Hole-doped Side Research Articles

Doping dependence of spin-momentum locking in bismuth-based high-temperature cuprate superconductors

Non-zero spin orbit coupling has been reported in several unconventional superconductors due to the absence of inversion symmetry breaking. This contrasts with cuprate superconductors, where such interaction has been neglected for a long time. The recent report of a non-trivial spin orbit coupling in overdoped Bi2212 cuprate superconductor, has re-opened an old debate on both the source and role of such interaction and its evolution throughout the superconducting dome. Using high-resolution spin- and angle-resolved photoemission spectroscopy, we reveal a momentum-dependent spin texture throughout the hole-doped side of the superconducting phase diagram for single- and double-layer bismuth-based cuprates. The universality of the reported effect among different dopings and the disappearance of spin polarization upon lead substitution, suggest a common source. We argue that local structural fluctuations of the CuO planes and the resulting charge imbalance may cause local inversion symmetry breaking and spin polarization, which might be crucial for understanding cuprates physics.

Coexistence of superconductivity with partially filled stripes in the Hubbard model

The Hubbard model is an iconic model in quantum many-body physics and has been intensely studied, especially since the discovery of high-temperature cuprate superconductors. Combining the complementary capabilities of two computational methods, we found superconductivity in both the electron- and hole-doped regimes of the two-dimensional Hubbard model with next-nearest-neighbor hopping. In the electron-doped regime, superconductivity was weaker and was accompanied by antiferromagnetic Néel correlations at low doping. The strong superconductivity on the hole-doped side coexisted with stripe order, which persisted into the overdoped region with weaker hole-density modulation. These stripe orders varied in fillings between 0.6 and 0.8. Our results suggest the applicability of the Hubbard model with next-nearest hopping for describing cuprate high–transition temperature ( T c ) superconductivity.

Emergent Superconductivity and Competing Charge Orders in Hole-Doped Square-Lattice t-J Model.

The square-lattice Hubbard and closely related t-J models are considered as basic paradigms for understanding strong correlation effects and unconventional superconductivity (SC). Recent large-scale density matrix renormalization group simulations on the extended t-J model have identified d-wave SC on the electron-doped side (with the next-nearest-neighbor hopping t_{2}>0) but a dominant charge density wave (CDW) order on the hole-doped side (t_{2}<0), which is inconsistent with the SC of hole-doped cuprate compounds. We re-examine the ground-state phase diagram of the extended t-J model by employing the state-of-the-art density matrix renormalization group calculations with much enhanced bond dimensions, allowing more accurate determination of the ground state. On six-leg cylinders, while different CDW phases are identified on the hole-doped side for the doping range δ=1/16-1/8, a SC phase emerges at a lower doping regime, with algebraically decaying pairing correlations and d-wave symmetry. On the wider eight-leg systems, the d-wave SC also emerges on the hole-doped side at the optimal 1/8 doping, demonstrating the winning of SC over CDW by increasing the system width. Our results not only suggest a new path to SC in general t-J model through weakening the competing charge orders, but also provide a unified understanding on the SC of both hole- and electron-doped cuprate superconductors.

Spin and charge fluctuation induced pairing in ABCB tetralayer graphene

Motivated by the recent experimental realization of ABCB stacked tetralayer graphene [Wirth , ], we study correlated phenomena in moiré-less graphene tetralayers for realistic interaction profiles using an orbital resolved random phase approximation approach. We demonstrate that magnetic fluctuations originating from local interactions are crucial close to the van Hove singularities on the electron- and hole-doped side promoting layer selective ferrimagnetic states. Spin fluctuations around these magnetic states enhance unconventional spin-triplet, valley-singlet superconductivity with f-wave symmetry due to intervalley scattering. Charge fluctuations arising from long range Coulomb interactions promote doubly degenerate p-wave superconductivity close to the van Hove singularities. At the conduction band edge of ABCB graphene, we find that both spin and charge fluctuations drive f-wave superconductivity. Our analysis suggests a strong competition between superconducting states emerging from long- and short-ranged Coulomb interactions and thus stresses the importance of microscopically derived interaction profiles to make reliable predictions for the origin of superconductivity in graphene-based heterostructures. Published by the American Physical Society 2024

Frustration- and doping-induced magnetism in a Fermi-Hubbard simulator.

