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arXiv:1910.08727 · Physical review. B./Physical review. B

Emergence of strongly correlated electronic states driven by the Andreev bound state in d -wave superconductors

Shun Matsubara, Hiroshi Kontani

Published Feb 12, 2020• 9 citations
arXivHTMLPDF

Abstract

As the surface Andreev bound state (ABS) forms at the open (1,1) edge of a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave superconductor, the local density of states increases. Therefore, a strong electron correlation and drastic phenomena may occur. However, a theoretical study on the effects of the ABS on the electron correlation has not been performed yet. To understand these effects, we study the large-cluster Hubbard model with an open (1,1) edge in the presence of a bulk $d$-wave gap. We calculate the site-dependent spin susceptibility by performing the random-phase approximation and modified fluctuation-exchange approximation in real space. We find that near the (1,1) edge, drastic ferromagnetic (FM) fluctuations occur owing to the ABS. In addition, as the temperature decreases, the system rapidly approaches a magnetic-order phase slightly below the transition temperature of the bulk $d$-wave superconductivity (SC). In this case, the FM fluctuations are expected to induce interesting phenomena such as edge-induced triplet SC and quantum critical phenomena.

DOI
10.1103/physrevb.101.075114

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As the surface Andreev bound state (ABS) forms at the open (1,1) edge of a dx2\ensuremath−y2{d}_{{x}^{2}\ensuremath{-}{y}^{2}}dx2\ensuremath−y2​-wave superconductor, the local density of states increases. Therefore, a strong electron correlation and drastic phenomena may occur. However, a theoretical study on the effects of the ABS on the electron correlation has not been performed yet. To understand these effects, we study the large-cluster Hubbard model with an open (1,1) edge in the presence of a bulk ddd-wave gap. We calculate the site-dependent spin susceptibility by performing the random-phase approximation and modified fluctuation-exchange approximation in real space. We find that near the (1,1) edge, drastic ferromagnetic (FM) fluctuations occur owing to the ABS. In addition, as the temperature decreases, the system rapidly approaches a magnetic-order phase slightly below the transition temperature of the bulk ddd-wave superconductivity (SC). In this case, the FM fluctuations are expected to induce interesting phenomena such as edge-induced triplet SC and quantum critical phenomena.
A supercurrent is well recognized as being of prime importance within mean-field theory, but remains largely unexplored in strongly correlated electron systems (SCES) and the quantum critical region. To clarify the impact of the supercurrent on magnetism and superconductivity near an antiferromagnetic quantum critical point, we study the two-dimensional Hubbard model based on a fluctuation exchange approximation for a current-carrying superconducting state. We show a supercurrent-induced antiferromagnetism and emergence of spin-triplet Cooper pairs. The former results from Bogoliubov Fermi surfaces, suppression in the superconducting gap, and strong correlation effects beyond the mean-field theory. Our results suggest that the supercurrent can bring out rich phenomena of superconductivity in SCES.
To understand nontrivial edge electronic states in strongly-correlated metals such as cuprate superconductors, we study the two-dimensional Hubbard models with open edge boundary. The position-dependences of the spin susceptibility and the self-energy are carefully analyzed self-consistently, by using the fluctuation-exchange (FLEX) approximation. It is found that spin susceptibilities are strongly enlarged near the (1,1) open edge when the system is near the half-filling. The enhancement is large even if the negative feedback from the self-energy is considered in the FLEX approximation. The present study predicts the emergence of nontrivial spin-fluctuation-driven phenomena near the edge, like the quantum criticality, edge superconductivity, and the bond-density-wave order.
We report results of a study of strongly correlated d -wave superconducting slabs within a t - model solved using the statistically consistent Gutzwiller approach. For different dopings, we model slabs cut at 45 ∘ relative to the main crystallographic a b axes, i.e., [110] orientation, and conclude that quasiparticle charge is drawn to the edges. Thus, the correlations are locally strengthened, and a region near the edge is closer to the Mott- insulating state with reduced hopping amplitudes on the links. Superconductivity is locally weakened near the edges in the correlated state, and the spectral weight of zero-energy Andreev bound states is substantially reduced compared to weak coupling theory. The renormalization of the edge states leaves no room for an extended s -wave component to form for hole dopings ranging from strongly underdoped to slightly overdoped.
We study the onset of spin-density wave order in itinerant electron systems via a two-dimensional lattice model amenable to numerically exact, sign-problem-free determinantal quantum Monte Carlo simulations. The finite-temperature phase diagram of the model reveals a dome-shaped d-wave superconducting phase near the magnetic quantum phase transition. Above the critical superconducting temperature, an extended fluctuation regime manifests itself in the opening of a gap in the electronic density of states and an enhanced diamagnetic response. While charge density wave fluctuations are moderately enhanced in the proximity of the magnetic quantum phase transition, they remain short ranged. The striking similarity of our results to the phenomenology of many unconventional superconductors points a way to a microscopic understanding of such strongly coupled systems in a controlled manner.
We investigate the superconducting Anderson impurity model for interacting quantum dot Josephson junctions with spin-orbit coupling and a term accounting for tunnelling through higher-energy orbitals. These elements establish the conditions required for spin polarization in the absence of external magnetic field at finite superconducting phase bias. This Hamiltonian has been previously used to model the Andreev spin qubit, where quantum information is encoded in spinful odd-parity subgap states. Here we instead analyse the even-parity sector, i.e., the Andreev pair qubit based on Andreev bound states (ABS). The model is solved using the zero-bandwidth approximation and the numerical renormalization group, with further insight from variational calculations. Electron-electron interaction admixes single-occupancy Yu-Shiba-Rusinov (YSR) components into the ABS states, thereby strongly enhancing spin transitions in the presence of spin-orbit coupling. The ABS states can thus become sensitive to local magnetic field fluctuations, which has implications for decoherence in Andreev pair qubits. For strong interaction U U , especially in the cross-over region between the ABS and YSR regimes for U \sim 2\Delta U ∼ 2 Δ , charge, spin, and inductive transitions can all become strong, offering avenues for spin control and quantum transduction.
We study superfluidity in strongly correlated systems by focusing three features as follows. First, interplay between superfluidity and other order parameters near quantum critical points is studied. The onset positions of the order parameters with or without superconductivity determines how they interact with each other. For the spin density wave (SDW) transition, we find that the quantum critical point shifts by order |∆|, where ∆ is pairing amplitude, so that the region of SDW order is smaller in the superconductor than in the metal. This shift is larger than the |∆|2 shift predicted by theories of competing orders which ignore Fermi surface effects. Second, we study a doped antiferromagnetic Mott insulator motivated by copper based high temperature superconductors. Based on spin and charge fractionalization, the algebraic charge liquid phase whose bosonic spinons have energy gap but fermionic holons form Fermi surfaces and its superconductivity are studied. We show fluctuations of local SDW order orientation lead to d-wave superconductivity, and its quantum critical pairing mechanisms are investigated. Also, a theory of bound states between spinons and holons is studied. We show that the fractionalization induces a doubling electron-like quasiparticles, which naturally induces the fractionalized Fermi liquid. The bound state theory describes exotic properties of the underdoped Cuprates such as “nodal-antinodal dichotomy” at a mean field level description. At last, we study superfluidity of fermions in optical lattices near the Feshbach resonance. Due to divergence of scattering length at the resonance, universality is observed and characteristics of superfluidity has been studied. We extend such universal properties by considering superfluid-insulator transition with an even integer number of fermions per unit cell. The resulting insulator interpolates between a band insulator of fermions and a Mott insulator of fermion pairs.