Superconducting Pair Correlations Research Articles

Pairing correlation of the three-band Hubbard model with the nearest attraction

To gain a deeper understanding of the high-temperature superconductivity in doped cuprates, the constrained-path quantum Monte Carlo method was used to explore the superconducting pairing correlation function and effective pairing interaction in the three-band Hubbard model. Our main observation was that in the low doping region, compared to other symmetries, [Formula: see text]-wave superconducting pairing dominates. The Coulomb interaction [Formula: see text] suppresses [Formula: see text]-wave pairing correlation, while the effective pairing interaction is both enhanced by the increasing [Formula: see text] and the nearest attraction. These results are used to understand the superconducting state in copper oxide high-temperature superconductors.

Temperature-tuned Fermi-surface topology and segmentation in noncentrosymmetric superconductors

We report the first comprehensive microscopic description of the thermal fluctuations tuned Fermi surface characteristics in a non-centrosymmetric superconductor, in presence of an in-plane Zeeman field. Using a non perturbative approach we demonstrate that short range fluctuating superconducting pair correlations give rise to segmentation of the Fermi surface with direction dependent pair breaking and hotspots for quasiparticle scattering. Further, a fluctuation driven change in the Fermi surface topology is realized, characterized by a shift of the corresponding Dirac point from the trivial ${\bf k}=0$ to the non trivial ${\bf k} \neq 0$. Our results provide key benchmarks for the thermal scales and regimes of thermal stability of the properties of these systems, that are important from the applied perspective to spintronic devices. Our theoretical estimates are in remarkable qualitative agreement with the recent differential conductance and quasiparticle interference measurements on Bi$_{2}$Te$_{3}$/NbSe$_{2}$ hybrid. A generic theoretical framework for the finite momentum scattering of quasiparticles and the associated spectroscopic features is proposed, which is expected to be applicable to a wide class of superconducting materials.

Coupled Hubbard ladders at weak coupling: Pairing and spin excitations

The Hubbard model provides a simple framework in which one can study how certain aspects of the electronic structure of strongly interacting systems can be tuned to optimize the superconducting pairing correlations and how these changes affect the mechanisms giving rise to them. Here we use a weak-coupling random phase approximation to study a two-dimensional Hubbard model with a unidirectional modulation of the hopping amplitudes as the system evolves from the uniform square lattice to an array of weakly coupled two-leg ladders. We find that the pairing correlations retain their dominant $d_{x^2-y^2}$-wave like structure and that they are significantly enhanced for a slightly modulated lattice. This enhancement is traced backed to an increase in the strength of the spin-fluctuation pairing interacting due to favorable Fermi surface nesting in the modulated system. We then use a random-phase approximation BCS framework to examine the evolution of the neutron resonance in the superconducting state. We find that it changes only weakly for moderate modulations, but breaks up into two distinct resonances at incommensurate wave-vectors in the limit of weakly coupled ladders.

Interplay of dark states and superconducting correlations in charge transport through quantum dot trimers

Electronic transport through a hybrid triple quantum dot system is theoretically studied by means of the real-time diagrammatic technique in the lowest order of perturbation theory. The central part of the system is arranged in a triangular geometry, with two quantum dots weakly coupled to metallic electrodes, while the third dot is proximitized by an s-wave superconductor. The focus is put on the transport regimes, where one- and two-electron dark states are formed due to the destructive interference of the electronic wavefunctions. This effect greatly influences the properties of the system, leading to the coherent population trapping and consequently to current blockade, negative differential conductance and enhanced shot-noise. It is shown that the presence of the superconducting pairing correlations in the system can lift the dark state blockade and reduce the shot-noise. Moreover, the current oscillations due to the magnetic flux enclosed by the triangular structure and the effect of superconducting correlations are considered. When the dark state has eigenenergy near the chemical potential of superconducting electrode, the amplitude of oscillations is strongly reduced while the current blockade is lifted. However, when the eigenenergy of the dark state is shifted away from the chemical potential of superconducting lead, the current oscillations remain unaffected.

Disorder-robust p -wave pairing with odd-frequency dependence in normal metal–conventional superconductor junctions

We investigate the induced superconducting pair correlations in junctions between a conventional spin-singlet $s$-wave superconductor and a disordered normal metal. Decomposing the pair amplitude based on its symmetries in the time domain, we demonstrate that the odd-time, or equivalently odd-frequency, spin-singlet $p$-wave correlations are both significant in size and entirely robust against random non-magnetic disorder. We find that these odd-frequency correlations can even be generated by disorder. Our results show that anisotropic odd-frequency pairing represent an important fraction of the proximity-induced correlations in disordered superconducting hybrid structures.

