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arXiv:1607.01770 · Physical review. B./Physical review. B

Charge- 4 e superconductors: A Majorana quantum Monte Carlo study

Yi‐Fan Jiang, Zixiang Li, Steven Allan Kivelson, Hong Yao

Published Jun 6, 2017• 41 citations
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Abstract

Many features of charge-$4e$ superconductors remain unknown because even the ``mean-field Hamiltonian'' describing them is an interacting model. Here we introduce an interacting model to describe a charge-$4e$ superconductor (SC) deep in the superconducting phase and explore its properties using quantum Monte Carlo (QMC) simulations. The QMC is sign-problem-free but only when a Majorana representation is employed. As a function of the chemical potential we observe two sharply-distinct behaviors: a ``strong'' quarteting phase in which charge-$4e$ quartets are tightly bound (like molecules) so that charge-$2e$ pairing does not occur even in the temperature $T\ensuremath{\rightarrow}0$ limit, and a ``weak'' quarteting phase in which a further transition to a charge-$2e$ superconducting phase occurs at a lower critical temperature. Analogous issues arise in a putative ${Z}_{4}$ spin liquid with a pseudo-Fermi surface and other interacting models with composite order parameters. Under certain circumstances, we also identified a stable $T=0$ charge-$4e$ SC phase with gapless nodal quasiparticles. We further discuss possible relevance of our results to various experimental observations in $\frac{1}{8}$-doped LBCO.