Geometrical frustration in strongly correlated systems can give rise toa plethora of novel ordered states and intriguing magnetic phases, such as quantum spin liquids1-3. Promising candidate materials for such phases4-6 can be described by the Hubbard model on an anisotropic triangular lattice, a paradigmaticmodel capturing the interplay between strong correlations and magnetic frustration7-11. However, the fate of frustrated magnetism in the presence of itinerant dopants remains unclear, as well as its connection to the doped phases of the square Hubbard model12. Here we investigate the local spin order of a Hubbard model with controllable frustration and doping, using ultracold fermions in anisotropic optical lattices continuously tunable from a square to a triangular geometry. At half-filling and strong interactions U/t ≈ 9, we observe at the single-site level how frustration reduces the range of magnetic correlations and drives a transition from a collinear Néel antiferromagnet to a short-range correlated 120° spiral phase. Away from half-filling, the triangular limit shows enhanced antiferromagnetic correlations on the hole-doped side and a reversal to ferromagnetic correlations at particle dopings above 20%, hinting at the role of kinetic magnetism in frustrated systems. This work paves the way towards exploring possible chiral ordered or superconducting phases in triangular lattices8,13 and realizing t-t' square lattice Hubbard models that may be essential to describe superconductivity in cuprate materials14.

Robust charge-density-wave correlations in the electron-doped single-band Hubbard model

There is growing evidence that the hole-doped single-band Hubbard and t − J models do not have a superconducting ground state reflective of the high-temperature cuprate superconductors but instead have striped spin- and charge-ordered ground states. Nevertheless, it is proposed that these models may still provide an effective low-energy model for electron-doped materials. Here we study the finite temperature spin and charge correlations in the electron-doped Hubbard model using quantum Monte Carlo dynamical cluster approximation calculations and contrast their behavior with those found on the hole-doped side of the phase diagram. We find evidence for a charge modulation with both checkerboard and unidirectional components decoupled from any spin-density modulations. These correlations are inconsistent with a weak-coupling description based on Fermi surface nesting, and their doping dependence agrees qualitatively with resonant inelastic x-ray scattering measurements. Our results provide evidence that the single-band Hubbard model describes the electron-doped cuprates.

Electron-Hole Asymmetry of Quantum Collective Excitations in High-Tc Copper Oxides

We carry out a systematic study of collective spin- and charge excitations for the canonical single-band Hubbard, $t$-$J$-$U$, and $t$-$J$ models of high-temperature copper-oxide superconductors, both on electron- and hole-doped side of the phase diagram. Recently developed variational wave function approach, combined with the expansion in inverse number of fermionic flavors, is employed. All three models exhibit a substantial electron-hole asymmetry of magnetic excitations, with a robust paramagnon emerging for hole-doping, in agreement with available resonant inelastic $x$-ray scattering data for the cuprates. The $t$-$J$ model yields additional high-energy peak in the magnetic spectrum that is not unambiguously identified in spectroscopy. For all considered Hamiltonians, the dynamical charge susceptibility contains a coherent mode for both hole- and electron doping, with overall bandwidth renormalization controlled by the on-site Coulomb repulsion. Away from the strong-coupling limit, the antiferromagnetic ordering tendency is more pronounced on electron-doped side of the phase diagram.