Dominant superconducting pairing symmetry in doped staggered-flux Hubbard model on a square lattice

A constrained path quantum Monte Carlo simulation is performed to investigate the superconducting pairing correlation in doped staggered-flux Hubbard model on a square lattice, which is an interesting platform to host Dirac fermions. For various electron fillings and interaction strengths, the [Formula: see text] pairing dominates over other pairing forms since its long-range correlation is larger over mostly distances. We deepen our study by including the nearest-neighbor interaction [Formula: see text] and found the [Formula: see text] pairing correlation is slightly suppressed by increasing [Formula: see text].

The germanium quantum information route

In the worldwide endeavor for disruptive quantum technologies, germanium is emerging as a versatile material to realize devices capable of encoding, processing, or transmitting quantum information. These devices leverage special properties of the germanium valence-band states, commonly known as holes, such as their inherently strong spin-orbit coupling and the ability to host superconducting pairing correlations. In this Review, we initially introduce the physics of holes in low-dimensional germanium structures with key insights from a theoretical perspective. We then examine the material science progress underpinning germanium-based planar heterostructures and nanowires. We review the most significant experimental results demonstrating key building blocks for quantum technology, such as an electrically driven universal quantum gate set with spin qubits in quantum dots and superconductor-semiconductor devices for hybrid quantum systems. We conclude by identifying the most promising prospects toward scalable quantum information processing.

Dynamically enhanced unconventional superconducting correlations in a Hubbard ladder

We propose theoretically how unconventional superconducting pairing in a repulsively interacting Hubbard ladder can be enhanced via the application of a Floquet driving. Initially the Hubbard ladder is prepared in its charge-density-wave dominated ground state. A periodic Floquet drive is applied which modulates oppositely the energy offset of the two chains and effectively reduces the tunneling along the rungs. This modulation of the energy offsets might be caused by the excitation of a suitable phononic mode in solids or a superlattice modulation in cold atomic gases. We use state-of-the-art density matrix renormalization group methods to monitor the resulting real-time dynamics of the system. We find an enormous enhancement of the unconventional superconducting pair correlations by approximately one order of magnitude.

Absence of Superconductivity in the Pure Two-Dimensional Hubbard Model

We study the superconducting pairing correlations in the ground state of the doped Hubbard model -- in its original form without hopping beyond nearest neighbor or other perturbing parameters -- in two dimensions at intermediate to strong coupling and near optimal doping. The nature of such correlations has been a central question ever since the discovery of cuprate high-temperature superconductors. Despite unprecedented effort and tremendous progress in understanding the properties of this fundamental model, a definitive answer to whether the ground state is superconducting in the parameter regime most relevant to cuprates has proved exceedingly difficult to establish. In this work, we employ two complementary, state-of-the-art many-body computational methods, constrained path (CP) auxiliary-field quantum Monte Carlo (AFQMC) and density matrix renormalization group (DMRG) methods, deploying the most recent algorithmic advances in each. Systematic and detailed comparisons between the two methods are performed. The DMRG is extremely reliable on small width cylinders, where we use it to validate the AFQMC. The AFQMC is then used to study wide systems as well as fully periodic systems, to establish that we have reached the thermodynamic limit. The ground state is found to be non-superconducting in the moderate to strong coupling regime in the vicinity of optimal hole doping.

Superconductivity-induced transverse plasma mode and phonon anomaly in the c -axis response of the bilayer compound RbCa2Fe4As4F2

With infrared spectroscopy we studied the out-of-plane ($c$-axis) response of the iron arsenide superconductor ACa$_2$Fe$_4$As$_4$F$_2$ (A = Rb,Cs) which has a bilayer structure similar to the high $T_c$ cuprates YBa$_2$Cu$_3$O$_7$ (YBCO) and Bi$_2$Sr$_2$CaCu$_2$O$_8$ (Bi2212). In analogy to the cuprates, we observe a superconductivity-induced transverse plasma mode (tPM) and a phonon anomaly that are both signatures of local electric field effects that arise from a large difference between the local conductivities in the intra- and inter-bilayer regions. Using a multilayer model developed for the cuprates, we obtain a good description of the $c$-axis response and derive the local conductivities at $T \simeq T_c$ of $\sigma_1^{\mathrm{bl}}(\omega \rightarrow 0) \simeq$ 1\,000 $\Omega^{-1}\mathrm{cm}^{-1}$ and $\sigma_1^{\mathrm{int}}(\omega \rightarrow 0) \simeq$ 15 $\Omega^{-1}\mathrm{cm}^{-1}$, respectively, that are similar to the ones previously found in underdoped YBCO. Different from the cuprates, we find no evidence of a normal state pseudogap in terms of a partial suppression of the low-energy electronic states that sets in already well above $T_c$. There is also no clear sign of an onset of precursor superconducting pairing correlations well above $T_c \simeq$ 30~K. This highlights that the pseudogap and the precursor superconducting pairing well above $T_c$ are unique features of the cuprates with their strong electronic correlations and, for example, not just the result of a strongly anisotropic electronic response due to the layered crystal structure.

