No Arabic abstract
We demonstrate that SrTiO$_3$ can be a platform for observing the bulk odd-frequency superconducting state owing to the multiorbital/multiband nature. We consider a three-orbital tight-binding model for SrTiO$_3$ 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 the 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 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 the odd-parity orbital hybridization, which is an essential ingredient for the ferroelectricity-induced odd-frequency pair correlations, can be observed in the spectral functions and density of states.
At an interface between a topological insulator (TI) and a conventional superconductor (SC), superconductivity has been predicted to change dramatically and exhibit novel correlations. In particular, the induced superconductivity by an $s$-wave SC in a TI can develop an order parameter with a $p$-wave component. Here we present experimental evidence for an unexpected proximity-induced novel superconducting state in a thin layer of the prototypical TI, Bi$_2$Se$_3$, proximity coupled to Nb. From depth-resolved magnetic field measurements below the superconducting transition temperature of Nb, we observe a local enhancement of the magnetic field in Bi$_2$Se$_3$ that exceeds the externally applied field, thus supporting the existence of an intrinsic paramagnetic Meissner effect arising from an odd-frequency superconducting state. Our experimental results are complemented by theoretical calculations supporting the appearance of such a component at the interface which extends into the TI. This state is topologically distinct from the conventional Bardeen-Cooper-Schrieffer state it originates from. To the best of our knowledge, these findings present a first observation of bulk odd-frequency superconductivity in a TI. We thus reaffirm the potential of the TI-SC interface as a versatile platform to produce novel superconducting states.
Advances in complex oxide heteroepitaxy have highlighted the enormous potential of utilizing strain engineering via lattice mismatch to control ferroelectricity in thin-film heterostructures. This approach, however, lacks the ability to produce large and continuously variable strain states, thus limiting the potential for designing and tuning the desired properties of ferroelectric films. Here, we observe and explore dynamic strain-induced ferroelectricity in SrTiO$_3$ by laminating freestanding oxide films onto a stretchable polymer substrate. Using a combination of scanning probe microscopy, optical second harmonic generation measurements, and atomistic modeling, we demonstrate robust room-temperature ferroelectricity in SrTiO$_3$ with 2.0% uniaxial tensile strain, corroborated by the notable features of 180{deg} ferroelectric domains and an extrapolated transition temperature of 400 K. Our work reveals the enormous potential of employing oxide membranes to create and enhance ferroelectricity in environmentally benign lead-free oxides, which hold great promise for applications ranging from non-volatile memories and microwave electronics.
We study the effect of the Fermi surface anisotropy on the odd-frequency spin-triplet pairing component of the induced pair potential. We consider a superconductor/ ferromagnetic insulator (S/FI) hybrid structure formed on the 3D topological insulator (TI) surface. In this case three ingredients insure the possibility of the odd-frequency pairing: 1) the topological surface states, 2) the induced pair potential, and 3) the magnetic moment of a nearby ferromagnetic insulator. We take into account the strong anisotropy of the Dirac cone in topological insulators when the chemical potential lies well above the Dirac cone and its constant energy contour has a snowflake shape. Within this model, we propose that the S/FI boundary should be properly aligned with respect to the snowflake constant energy contour to have an odd-frequency symmetry of the corresponding pairing component and to insure the Majorana bound state at the S/FI boundary. For arbitrary orientation of the boundary the Majorana bound state is absent. This provides a selection rule to the realization of Majorana modes in S/FI hybrid structures, formed on the topological insulator surface.
We formulate a general framework for addressing both odd- and even-frequency superconductivity in Dirac semimetals and demonstrate that the odd-frequency or the Berezinskii pairing can naturally appear in these materials because of the chirality degree of freedom. We show that repulsive frequency-dependent interactions favor the Berezinskii pairing while an attractive electron-electron interaction allows for the BCS pairing. In the case of compensated Dirac and Weyl semimetals, both the conventional BCS and odd-frequency Berezinskii pairings require critical coupling. Since these pairings could originate from physically different mechanisms, our findings pave the way for controlling the realization of the Berezinskii superconductivity in topological semimetals. We also present the density of states with several cusp-like features that can serve as an experimentally verifiable signature of the odd-frequency gap.
SrTiO$_3$ is an incipient ferroelectric on the verge of a polar instability, which is avoided at low temperatures by quantum fluctuations. Within this unusual quantum paraelectric phase, superconductivity persists despite extremely dilute carrier densities. Ferroelectric fluctuations have been suspected to play a role in the origin of superconductivity by contributing to electron pairing. To investigate this possibility, we used optical second harmonic generation to measure the doping and temperature dependence of the ferroelectric order parameter in compressively strained SrTiO$_3$ thin films. At low temperatures, we uncover a spontaneous out-of-plane ferroelectric polarization with an onset that correlates perfectly with normal-state electrical resistivity anomalies. These anomalies have previously been associated with an enhancement of the superconducting critical temperature in doped SrTiO$_3$ films, directly linking the ferroelectric and superconducting phases. We develop a long-range mean-field Ising model of the ferroelectric phase transition to interpret the data and extract the relevant energy scales in the system. Our results support a long-suspected connection between ferroelectricity and superconductivity in SrTiO$_3$, but call into question the role played by ferroelectric fluctuations.