P -wave superconductivity in Luttinger semimetals

We consider the three-dimensional spin-orbit-coupled Luttinger semimetal of ``spin'' $3/2$ particles in presence of weak attractive interaction in the $l=1$ ($p$-wave) channel, and determine the low-temperature phase diagram for both particle- and hole dopings. The phase diagram depends crucially on the sign of the chemical potential, with two different states (with total angular momentum $j=0$ and $j=3$) competing on the hole-doped side, and three (one $j=1$ and two different $j=2$) states on the particle-doped side. The ground-state condensates of Cooper pairs with the total angular momentum $j=1,2,3$ are selected by the quartic, and even sextic terms in the Ginzburg-Landau free energy. Interestingly, we find that all the $p$-wave ground states appearing in the phase diagram, while displaying different patterns of reduction of the rotational symmetry, preserve time reversal. The resulting quasiparticle spectrum is either fully gapped or with point nodes, with nodal lines being absent.

Ground-state phase diagram of the three-band Hubbard model from density matrix embedding theory

We determine the ground-state phase diagram of the three-band Hubbard model across a range of model parameters using density matrix embedding theory. We study the atomic-scale nature of the antiferromagnetic (AFM) and superconducting (SC) orders, explicitly including the oxygen degrees of freedom. All parametrizations of the model display AFM and SC phases, but the decay of AFM order with doping is too slow compared to the experimental phase diagram, and further, coexistence of AFM and SC orders occurs in all parameter sets. The local magnetic moment localizes entirely at the copper sites. The magnetic phase diagram is particularly sensitive to $\Delta_{pd}$ and $t_{pp}$, and existing estimates of the charge transfer gap $\Delta_{pd}$ appear too large in so-called minimal model parametrizations. The electron-doped side of the phase diagram is qualitatively distinct from hole-doped side and we find an unusual two-peak structure in the SC in the full model parametrization. Examining the SC order at the atomic scale, within the larger scale $d_{x^2 - y^2}$-wave SC pairing order between Cu-Cu and O-O, we also observe a local $p_{x (y)}$ [or $d_{xz (yz)}$]-symmetry modulation of the pair density on the Cu-O bonds. Our work highlights some of the features that arise in a three-band versus one-band picture, the role of the oxygen degrees of freedom in new kinds of atomic-scale SC orders, and the necessity of re-evaluating current parametrizations of the three-band Hubbard model.

Nodeless superconducting gap induced by odd parity pair density wave in underdoped cuprates

We present a theoretical model to show that the transition from an antiferromagnetic (AFM) phase to the dx2−y2-wave superconductivity occurs through a robust companion of a finite momentum pairing between (k,↑) and (−k−Q,↓) electrons, namely a pair-density wave (PDW) state, where Q=(π,π) is the AFM wavevector. Interestingly, the spatial structure of the PDW is constrained to be a p+ip-wave symmetry, which follows pk=p−k−Q under fermions exchange in cuprates, dictating a spin–singlet pairing. Furthermore, the PDW state produces a fully gapped quasiparticle spectrum which explains recent observations of the fully gapped quasiparticle structure of lightly doped cuprates in the hole doping side. We study the stability of all three phases within the self-consistent mean-field theory. Finally, we calculate the superfluid density to propose its exponential temperature dependence as a test to the superconducting origin of this fully gapped state, while the phase modulation of the PDW state can be visualized by scanning probes.

Modifications of magnetic anisotropy of Fe3GeTe2 by the electric field effect

The Fe3GeTe2 material is the only metallic ferromagnet with a van der Waals layered structure, which has been used as a ferromagnetic electrode in spintronic devices. The tunability of magnetic properties of few-layer Fe3GeTe2 by electrostatic gating is demonstrated in experiments. In this work, we present a theoretical investigation of the electric field effect on the magnetic anisotropy of the Fe3GeTe2 monolayer using the first-principles approach. The calculated magnetic anisotropy energy exhibits strongly oscillating behavior at the electron-doping side, in strong contrast to the hole-doping side. The significant variation of the magnetic anisotropy energy vs electron doping concentration agrees well with experimental results. While the rigid-band approximation works well at the hole-doping side, electron doping induces significant changes in the electronic structure near the Fermi energy. The analysis of the electronic structure shows that the occupation and splitting of the Te(pz)-Fe(dz2) bond states play a critical role in modifying the magnetic anisotropy.

