Superconductivity In Multiband Systems Research Articles

Interplay between charge density wave and superconductivity in multiband systems with interband Coulomb interaction

In this work we study the competition or coexistence between charge density wave (CDW) and superconductivity (SC) in a two-band model system in a square lattice. One of the bands has a net attractive interaction ($J_d$) that is responsible for SC. The model includes on-site Coulomb repulsion between quasi-particles in different bands ($U_{dc}$) and the hybridization ($V$) between them. We are interested in describing inter-metallic systems with a $d$-band of moderately correlated electrons, for which a mean-field approximation is adequate, coexisting with a large $sp$-band. For simplicity, all interactions and the hybridization $V$ are considered site-independent. We obtain the eigenvalues of the Hamiltonian numerically and minimize the free energy density with respect to the relevant parameters to obtain the phase diagrams as function of $J_d$, $U_{dc}$, $V$, composition ($n_{\mathrm{tot}}$) and the relative depth of the bands ($\epsilon_{d0}$). We consider two types of superconducting ground states coexisting with the CDW. One is a homogeneous ground state and the other is a pair density wave where the SC order parameter has the same spatial modulation of the CDW. Our results show that the CDW and SC orders compete, but depending on the parameters of the model these phases may coexist. The model reproduces most of the experimental features of high dimensionality ($d>1$) metals with competing CDW and SC states, including the existence of first and second-order phase transitions in their phase diagrams.

Multipolar superconductivity in Luttinger semimetals

Topological superconductivity in multiband systems has received much attention due to a variety of possible exotic superconducting order parameters as well as non-trivial bulk and surface states. While the impact of coexisting magnetic order on superconductivity has been studied for many years, such as ferromagnetic superconductors, the implication of coexisting multipolar order has not been explored much despite the possibility of multipolar hidden order in a number of $f$-electron materials. In this work, we investigate topological properties of multipolar superconductors that may arise when quadrupolar local moments are coupled to conduction electrons in the multiband Luttinger semimetal. We show that the multipolar ordering of local moments leads to various multipolar superconductors with distinct topological properties. We apply these results to the quadrupolar Kondo semimetal system, PrBi, by deriving the microscopic multipolar Kondo model and examining the possible superconducting order parameters. We also discuss how to experimentally probe the topological nature of the Bogoliubov quasiparticles in distinct multipolar superconductors via doping and external pressure, especially in the context of PrBi.

Robustness of unconventional s -wave superconducting states against disorder

We investigate the robustness against disorder of superconductivity in multiband systems where the fermions have four internal degrees of freedom. This permits unconventional $s$-wave pairing states, which may transform nontrivially under crystal symmetries. Using the self-consistent Born approximation, we develop a general theory for the effect of impurities on the critical temperature, and find that the presence of these novel $s$-wave channels significantly modifies the conclusions of single-band theories. We apply our theory to two candidate topological superconductors, YPtBi and Cu$_x$Bi$_2$Se$_3$, and show that the novel $s$-wave states display an enhanced resilience against disorder, which extends to momentum-dependent pairing states with the same crystal symmetry. The robustness of the $s$-wave states can be quantified in terms of their superconducting fitness, which can be readily evaluated for model systems.

Momentum dependence of the superconducting gap and in-gap states inMgB2multiband superconductor

We use tunable laser-based angle-resolved photoemission spectroscopy to study the electronic structure of the multiband superconductor ${\mathrm{MgB}}_{2}$. These results form the baseline for detailed studies of superconductivity in multiband systems. We find that the magnitude of the superconducting gap on both $\ensuremath{\sigma}$ bands follows a BCS-like variation with temperature with ${\mathrm{\ensuremath{\Delta}}}_{0}\ensuremath{\sim}7\phantom{\rule{0.28em}{0ex}}\mathrm{meV}$. The value of the gap is isotropic within experimental uncertainty and in agreement with a pure $s$-wave pairing symmetry. We also observe in-gap states confined to ${k}_{F}$ of the $\ensuremath{\sigma}$ band that occur at some locations of the sample surface. The energy of this excitation, $\ensuremath{\sim}3$ meV, is somewhat larger than the previously reported gap on $\ensuremath{\pi}$ Fermi sheet and therefore we cannot exclude the possibility of interband scattering as its origin.

Mechanism for enhancement of superconductivity in multi-band systems with odd parity hybridization

.The study of multi-band superconductivity is relevant for a variety of systems, from ultra-cold atoms with population imbalance to particle physics and condensed matter. As a consequence, this problem has been widely investigated and has brought to light many new and interesting phenomena. In this work we point out and explore a correspondence between a two-band metal with a k-dependent hybridization and a uniformly polarized fermionic system in the presence of spin–orbit coupling (SOC). We study the ground state phase diagram of this metal in the presence of an attractive interaction. We find remarkable superconducting properties whenever hybridization mixes orbitals of different parities in neighboring sites. We show that in this case hybridization enhances superconductivity and drives the crossover from weak to strong coupling which is analogous with the SOC in cold atoms. We obtain the quantum phase transitions between the normal and superfluid states, as the intensities of different parameters characterizing the metal are varied, including Lifshitz transitions, with no symmetry breaking associated with the appearance of soft modes in the Fermi surface.

The role of local repulsive interactions on superconductor quantum critical points

The study of superconductivity in multi-band systems is relevant for a variety of materials of actual interest. High Tc cuprates, the new Fe-based materials and heavy fermion superconductors are multi-band systems and this feature must be taken into account for a proper description of their properties. In this paper we study superconductivity in two-band systems. One of the bands is a wide band of conduction electrons. The other is a narrow band of f or d character with an attractive interaction among quasi-particles in neighboring sites and a local repulsive interaction U. These bands are coupled by hybridization, which can be controlled by external pressure allowing to probe the phase diagram of these systems. First, we consider the case of weak repulsive interactions for which a mean-field approximation is satisfactory. We obtain the zero temperature phase diagram for weak and strong attractive interactions. We show that in the presence of U the crossover from the BCS to the Bose–Einstein Condensation (BEC) regime at strong attractive couplings remains smooth. Next we consider the case of strong repulsive U and introduce a Hubbard-I approximation to deal with this interaction. We obtain zero temperature phase diagrams as functions of hybridization and the strength of the repulsive and attractive interactions. We consider the cases of extended s-wave and d-wave symmetry of the order parameter.

Microscopic theory of type-1.5 superconductivity in multiband systems

We report a self-consistent microscopic theory of characteristic length scales, vortex structure and type-1.5 superconducting state in two-band systems using two-band Eilenberger formalism.

Crossover from weak to strong coupling superconductivity in multi-band systems

The study of superconductivity in correlated systems is an exciting area of condensedmatter physics. In this paper we consider superconducting ground states in systemsdescribed by two-band models with different effective masses. These two bandsare coupled through an effective hybridization that can be directly tunedby pressure. We consider the cases of s-wave superconductivity associated withthe electrons in a narrow band and also with inter-band pairing. To study thesystem in the strong coupling regime we introduce the s-wave scattering lengthas, and obtainthe superconducting order parameters and the chemical potential as functions of the interaction strength1/kFas along the BCS–BECcrossover at T = 0. Finally, we discuss the phase diagram of this model as a function of external pressure andhow our results can be applied for two-band systems as Fe pnictides or heavy fermions. Themain result of this study is the occurrence of a superconducting quantum critical point(SQCP) in this two-band model.