Effects of competing orders and quantum phase fluctuations on the low-energy excitations and pseudogap phenomena of cuprate superconductors

Abstract

We investigate the low-energy quasiparticle excitation spectra of cuprate superconductors by incorporating both superconductivity (SC) and competing orders (CO) in the bare Green's function and quantum phase fluctuations in the proper self-energy. Our approach provides consistent explanations for various empirical observations, including the excess subgap quasiparticle density of states, "dichotomy" in the momentum-dependent quasiparticle coherence and the temperature-dependent gap evolution, and the presence (absence) of the low-energy pseudogap in hole-(electron-) type cuprates depending on the relative scale of the CO and SC energy gaps. 74.25.Jb, 74.50.+r Keywords: Quasiparticle spectra; pseudogap; competing orders; cuprate superconductors Cuprate superconductors differ fundamentally from conventional superconductors in that they are doped Mott insulators with strong electronic correlation that leads to possibilities of different competing orders (CO) in the ground state besides superconductivity (SC) [1][2][3][4][5][6][7][8]. The existence of competing orders and the proximity to quantum criticality [2,3,7,8] gives rise to unconventional low-energy excitations of the cuprates, manifested as weakened superconducting phase stiffness [6], occurrence of excess subgap quasiparticle density of states (DOS) [9], spatial modulations in the lowtemperature quasiparticle spectra that are unaccounted for by Bogoliubov quasiparticles alone [10][11][12], "dichotomy" in the momentum-dependent quasiparticle coherence [13] and temperature-dependent gap evolution [14], and the presence (absence) of the low-energy pseudogap (PG) [9,15,16] and Nernst effect [17] in the hole (electron)-type cuprates above the SC transition. Microscopically, the existence of CO is likely responsible for various non-universal phenomena among different cuprates [8,9,18,19]. Macroscopically, the weakened superconducting phase stiffness and proximity to CO can give rise to strong fluctuations that lead to the extreme type-II nature and rich vortex dynamics [8,20,21].To date there are two typical theoretical approaches to describing the quasiparticle excitation spectra of the cuprates. One approach takes the BCS-like Hamiltonian as the unperturbed mean-field state and a competing order, pinned by disorder, as the perturbation that gives rise to a weak scattering potential for the Bogoliubov quasiparticles [11,[22][23][24]. The other approach begins with the BCS-like Hamiltonian and includes superconducting phase fluctuations in the proper self-energy correction [25,26]. However, no quantitative calculations have been made by incorporating both CO and quantum phase fluctuations in the SC state. The objective of this work is to consider the latter scenario and compute the corresponding low-energy excitation spectra with realistic physical parameters for comparison with experiments. We find that the low-energy excitations thus derived differ from typical Bogoliubov quasiparticles and can account for various puzzling phenomena aforementioned....

Macroscopic evidence for quantum criticality and field-induced quantum fluctuations in cuprate superconductors

“…9 Given that competing orders ͑COs͒ can exist in the ground state of these doped Mott insulators besides superconductivity ͑SC͒, 9-15 the occurrence of quantum criticality may be expected. 11,13,16 The proximity to quantum criticality and the existence of COs can significantly affect the low-energy excitations of the cuprates due to strong quantum fluctuations 8,9 and the redistribution of quasiparticle spectral weight among SC and COs. 9,17,18 Indeed, empirically the low-energy excitations of cuprate superconductors appear to be unconventional, exhibiting intriguing properties unaccounted for by conventional Bogoliubov quasiparticles.9,17-19 Moreover, external variables such as temperature ͑T͒ and applied magnetic field ͑H͒ can vary the interplay of SC and COs, such as inducing or enhancing 20,21 the COs at the price of more rapid suppression of SC, thereby leading to weakened superconducting stiffness and strong thermal and field-induced fluctuations.1-3 On the other hand, the quasi-two-dimensional nature of the cuprates can also lead to quantum criticality in the limit of decoupling of CuO 2 planes. 6 In this work we demonstrate experimental evidence from macroscopic magnetization measurements for field-induced quantum fluctuations among a wide variety of cuprate superconductors with different microscopic variables such as the doping level ͑␦͒ of holes or electrons, and the number of CuO 2 layers per unit cell ͑n͒.…”

“…9 Given that competing orders ͑COs͒ can exist in the ground state of these doped Mott insulators besides superconductivity ͑SC͒, 9-15 the occurrence of quantum criticality may be expected. 11,13,16 The proximity to quantum criticality and the existence of COs can significantly affect the low-energy excitations of the cuprates due to strong quantum fluctuations 8,9 and the redistribution of quasiparticle spectral weight among SC and COs. 9,17,18 Indeed, empirically the low-energy excitations of cuprate superconductors appear to be unconventional, exhibiting intriguing properties unaccounted for by conventional Bogoliubov quasiparticles.…”

“…9 Given that competing orders ͑COs͒ can exist in the ground state of these doped Mott insulators besides superconductivity ͑SC͒, [9][10][11][12][13][14][15] the occurrence of quantum criticality may be expected. 11,13,16 The proximity to quantum criticality and the existence of COs can significantly affect the low-energy excitations of the cuprates due to strong quantum fluctuations 8,9 and the redistribution of quasiparticle spectral weight among SC and COs. 9,17,18 Indeed, empirically the low-energy excitations of cuprate superconductors appear to be unconventional, exhibiting intriguing properties unaccounted for by conventional Bogoliubov quasiparticles. 9,[17][18][19] Moreover, external variables such as temperature ͑T͒ and applied magnetic field ͑H͒ can vary the interplay of SC and COs, such as inducing or enhancing 20,21 the COs at the price of more rapid suppression of SC, thereby leading to weakened superconducting stiffness and strong thermal and field-induced fluctuations.…”

Scanning Tunneling Spectroscopic Studies of the Low-Energy Quasiparticle Excitations in Cuprate Superconductors

“…The low-energy quasiparticle excitations of cuprate superconductors exhibit various spectral characteristics that differ from those of simple Bogoliubov quasiparticles for pure superconductors because of the presence of competing orders (COs) in the ground state of under-and optimally doped cuprates [1][2][3][4][5][6][7][8][9][10].…”

“…Some of the best known unconventional spectral characteristics include: the presence (absence) of pseudogap and Fermi arc phenomena in hole-type (electrontype) cuprates [4][5][6][7][8][9][10][11][12]; dichotomy of the quasiparticle coherence for momentum near the nodal and anti-nodal parts of the Fermi surface [9,12,13]; pseudogap (PG)-like spectral features inside vortex cores [4][5][6][7]; and non-universal spectral homogeneity among different types of cuprates [4,5,[14][15][16][17][18].…”