization term proportional to the ferroelectric order parameter. We also perform a group theoretical classification of the odd-frequency pair amplitudes based on the fermionic and space group symmetries of the system. The classification table enables us to predict the dominant components of the odd-frequency pair correlations based on the symmetry of the normal state Hamiltonian that we take into account. Furthermore, we show that experimental signatures of odd-parity orbital hybridization, which is an essential ingredient for ferroelectricity-induced odd-frequency pair correlations, can be observed in the spectral functions and density of states.

Superconductor-ferromagnetic heterostructures have been suggested as one of the most promising alternatives of realizing odd-frequency superconductivity. In this work we consider the limit of shrinking the ferromagnetic region to the limit of a single impurity embedded in a conventional superconductor, which gives rise to localized Yu-Shiba-Rusinov (YSR) bound states with energies inside the superconducting gap. We demonstrate that all the sufficient ingredients for generating odd-frequency pairing are present at the vicinity of these impurities. We investigate the appearance of all possible pair amplitudes in accordance with the Berezinskii SP* OT * = -1 rule, with the symmetry under the exchange of spin, spatial, orbital (in our case O = +1), and time index, respectively. We study the spatial and frequency dependence of the possible pairing amplitudes, analyzing their evolution with impurity strength and identifying a reciprocity between different symmetries related through impurity scattering. We show that the odd-frequency spin-triplet pairing amplitude dominates at the critical impurity strength, where the YSR states merge at the middle of the gap, while the even components are quenched close to the impurity. We also show that the spin-polarized local density of states exhibits the same spatial and frequency behavior as the odd-co spin-triplet component at the critical impurity strength.

Odd-frequency (odd−ω) electron pair correlations naturally appear at the interface between BCS superconductors and other materials. The detection of odd−ω pairs, which are necessarily nonlocal in time, is still an open problem. The main reason is that they do not contribute to static measurements described by time-local correlation functions. Therefore, dynamical measurements, which depend on nonlocal time correlations, are suitable for detecting these pairs. In this work, we study the signatures of odd−ω pairs in the supercurrent noise through a weak link between two superconductors at different superconducting phases. We show that the finite-frequency current noise can be decomposed into three different contributions coming from even-frequency (even−ω), odd−ω pair amplitudes, and electron-hole correlation functions. Odd−ω pairing, which is interlead (between electrons at different sides of the junction), provides a positive contribution to the noise, becoming maximal at a superconducting phase difference of π. In contrast, intralead even−ω pair amplitude tends to reduce the noise, except for a region close to π controlled by the transmission of the junction.

Odd-frequency superconductivity is an exotic phase of matter in which Cooper pairing between electrons is entirely dynamical in nature. Majorana zero modes exhibit pure odd-frequency superconducting correlations due to their specific properties. Thus, by tunnel-coupling an array of Majorana zero modes to a spin-polarized wire, it is in principle possible to engineer a bulk one-dimensional odd-frequency spinless s-wave superconductor. We point out here that each tunnel coupling element, being dependent on a large number of material-specific parameters, is generically complex with sample variability in both its magnitude and phase. Using this, we demonstrate that, upon averaging over phase disorder, the induced superconducting, including odd-frequency, correlations in the spin-polarized wire are significantly suppressed. We perform both a rigorous analytical evaluation of the disorder-averaged T matrix in the wire, as well as numerical calculations based on a tight-binding model, and find that the anomalous, i.e., superconducting, part of the T matrix is highly suppressed with phase disorder. We also demonstrate that this suppression is concurrent with the filling of the single-particle excitation gap by smearing the near-zero-frequency peaks, due to formation of bound states that satisfy phase-matching conditions between spatially separated Majorana zero modes. Our results convey important constraints on the parameter control needed in practical realizations of Majorana zero mode structures and suggest that the achievement of a bulk one-dimensional odd-omega superconductivity from Majorana zero modes demand full control of the system parameters.