Superfluid stiffness in cuprates: Effect of Mott transition and phase competition

Superfluid stiffness $\rho_s$ is a defining characteristic of the superconducting state, allowing phase coherence and supercurrent. It is accessible experimentally through the penetration depth. Coexistence of $d$-wave superconductivity with other phases in underdoped cuprates, such as antiferromagnetism (AF) or charge-density waves (CDW), may drastically alter $\rho_s$. To shed light on this physics, the zero-temperature value of $\rho_s=\rho_{zz}$ along the $c$-axis was computed for different values of Hubbard interaction $U$ and different sets of tight-binding parameters describing the high-temperature superconductors YBCO and NCCO. We used Cellular Dynamical Mean-Field Theory for the one-band Hubbard model with exact diagonalization as impurity solver and state-of-the-art bath parametrization. We conclude that Mott physics plays a dominant role in determining the superfluid stiffness on the hole-doped side of the phase diagram. On the electron-doped side, antiferromagnetism wins over superconductivity near half-filling. But upon approaching optimal electron-doping, homogeneous coexistence between superconductivity and antiferromagnetism causes the superfluid stiffness to drop sharply. Hence, on the electron-doped side, it is competition between antiferromagnetism and $d$-wave superconductivity that plays a dominant role in determining the value of $\rho_{zz}$ near half-filling. At large overdoping, $\rho_{zz}$ behaves in a more BCS-like manner in both the electron- and hole-doped cases. We comment on some qualitative implications of these results for the superconducting transition temperature.

Phase stiffness in an antiferromagnetic superconductor

We analyze the suppression of the phase stiffness in a superconductor by antiferromagnetic order. The analysis is based on a general expression for the phase stiffness in a mean-field state with coexisting spin-singlet superconductivity and spiral magnetism. Neel order is included as a special case. Close to half-filling, where the pairing gap is much smaller than the magnetic gap, a simple formula for the phase stiffness in terms of magnetic quasi-particle bands is derived. The phase stiffness is determined by charge carriers in small electron or hole pockets in this regime. The general analysis is complemented by a numerical calculation for the two-dimensional Hubbard model with nearest and next-to-nearest neighbor hopping amplitudes at a moderate interaction strength. The resulting phase stiffness exhibits a striking electron-hole asymmetry. In the ground state, it is larger than the pairing gap on the hole-doped side, and smaller for electron doping. Hence, in the hole-doped regime near half-filling the ground state pairing gap sets the scale for the Kosterlitz-Thouless temperature T_c^{KT}, while in the slightly electron-doped regime T_c^{KT} is determined essentially by the ground state phase stiffness.

Superconductivity on Hole-Doping Side of (La0.5-xNa0.5+x)Fe2As2.

(La0.5-xNa0.5+x)Fe2As2 ((La,Na)122) is an interesting system in the sense that either electrons (x < 0) or holes (x > 0) can be doped into the Fe2As2 layers, simply by changing the composition value x. However, only nonbulk superconducting samples (single crystals) with x = 0.1 have been synthesized to date. Here, we successfully synthesize polycrystalline samples with a wide hole-doping composition range of 0 ≤ x ≤ 0.35 via a conventional solid-state reaction, by tuning the reaction temperature according to x. The parent compound, (La0.5Na0.5)Fe2As2 (x = 0), is a nonsuperconductor with a resistivity anomaly at 130 K due to structural and antiferromagnetic transitions. We find that the temperature of the resistivity anomaly decreases with increasing x and that bulk superconductivity emerges for 0.15 ≤ x ≤ 0.35. The maximum transition temperature is 27.0 K, for x = 0.3. An electronic phase diagram for the hole-doping side is constructed. However, electron-doped samples (x < 0) cannot be synthesized; thus, the other half of the electronic phase diagram of (La,Na)122 requires resolution to study the electron-hole symmetry in Fe-based superconductors.