DOI
10.1103/physrevb.95.241103

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Many features of charge-4e4e4e superconductors remain unknown because even the mean-field Hamiltonian'' describing them is an interacting model. Here we introduce an interacting model to describe a charge-$4e$ superconductor (SC) deep in the superconducting phase and explore its properties using quantum Monte Carlo (QMC) simulations. The QMC is sign-problem-free but only when a Majorana representation is employed. As a function of the chemical potential we observe two sharply-distinct behaviors: a strong'' quarteting phase in which charge-4e4e4e quartets are tightly bound (like molecules) so that charge-2e2e2e pairing does not occur even in the temperature T\ensuremath→0T\ensuremath{\rightarrow}0T\ensuremath→0 limit, and a ``weak'' quarteting phase in which a further transition to a charge-2e2e2e superconducting phase occurs at a lower critical temperature. Analogous issues arise in a putative Z4{Z}_{4}Z4​ spin liquid with a pseudo-Fermi surface and other interacting models with composite order parameters. Under certain circumstances, we also identified a stable T=0T=0T=0 charge-4e4e4e SC phase with gapless nodal quasiparticles. We further discuss possible relevance of our results to various experimental observations in 18\frac{1}{8}81​-doped LBCO.
The condensation of electron quartets, known as charge-4e superconductivity (SC), represents a novel quantum state of matter beyond the standard paradigm of Cooper pairing. However, concrete microscopic models realizing this phase in two dimensions remain a central challenge. Here, we introduce a non-engineered and sign-problem-free model, unambiguously demonstrating the emergence of a robust and high-temperature charge-4e SC phase using unbiased quantum Monte Carlo simulations. At zero temperature, the phase diagram reveals that charge-4e SC is the primary ground state in the strong-coupling regime. At finite temperature in the absence of charge-2e SC, we identify charge-4e SC through a Berezinskii-Kosterlitz-Thouless transition, marked by a universal jump in the superfluid stiffness consistent with a condensate of charge 4e. Remarkably, the transition temperature Tc increases nearly linearly with interaction strength, providing a robust mechanism for high-Tc quartet superconductivity. Furthermore, spectral analysis reveals a prominent pseudogap above Tc arising from strong phase fluctuations. Our results establish a canonical and numerically exact model system for charge-4e superconductivity, offering crucial guidance for its realization in experimental platforms such as moiré materials and ultracold atomic systems.
Unlike conventional charge-2e superconductors, a charge-4e superconductor exhibits long-range coherence of electron quartets rather than Cooper pairs. Clear zero-temperature realizations of charge-4e superconductivity remain rare. Here, we investigate the zero-temperature phase diagram of the attractive SU(4) Hubbard model with numerically exact, large-scale quantum Monte Carlo (QMC) simulations overcoming major technical hurdles. We identify both charge-2e and charge-4e superconducting phases. Upon increasing interaction, charge-2e correlations are suppressed and eventually vanish, while the charge-4e correlations remain robust and converge with system size, signaling the onset of a quartet-condensed phase. Interestingly, across the charge-2e--charge-4e transition, single electrons remain gapped, while charge-2e correlations exhibit a scaling behavior inconsistent with a conventional Landau description. These features are naturally captured by a fractionalized framework in which the physical charge-2e order parameter is a composite field coupled to an emergent non-Abelian gauge structure. We formulate an Sp(4) gauge-Higgs theory that realizes deconfined quantum pseudocriticality between the Higgs (charge-2e) phase and the confined (charge-4e) phase. The Sp(4) gauge-Higgs theory yields pseudocriticality through a fixed-point collision, and its one-loop collision-point exponents quantitatively track the QMC results. Our results establish charge-4e superconductivity as a bona fide zero-temperature phase, provide a simple model for future studies in a numerically exact framework, and reveal an unconventional route to superconducting criticality.
A charge-4e4e4e superconductor forms due to the condensation of quartets of electrons. While in previous works, the mechanism for the formation of charge-4e4e4e superconductivity has been analyzed in terms of the binding of Cooper pairs in unconventional superconductors, its properties in the fermionic sector have not been studied systematically due to its inherently interacting nature even at the mean-field level. Here we propose a solvable model for a charge-4e4e4e superconductor---a spinful version of the Sachdev-Ye-Kitaev model with an anomalous quartic term. We show that the ground state is gapless and resembles a heavy Fermi liquid. We analytically solve for the superfluid density and show that it is perturbative in the strength of the charge-4e4e4e order parameter, in sharp contrast with a regular (charge-2e2e2e) superconductor. Upon lowering the temperature, we show that the correlation between charge-4e4e4e order and regular interaction terms can drive a first-order phase transition to a charge-2e2e2e superconducting state.
Reliable simulations of correlated quantum systems, including high-temperature superconductors and frustrated magnets, are increasingly desired nowadays to further our understanding of essential features in such systems. Quantum Monte Carlo (QMC) is a unique numerically exact and intrinsically unbiased method to simulate interacting quantum many-body systems. More importantly, when QMC simulations are free from the notorious fermion sign problem, they can reliably simulate interacting quantum models with large system size and low temperature to reveal low-energy physics such as spontaneously broken symmetries and universal quantum critical behaviors. Here, we concisely review recent progress made in developing new sign-problem-free QMC algorithms, including those employing Majorana representation and those utilizing hot-spot physics. We also discuss applications of these novel sign-problem-free QMC algorithms in simulations of various interesting quantum many-body models. Finally, we discuss possible future directions of designing sign-problem-free QMC methods.
We compute transport and thermodynamic properties of a two-band spin-fermion model describing itinerant fermions in two dimensions interacting via Z2{Z}_{2}Z2​ antiferromagnetic quantum critical fluctuations by means of a sign-problem-free quantum Monte Carlo approach. We show that the phase diagram of this model indeed contains a ddd-wave superconducting phase at low enough temperatures. However, a crucial question that arises is whether a non-Fermi-liquid metallic regime exists above Tc{T}_{c}Tc​, exhibiting hallmark strange-metal transport phenomenology. Interestingly, we find that this version of the model describes a non-Fermi-liquid metallic regime that displays an approximately TTT-linear resistivity above Tc{T}_{c}Tc​ for a strong fermion-boson interaction. Using the Nernst-Einstein relation, our QMC results also show that this strange metal phase exhibits a crossover from being characterized by a charge compressibility given approximately by ${\ensuremath{\chi}}_{c}\ensuremath{\sim}1/T$ at high temperatures to being described by a charge diffusivity consistent with the scaling ${D}_{c}\ensuremath{\sim}1/T$ at low temperatures. Therefore, our paper adds support to the view that the Z2{Z}_{2}Z2​ antiferromagnetic spin-fermion model at strong coupling can be considered a minimal model that describes both unconventional superconductivity and strange metallicity, which are fundamentally interconnected in many important strongly correlated quantum materials.
We present recent theoretical results on superconductivity in correlated-electron systems, especially in the two-dimensional Hubbard model and the three-band d-p model. The mechanism of superconductivity in high-temperature superconductors has been extensively studied on the basis of various electronic models and also electron-phonon models. In this study, we investigate the properties of superconductivity in correlated-electron systems by using numerical methods such as the variational Monte Carlo method and the quantum Monte Carlomethod. The Hubbard model is one of basic models for strongly correlated electron systems, and is regarded as the model of cuprate high temperature superconductors. The d-p model is more realistic model for cuprates. The superconducting condensation energy obtained by adopting the Gutzwiller ansatz is in reasonable agreement with the condensation energy estimated for YBa2Cu3O7. We show the phase diagram of the ground state using this method. We have further investigated the stability of striped and checkerboard states in the under-doped region. Holes doped in a half-filled square lattice lead to an incommensurate spin and charge density wave. The relationship of the hole density x and incommensurability δ, δ~x, is satisfied in the lower doping region, as indicated by the variationalMonte Carlocalculations for the two-dimensional Hubbard model. A checkerboard-like charge-density modulation with a roughly period has also been observed by scanning tunneling microscopy experiments in Bi2212 and Na-CCOC compounds. We have performed a variational Monte Carlo simulation on a two-dimensional t-t′-t″- U Hubbard model with a Bi-2212 type band structure and found that the period checkerboard spin modulation, that is characterized by multi Q vectors, is indeed stabilized. We have further performed an investigation by using a quantumMonte Carlomethod, which is a numerical method that can be used to simulate the behavior of correlated electron systems. We present a new algorithm of the quantum Monte Carlo diagonalization that is a method for the evaluation of expectation value without the negative sign problem. We compute pair correlation functions and show that pair correlation is indeed enhanced with hole doping.