Odd-frequency superconductivity and Meissner effect in the doped topological insulator Bi2Se3

Doped ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ is proposed to be a nematic superconductor originating from unusual interorbital pairing. We calculate all induced superconducting pair correlations in ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ and discover that intraorbital odd-frequency pairing clearly dominates over a significant range of frequencies. Moreover, we explore the contributions of even- and odd-frequency pairing to the Meissner effect, including separating intra- and interband processes in the response function. Contrary to expectations, and due to interband contributions, we find a diamagnetic Meissner effect from the odd-frequency pairing that stabilizes the superconducting order.

Phase diagram of the two-dimensional Hubbard-Holstein model

The electron–electron and electron–phonon interactions play an important role in correlated materials, being key features for spin, charge and pair correlations. Thus, here we investigate their effects in strongly correlated systems by performing unbiased quantum Monte Carlo simulations in the square lattice Hubbard-Holstein model at half-filling. We study the competition and interplay between antiferromagnetism (AFM) and charge-density wave (CDW), establishing its very rich phase diagram. In the region between AFM and CDW phases, we have found an enhancement of superconducting pairing correlations, favouring (nonlocal) s-wave pairs. Our study sheds light over past inconsistencies in the literature, in particular the emergence of CDW in the pure Holstein model case.

Role of long-range interaction on the photon-excited η-pairing of electrons

We report studies on the influence of a time-dependent external driving fields of the photons on a quantum system described by Hubbard model with long-range interactions. Through the exact diagonalization method to calculate the superconducting pair correlation functions, we show that a weak repulsive long-range Coulomb interaction can help enhance superconducting pair correlation function in some parameter space, which may appear in cuprates, while the number of doublons is increased by the attractive long-range interaction. Out of the parameter space, long-range interaction can be harmful to η-pairing and on-site pairing of electrons. Our results may help people find and design new materials with significant enhancement of transient superconductivity induced by light pulse irradiations.

Metal-insulator transition and dominant d+id pairing symmetry in twisted bilayer graphene

Motivated by recent experimental studies that have found signatures of a correlated insulator phase and tuning superconductivity in twisted bilayer graphene, we study the temperature-dependent conductivity, the spin correlation and the superconducting pairing correlation within a two-orbital Hubbard model on an emergent honeycomb lattice. The evaluation of the temperature dependence of the conductivity demonstrates that there is a metal-insulator transition, and the Mott phase at strong coupling is accompanied by antiferromagnetic order. The electronic correlation drives a $d+id$ superconducting pairing to be dominant over a wide filling region. All of the dc conductivity, the spin correlation and the superconductivity are suppressed as the interlayer coupling strength increases, and the critical $U_c$ for the metal-insulator transition is also reduced. Our intensive numerical results reveal that twisted bilayer graphene should be a uniquely tunable platform for exploring strongly correlated phenomena.

Topological superconducting phases and Josephson effect in curved superconductors with time reversal invariance

We consider a Rashba spin-orbit coupled nanowire with anisotropic spin-singlet superconducting pairing and time-reversal-invariant symmetry. We explore the evolution of the topological superconducting phases of this system due to geometric deformations for the representative case of a wire bent in a semielliptical shape. We find that when the system is in its topological superconducting phase, strong inhomogeneities in the profile curvature can produce a pair of localized eigenmodes, which can be attributed to a nonuniform topological phase. The curved geometric profile also allows to tune the spin correlations of the superconducting state via the induced inhomogeneity of the spin-orbit coupling (SOC). The geometric control of the superconducting pair correlations allows to manipulate the critical current in Josephson junctions made up of two time reversal invariant topological superconductors separated by a spin-orbit coupled normal metal. In particular, we find that the curvature inhomogeneity can be exploited for amplifying the current intensity, but also to generate a $0-\pi$ transition, and a second harmonic contribution, which generates, for some specific geometric configurations, a $\varphi$-junction behavior.