Interaction between counter-propagating quantum Hall edge channels in the 3D topological insulator BiSbTeSe2

The quantum Hall effect is studied in the topological insulator BiSbTeSe$_2$. By employing top- and back-gate electric fields at high magnetic field, the Landau levels of the Dirac cones in the top and bottom topological surface states can be tuned independently. When one surface is tuned to the electron-doped side of the Dirac cone and the other surface to the hole-doped side, the quantum Hall edge channels are counter-propagating. The opposite edge mode direction, combined with the opposite helicities of top and bottom surfaces, allows for scattering between these counter-propagating edge modes. The total Hall conductance is integer valued only when the scattering is strong. For weaker interaction, a non-integer quantum Hall effect is expected and measured.

Momentum and Doping Dependence of Spin Excitations in Electron-Doped Cuprate Superconductors

Superconductivity in copper oxides emerges on doping holes or electrons into their Mott insulating parent compounds. The spin excitations are thought to be the mediating glue for the pairing in superconductivity. Here the momentum and doping dependence of the dynamical spin response in the electron-doped cuprate superconductors is studied based on the kinetic-energy-driven superconducting mechanism. It is shown that the dispersion of the low-energy spin excitations changes strongly upon electron doping, however, the hour-glass-shaped dispersion of the low-energy spin excitations appeared in the hole-doped side is absent in the electron-doped case due to the electron-hole asymmetry. In particular, the commensurate resonance appears in the superconducting-state with the resonance energy that correlates with the dome-shaped doping dependence of the superconducting gap. Moreover, the spectral weight and dispersion of the high-energy spin excitations in the superconducting-state are comparable with those in the corresponding normal-state, indicating that the high-energy spin excitations do not play an important part in the pair formation.

Doping and Raman scattering of strong spin-orbit-coupling compound Sr2-xLaxIrO4

Novel unconventional physical phenomena, such as metal-insulator transition, high temperature superconductivity, colossal magneto-resistance and quantum criticality, are usually found in transition metal oxides (TMOs) with layered perovskite structures. Great success has been achieved in 3d TMOs, in which the localized 3d states yield strongly correlated narrow bands with a large on-site Coulomb repulsion U and a small band width W. Anomalous insulating behaviors are reported in the 5d TMOs, such as Sr2IrO4 system, which is surprising since the 5d TMOs are usually considered as weakly correlated wide band systems with largely reduced on-site Coulomb repulsion U due to delocalized 5d states. The crystal structure of Sr2IrO4 consists of two-dimensional (2D) IrO2 layers, similar to the parent compound La2CuO4 of the cuprates. Theoretically, a variational Monte Carlo study of Sr2IrO4 suggests that d-wave like superconductivity may appear but only within a narrow region of electron doping. In contrast, an s±*-wave phase is established for hole doping deduced from functional renormalization group, and triggered by spin fluctuations within and across the two conduction bands. Moreover, triplet p-wave pairing state with relatively high transition temperature emerges on the hole-doped side when the Hund's coupling is comparable to spin-orbit coupling. Several experiments are tried to search for the predicted unconventional superconductivity due to both electron-and hole-doping. However, to the best of our knowledge, it has not been found yet in the carrier-doped Sr2IrO4 system. Hence, more detailed studies are needed to explore the potential superconductivity.#br#A series of La doped Sr2-xLaxIrO4 samples is synthesized based on solid state reaction method. The evolution of the crystal structure is studied by the X-ray diffraction, scanning electron microscopy, together with the Raman spectrum. It is found that the crystal constant of the c-axis decreases with increasing doping level as well as the apical Ir—O1 bond length, indicating the lattice construction. Moreover, the distortion of the IrO6 octahedron reduces with increasing doping level. Therefore, blue shift occurs of the Raman scattering peaks. The temperature dependence of the Raman spectrum is also studied. It is found that the frequencies of the A1g and B1g vibration modes increase with temperature decreasing and an abnormal jump occurs around 110 K, which is believed to be correlated with the structural change and the magnetic transition around this temperature.

