Strong competition between $\Theta_{II}$-loop-current order and $d$-wave charge order along the diagonal direction in a two-dimensional hot spot model - Archive ouverte HAL Access content directly
Journal Articles Physical Review B: Condensed Matter and Materials Physics (1998-2015) Year : 2015

## Strong competition between $\Theta_{II}$-loop-current order and $d$-wave charge order along the diagonal direction in a two-dimensional hot spot model

Thomas Kloss
• Function : Author
Xavier Montiel
• Function : Author
Hermann Freire
• Function : Correspondent author
• PersonId : 984264

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Catherine Pépin
• Function : Author

#### Abstract

We study the fate of the so-called $\Theta_{II}$-loop-current order that breaks both time-reversal and parity symmetries in a two-dimensional hot spot model with antiferromagnetically mediated interactions, using Fermi surfaces relevant to the phenomenology of the cuprate superconductors. We start from a three-band Emery model describing the hopping of holes in the CuO$_{2}$ plane that includes two hopping parameters $t_{pp}$ and $t_{pd}$, local on-site Coulomb interactions $U_{d}$ and $U_{p}$ and nearest-neighbor $V_{pd}$ couplings between the fermions in the copper [Cu$(3d_{x^{2}-y^{2}})$] and oxygen [O$(2p_{x})$ and O$(2p_{y})$] orbitals. By focusing on the lowest-energy band, we proceed to decouple the local interaction $U_{d}$ of the Cu orbital in the spin channel using a Hubbard-Stratonovich transformation to arrive at the interacting part of the so-called spin-fermion model. We also decouple the nearest-neighbor interaction $V_{pd}$ to introduce the order parameter of the $\Theta_{II}$-loop-current order. In this way, we are able to construct a consistent mean-field theory that describes the strong competition between the composite order parameter made of a quadrupole-density-wave and $d$-wave pairing fluctuations proposed in Efetov \emph{et al.} [Nat. Phys. \textbf{9}, 442 (2013)] with the $\Theta_{II}$-loop-current order parameter that is argued to be relevant for explaining important aspects of the physics of the pseudogap phase displayed in the underdoped cuprates.

#### Domains

Physics [physics]

### Dates and versions

cea-01339333 , version 1 (29-06-2016)
cea-01339333 , version 2 (18-10-2022)

### Identifiers

• HAL Id : cea-01339333 , version 2
• DOI :

### Cite

Vanuildo S. de Carvalho, Thomas Kloss, Xavier Montiel, Hermann Freire, Catherine Pépin. Strong competition between $\Theta_{II}$-loop-current order and $d$-wave charge order along the diagonal direction in a two-dimensional hot spot model. Physical Review B: Condensed Matter and Materials Physics (1998-2015), 2015, 92 (7), pp.075123. ⟨10.1103/PhysRevB.92.075123⟩. ⟨cea-01339333v2⟩

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