Evolution of pair correlation symmetries and supercurrent reversal in tilted Weyl semimetals

We study the effective symmetry profiles of superconducting pair correlations and the flow of charge supercurrent in ballistic Weyl semimetal systems with a tilted dispersion relation. Utilizing a microscopic method in the ballistic regime and starting from both opposite-pseudospin and equal-pseudospin phonon-mediated opposite-spin electron-electron couplings, we calculate the anomalous Green's function to study various superconducting pair correlations that Weyl semimetal systems may develop. The momentum-space profile reveals that by properly manipulating the parameters of Weyl semimetal systems, including the tilting parameter, the effective symmetry class of even-parity s-wave (odd-parity p-wave) superconducting correlations can be converted into a d-wave (f-wave) symmetry class that consists of equal-pseudospin and opposite-pseudospin channels. We also find that the supercurrent in a ballistic Weyl Josephson junction can be made to vanish or switch directions, depending on the tilt of the Weyl cones, in addition to the relevant parameters characterizing the Weyl semimetal and junction. We show that inversion symmetry breaking terms introduce transitions that result in the appearance of self-biased current at zero difference between the macroscopic phases of the superconducting segments, creating a phi0 Josephson state. Weyl semimetal systems are shown to offer several experimentally tunable parameters to control the induction of higher harmonics into the current phase relations.

Induced superconducting pair correlations in a quasicrystal coupled to a BCS superconductor

We investigate the superconducting pair correlations induced within a 1D quasiperiodic chain when placed in contact with a superconductor. We show that these decay as a power law with distance from the interface. We also show that the induced correlations carry information on the topological properties of the spectrum of the quasiperiodic chain.

Van Der Waals Heterostructures with Spin‐Orbit Coupling

AbstractHerein, recent work on van der Waals (vdW) systems in which at least one of the components has strong spin‐orbit coupling is reviewed, focussing on a selection of vdW heterostructures to exemplify the type of interesting electronic properties that can arise in these systems. First a general effective model to describe the low energy electronic degrees of freedom in these systems is presented. The model is then applied to study the case of (vdW) systems formed by a graphene sheet and a topological insulator. The electronic transport properties of such systems are discussed and it is shown how they exhibit much stronger spin‐dependent transport effects than isolated topological insulators. Then, vdW systems are considered in which the layer with strong spin‐orbit coupling is a monolayer transition metal dichalcogenide (TMD) and graphene‐TMD systems are briefly discussed. In the second part of the article, a case is discussed in which the vdW system includes a superconducting layer in addition to the layer with strong spin‐orbit coupling. It is shown in detail how these systems can be designed to realize odd‐frequency superconducting pair correlations. Finally, twisted graphene‐NbSe2 bilayer systems are discussed as an example in which the strength of the proximity‐induced superconducting pairing in the normal layer, and its Ising character, can be tuned via the relative twist angle between the two layers forming the heterostructure.

Ground state superconducting pair correlations in twisted bilayer graphene

Motivated by the recent novel electronic features extracted from the magic-angle graphene superlattices, we studied the ground state superconducting pairing correlations within the Hubbard model on a twisted bilayer honeycomb lattice. Using Constrained-Path Quantum Monte Carlo method, we found that the [Formula: see text] pairing correlation dominates over other pairing patterns among various electron fillings and interaction strengths, and the effective pairing interaction was enhanced as the on-site Coulomb interaction increased. We further examined the effect of the nearest neighbor interaction [Formula: see text], and the effective pairing interaction with [Formula: see text] pairing symmetry was also enhanced by either a repulsive or attractive interaction. Our intensive numerical results confirm the interaction driven superconductivity with a dominant [Formula: see text] pairing symmetry in twisted bilayer graphene.

Theory of triangular lattice quasi-one-dimensional charge-transfer solids

Recent investigations of the magnetic properties and the discovery of superconductivity in quasi-one-dimensional triangular lattice organic charge-transfer solids have indicated the severe limitations of the effective 1/2-filled band Hubbard model for these and related systems. Our computational studies of these materials within a 1/4-filled band Hubbard model in which the organic monomer molecules, and not their dimers, constitute the sites of the Hamiltonian are able to reproduce the experimental results. We ascribe the spin gap transition in kappa-(BEDT-TTF)_2B(CN)_4 to the formation of a two-dimensional paired-electron crystal and make the testable prediction that the spin gap will be accompanied by charge-ordering and period doubling in two directions. We find enhancement of the long-range component of superconducting pairing correlations by the Hubbard repulsive interaction for band parameters corresponding to kappa-(BEDT-TTF)_2CF_3SO_3. The overall results strongly support a valence bond theory of superconductivity we have proposed recently.