Odd-parity triplet superconducting phase in multiorbital materials with a strong spin-orbit coupling: application to doped Sr₂IrO₄.

We explore possible superconducting states in t(2g) multiorbital correlated electron systems with strong spin-orbit coupling (SOC). In order to study such systems in a controlled manner, we employ large-scale dynamical mean-field theory (DMFT) simulations with the hybridization expansion continuous-time quantum Monte Carlo (CTQMC) impurity solver. To determine the pairing symmetry, we go beyond the local DMFT formalism using parquet equations to introduce the momentum dependence in the two-particle vertex and correlation functions. In the strong SOC limit, a singlet, d-wave pairing state in the electron-doped side of the phase diagram is observed at weak Hund's coupling, which is triggered by antiferromagnetic fluctuations. When the Hund's coupling is comparable to SOC, a twofold degenerate, triplet p-wave pairing state with relatively high transition temperature emerges in the hole-doped side of the phase diagram, which is associated with enhanced charge fluctuations. Experimental implications to doped Sr2IrO4 are discussed.

Inhomogeneous state of the extendedt-Jmodel on a square lattice: A variational Monte Carlo and Gutzwiller approximation study

We carry out the variational Monte Carlo calculation to examine spatially inhomogeneous states in hole- and electron-doped cuprates. By using Gutzwiller approximation, we consider the excitations, arising from charge density, spin density, and pair field, of the mean-field ground state of the $t$-$J$ model. It leads to the stripe patterns we have found numerically in a generalized $t$-$J$-type model including mass renormalization from the electron-phonon coupling. In the hole-doped side, a robust $d$-wave superconducting order results in the formation of the half-doped antiferromagnetic resonating-valence-bond (AF-RVB) stripes shown by the well-known Yamada plot. On the other hand, due to a long-range AF order in electron-doped materials, a stripe structure with the ``in-phase'' magnetic domain (IPMD) is obtained in the underdoped regime instead of the AF-RVB stripe. The IPMD stripe with the largest period permitted by lattice size is stabilized near the underdoped region and it excludes the Yamada plot from electron-doped cases. Based on finite lattice size to which we can reach, the existence of IPMD stripes may imply an electronic phase separation into an electron-rich and an insulating half-filled AF long-range ordered domains in electron-doped compounds.

Momentum-space anisotropy and pseudogaps: A comparative cluster dynamical mean-field analysis of the doping-driven metal-insulator transition in the two-dimensional Hubbard model

Cluster dynamical mean field calculations based on 2, 4, 8 and 16 site clusters are used to analyze the doping-driven metal-insulator transition in the two dimensional Hubbard model. Comparison of results obtained on different clusters enables a determination of those aspects of the physics that are common to all clusters and permits identification of artifacts associated with particular cluster geometries. A modest particle-hole asymmetry in the underlying band structure is shown to lead to qualitatively different behavior on the hole doped side than on the electron doped side. For particle-hole asymmetry of the sign and magnitude appropriate to high-$T_c$ cuprates, the approach to the insulator from the hole-doping side is found to proceed in two stages from a high-doping region where the properties are those of a Fermi liquid with moderately renormalized parameters and very weak momentum dependence. As doping is reduced the system first enters an intermediate doping regime where the Fermi liquid renormalizations are larger and the electron self energy varies significantly around the Fermi surface and then passes to a small doping regime characterized by a gap in some regions of the Fermi surface but gapless behavior in other regions. On the electron doped side the partially gapped regime does not occur, and the momentum dependence of the electron self energy is less pronounced. Implications for the high-$T_c$ cuprates and for the use of cluster dynamical mean field methods in wider classes of problems are discussed.