Theoretical Studies On Superconductivity At The Interface Of SrTiO₃ And LaAlO₃

The two-dimensional electron system(2DES)can be formed at the interface of strontium titanate and lanthanum aluminate(STO/LAO).The system demonstrates the coexistence of ferromagnetism and superconductivity,ferroelectricity,electron pairing without superconductivity,etc.Thus,it is of significant importance for the basic condensed matter theory.Moreover,the 2DES at the STO/LAO interface is supposed to be applied in the spintronics,memory material,quantum computation,quantum simulation,quantum sensing,etc.,which is very promising for future applications.However,the microscopic superconducting mechani sm of the 2DES is a hard problem and still elusive even at present.First of all,the 2DES is the most dilute superconductor,and its Fermi energy is smaller than Debye energy.This violates the retarded condition in BCS theory.The fact indicates that the mechanism cannot be explained by BCS theory.In order to reveal the microscopic mechanism of superconductivity,several theoretical explanations on the origin of superconductivity have been proposed,such as plasmon-induced superconductivity,phonon-induced superconductivity,etc.Nevertheless,the present theories have many limitations.For example,the plasmon-induced mechanism cannot explain the dome-like curve of the transition temperature as the carrier concentration is increased,while the phonon-electron-interaction-induced mechanism lacks of the support from the isotopic effects and other experiments.Due to the shortage of evidences,the discussions still last even until today.Among them,we propose an improved phenomenological boson-fermion model to describe the low-dimensional system.Our model can better describe experiments on single-electron device,Josephson junctions,STS,etc.and capture the characteristics of the electron pairing in the STO/LAO system above superconducting transition temperature.With the model,the even-odd effects,pseudo-gap phase and Josephson effects can be explained self-consistently.Moreover,it is predicted that the transient amplification of superconductivity is supposed to appear in the STO/LAO system.The main work and innovations are:Firstly,the improved phenomenological boson-fermion model is proposed.The Green's function and spectral function are calculated within the perturbation theory,and the density of states predicted by the model is consistent with the experiments.Moreover,with the number parity projection formalism,the calculated results of the even/odd free energy difference and the effective excitation numb er for the unpaired electron in the odd parity state are in good agreement with the experimental data.This indicates the formation and decay of the electron pairs have an important role in the even-odd effects of the superconducting single-electron transistors.Moreover,it can be inferred that if the magnetic field can reduce the lifetime o f the electron pairs,the even-odd free energy difference and the effective excitation state number will change accordingly.This prediction can be tested by the experiments.Secondly,the current-voltage and resistance-voltage are computed with the Green's function technique.The calculations suggest the gap states come from the pairing of quasi-particles with finite total momentum,and the Josephson current comes from the tunneling of the electron pairs with zero total momentum.In addition,we applied Kulik formula to the fitting of the experimental data.The quantitative agreement implies the Josephson junction has a point contact and the material is clean.Thirdly,we investigate the pulse-induced superconductivity described by Hubbard model with long-range interactions.We calculate the pair correlation function by the exact diagonalization method and find that the well-screened repulsive long-range Coulomb interaction can enhance superconductivity.Furthermore,the attractive longrange interaction can increase the number of doublons in the system.The research can help people find and design novel materials with the light-induced enhancement of the superconducting pair correlation function.The research needs to be developed to the following points:First of all,the improved phenomenological boson-fermion model contains a phenomenological interaction potential,which can cause some problems.For example,it cannot give a correct prediction for superconducting gap.Secondly,in order to obtain an analytic solution,we employed several approximations,when plotting the current-voltage,conductance-voltage curve.This leads to a huge distinction with the experimental value of the superconducting gap.If the lifetime effects of electron pairs are considered,the solution may be more accurate with numerical methods.Thirdly,the amplification effects of non-equilibrium superconductivity at the STO/LAO interface still need experimental verification.Although some theoretical evidence indicates the amplificatio n effects may appear in the system,the effects are not guaranteed to happen due to the complexity of the many-body system.As a result,it is one of the main directions for the future works to find the microscopic mechanism of the interaction potential.W hether it can give a better prediction to superconducting gap and other physical quantities is the key factor to examine if the work is correct.