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arXiv:2404.16770

Pseudogap phase as fluctuating pair density wave

Zheng-Yuan Yue, Zheng-Tao Xu, Shuo Yang, Zheng‐Cheng Gu

Published Apr 25, 2024• 0 citations
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Abstract

The physical nature of pseudogap phase is one of the most important and intriguing problems towards understanding the key mechanism of high temperature superconductivity in cuprates. Theoretically, the square-lattice $t$-$J$ model is widely believed to be the simplest toy model that captures the essential physics of cuprate superconductors. We employ the Grassmann tensor product state approach to investigate uniform states in the underdoped ($δ\lesssim 0.1$) region. In addition to the previously known uniform $d$-wave state, we discover a strongly fluctuating pair density wave (PDW) state with wave vector $Q = (π, π)$. This fluctuating PDW state weakly breaks the $C_4$ rotational symmetry of the square lattice and has a lower or comparable energy to the $d$-wave state (depending on doping and the $t/J$ ratio), making it a promising candidate state for describing the pseudogap phase.

DOI
10.48550/arxiv.2404.16770

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The physical nature of pseudogap phase is one of the most important and intriguing problems towards understanding the key mechanism of high temperature superconductivity in cuprates. Theoretically, the square-lattice ttt-JJJ model is widely believed to be the simplest toy model that captures the essential physics of cuprate superconductors. We employ the Grassmann tensor product state approach to investigate uniform states in the underdoped (δ≲0.1δ\lesssim 0.1δ≲0.1) region. In addition to the previously known uniform ddd-wave state, we discover a strongly fluctuating pair density wave (PDW) state with wave vector Q=(π,π)Q = (π, π)Q=(π,π). This fluctuating PDW state weakly breaks the C4C_4C4​ rotational symmetry of the square lattice and has a lower or comparable energy to the ddd-wave state (depending on doping and the t/Jt/Jt/J ratio), making it a promising candidate state for describing the pseudogap phase.
Abstract Over the last two decades, the competing orders in high- T c cuprates have been intensely studied, such as charge density waves (CDW) and pair density waves (PDW), which are thought to play a crucial role in high-temperature superconductivity. Using the t - J model on a square lattice as the simplest model for high- T c cuprates, we employed the fermionic tensor product state (fTPS) method for numerical investigations. Here we show, to the best of our knowledge, several types of PDW states within the low-energy subspace of the t - J model are unveiled thanks to the fermionic cluster update method, alongside the well-known d -wave state. In particular, a kind of C 4 symmetric plaquette PDW state is most likely to survive at low dopings δ < 5%. We believe that the competition among these states in the underdoped region suggests the potential existence of a fluctuating quantum liquid of PDW states, which could serve as a natural starting point for exploring the pseudogap phase and understanding the key mechanisms of d-wave superconductivity. Furthermore, we discuss the potential experimental implications of our discovery.
Fluctuating Pair Density Wave in Finite-temperature Phase Diagram of the ttt-t′t^\primet′ Hubbard Model
The Hubbard model and its extensions are canonical theoretical frameworks for understanding correlated electronic states, including those in high-TcT_cTc​ cuprates. Here, we use state-of-the-art thermal tensor network method to map out the temperature-doping phase diagram of the ttt-t′t^\primet′ Hubbard model. On the electron-doped side, we find a ddd-wave superconducting (dSC) regime, supporting the scenario of high-TcT_cTc​ superconductivity. In contrast, on the hole-doped side, no robust dSC phase is detected. Instead, a finite-temperature regime dominated by strong pair-density-wave (PDW) fluctuations emerges, which may eventually give way to charge density wave order upon further cooling. The PDW state exhibits inter-arc pairing with net momentum near (0,π)(0, π)(0,π), distinct from the zero-momentum pairing in conventional dSC. Furthermore, these fluctuating PDW states occupy the lower portion of the pseudogap regime on the hole-doped side. We provide a comprehensive finite-temperature perspective consistent with previous ground-state studies, shedding new light on pairing instabilities and exotic electronic states in high-TcT_cTc​ superconductors.
Abstract In weakly coupled BCS superconductors, only electrons within a tiny energy window around the Fermi energy, EF, form Cooper pairs. This may not be the case in strong coupling superconductors such as cuprates, FeSe, SrTiO3 or cold atom condensates where the pairing scale, EB, becomes comparable or even larger than EF. In cuprates, for example, a plausible candidate for the pseudogap state at low doping is a fluctuating pair density wave, but no microscopic model has yet been found which supports such a state. In this work, we write an analytically solvable model to examine pairing phases in the strongly coupled regime and in the presence of anisotropic interactions. Already for moderate coupling we find an unusual finite temperature phase, below an instability temperature Ti, where local pair correlations have non-zero center-of-mass momentum but lack long-range order. At low temperature, this fluctuating pair density wave can condense either to a uniform d-wave super- conductor or the widely postulated pair-density wave phase depending on the interaction strength. Our minimal model offers a unified microscopic framework to understand the emergence of both fluctuating and long range pair density waves in realistic systems.
We investigate the Hatsugai-Kohmoto (HK) model on a square lattice, which describes both a Mott insulator at half-filling and a non-Fermi liquid phase on doping. Through the solution of this exactly solvable model with the inclusion of pairing interactions, we demonstrate the emergence of strong pair-density-wave (PDW) fluctuations associated with center-of-mass momentum $\mathbf{Q}=(\ensuremath{\pi},\ensuremath{\pi})$ at finite temperatures for low dopings up to a critical doping and intermediate UUU interaction. Furthermore, we also confirm that a superconducting instability appears in the model within a wide regime of interaction UUU and doping parameter xxx. In view of the fact that it has been recently put forward that the metal-insulator transition of the HK model belongs to the same universality class as the Mott transition of the paradigmatic Hubbard model [Huang et al., Nat. Phys. 18, 511 (2022)], our work may thus shed light on an interesting scenario regarding the emergence of a fluctuating PDW phase on doping a Mott insulator, which has been argued to be relevant for understanding the physics of the cuprate superconductors in the underdoped regime.
The Hubbard and closely related t-J models are exciting platforms for unconventional superconductivity (SC). Through state-of-the-art density matrix renormalization group calculations using the grand canonical ensemble, we address open issues regarding the ground-state phase diagram of the extended t-J model on a square lattice in the parameter regime relevant to cuprate superconductors. On large 8-leg cylinders, we demonstrate that the pure t-J model with only nearest-neighbor hoppings and superexchange interactions, for a wide range of doping ( δ = 0.1 to 0.2 ), hosts robust d-wave superconductivity possibly coexisting with weak unidirectional pair density wave. Furthermore, a small next nearest neighbor hopping t 2 suppresses pair and charge density waves, resulting in a uniform d-wave SC phase in both electron- and hole-doped cuprate model systems. Our work validates the t-J model as a proper minimum model for the emergence of superconductivity in cuprate superconductors.
One of the most prominent problems in high temperature superconductivity is the nature of the pseudogap phase in underdoped regimes; particularly important is the role of phase fluctuations. The Gutzwiller-projected BCS Hamiltonian is a useful model for high temperature superconductivity due to an exact mapping to the Heisenberg model at half filling and generally a very close connection to the t-J model at moderate doping. We develop the dynamical mean field theory for the d-wave BCS Hamiltonian with on-site repulsive interaction, UUU, physically imposing the partial Gutzwiller projection. For results, two pseudogap energy scales are identified: one associated with the bare pairing gap for the singlet formation and the other with the local phase coherence. The real superconducting gap determined from sharp coherence peaks in the density of states shows strong renormalization from the bare value due to UUU.