#
Absence of Superconductivity in the Hubbard Dimer Model for κ-(BEDT-TTF)_{2}X

^{1}

^{2}Center for Computational Sciences, Mississippi State University, Starkville, MS 39762, USA

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Methods

## 3. Results

## 4. Discussion

## Author Contributions

## Funding

## Data Availability Statements

## Conflicts of Interest

## References

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**Figure 1.**The dimer lattice we consider. Thick lines are the intra-dimer hopping ${t}_{d}$, thin lines are the inter-dimer hopping t, and dashed lines are the frustrating bond ${t}^{\prime}$. Boundary conditions in our DMRG calculations are open in x and periodic in y.

**Figure 2.**Dimer spin-spin correlations $\langle {S}_{z}^{d}(1,j)\rangle $ for a 16 × 4 lattice between the first dimer on chain 1 and dimer j on chain 2, multiplied by ${(-1)}^{j}$, the expected sign for Néel AFM. (

**a**) ${t}^{\prime}=0.2$. The inset shows the U dependence of a single spin-spin correlation at long distance. Néel AFM order is present at ${t}^{\prime}$ for $U\u2a868$. (

**b**) ${t}^{\prime}=0.4$. Here, we find no AFM order.

**Figure 3.**Pair–pair correlation for ${t}^{\prime}=0.2$ for parallel-oriented n.n. pairs on a 16 × 4 lattice. (

**a**) Pair-pair correlation ${P}_{\left|\right|}\left(r\right)$ for n.n. x-axis pairs on chain 1 (

**b**) ${P}_{\left|\right|}\left(r\right)$ for n.n. x-axis pairs on chains 1 and 2 (

**c**) ${P}_{\left|\right|}\left(r\right)$ for n.n. x-axis pairs on chains 1 and 3. In (

**a**–

**c**), r is the center-to-center pair distance. In (

**a**) we show the function ${r}^{-1}$ for comparison as the dashed curve. In panels (

**d**) we plot the U dependence of the average long-range correlation $\overline{{P}_{\left|\right|}}$ (see text) for the chain 1—chain 1 correlations in (

**a**); panels (

**e**,

**f**) are similar for chain 1—chain 2 and chain 1—chain 3 correlations, respectively.

**Figure 4.**Panels (

**a**–

**f**) are the same as in Figure 3 except that the pair-pair correlation ${P}_{\perp}\left(r\right)$ is for the perpendicular orientation of pairs. Note that in (

**d**–

**f**), ${\overline{P}}_{\perp}$ is negative, with decreasing magnitude as U increases. ${\overline{P}}_{\perp}$ in (

**e**) is strongly affected by shorter-range correlations which lead to the unusual U dependence (see text).

**Figure 7.**Pair–pair correlations for ${t}^{\prime}$ = 0.4 for parallel-oriented n.n. pairs on chain 1. In (

**a**) points connected with solid (dashed) lines are for a 16 × 4 (32 × 4) lattice. For comparison we show the power law functions ${r}^{-1}$ and ${r}^{-2}$. In (

**b**), the U dependence of the average long-range correlation ${\overline{P}}_{\left|\right|}$ for both lattices.

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**MDPI and ACS Style**

Roy, D.; Clay, R.T.; Mazumdar, S.
Absence of Superconductivity in the Hubbard Dimer Model for *κ*-(BEDT-TTF)_{2}X. *Crystals* **2021**, *11*, 580.
https://doi.org/10.3390/cryst11060580

**AMA Style**

Roy D, Clay RT, Mazumdar S.
Absence of Superconductivity in the Hubbard Dimer Model for *κ*-(BEDT-TTF)_{2}X. *Crystals*. 2021; 11(6):580.
https://doi.org/10.3390/cryst11060580

**Chicago/Turabian Style**

Roy, Dipayan, R. Torsten Clay, and Sumit Mazumdar.
2021. "Absence of Superconductivity in the Hubbard Dimer Model for *κ*-(BEDT-TTF)_{2}X" *Crystals* 11, no. 6: 580.
https://doi.org/10.3390/cryst11060580