The Charged AdS Domain-wall As Holographic Superconductors

Through the gauge-gravity dualities, string theory ofers powerful methods to studystrongly coupled feld theories. In this dissertation, we will use this method to studyrelated topics in condensed matter physics. We study the following two distinct phenom-ena: superconductivity and non-Fermi liquids.Our studying objects is the Abelian-Higgs model couple to asymptotical AdS space-time, which provides a gravitational description for strongly coupled system of super-conducting or superfuid phases. We reconsider Gubser et al’s idea of using the chargedAdS domain wall as holographic description of quantum critical phase transitions, andpoint out that their statement about the uniqueness of gravity solutions was wrong. Wepropose new ansatz for the solution and get numerical solution families featured by theparameter aψ. We then ft the numerical solutions into simple analytical formulas. Wegeneralize their explorations from3+1dimensions to arbitrary n+1Ds. While in thestudy of conductivity-frequency relation, we verify the power law behavior of conduc-tivities at low frequencies. We fnd that as n+1≥5, the charged AdS domain wallsare unstable against electric perturbations. We provide two exactly solvable quantumscattering problems, which exhibit the possibility of negative conductivities.In the second part of this dissertation, we studied the classical solution of spin-1Dirac feld in the charged AdS-domain walls. Through calculating spectral functions ofparticles excited by the dual operators, we fnd continuous band structures. These bandscan be either partially flled (conduction bands, bands are partially flled with electrons)or totally empty (unoccupied bands, bands are unflled with electrons, made up of excita-tion energy levels) and gapped (forbidden bands, energy region between bands cannot beflled with electrons). In the calculations, we need to consider two kinds of modes of theclassical Dirac feld in AdS domain wall background. We deal with these two cases equal-ly and fnd that the band structure of these two kinds of modes are smoothly connectedin the whole momentum space. For charged domain wall with diferent dimensions, wefnd distribution of normalizable modes of Dirac feld are similar. Fermi surfaces or bandgaps are controlled by parameter aψwhich determine the behavior of spacetime and themass parameter mfof the probing Dirac feld. Most features observed in the spectralfunctions are qualitatively consistent with results observed in ARPES experiments ofhigh T c superconductors.