Coexistence of superconductivity with partially filled stripes in the Hubbard model

Chia-Min Chung^1*, Hao Xu², Mingpu Qin⁶, Ulrich Schollwöck⁴, Steven R. White³, Shiwei Zhang⁵

¹Department of Physics, National Sun Yat-sen University, Kaohsiung, Taiwan
²Department of Physics, College of William and Mary, Williamsburg, VA, USA
³Department of Physics and Astronomy, University of California, Irvine, Irvine, CA, USA
⁴Arnold Sommerfeld Center for Theoretical Physics, Ludwig- Maximilians-Universität München, Munich, Germany
⁵Center for Computational Quantum Physics, Flatiron Institute, New York, NY, USA
⁶Key Laboratory of Artificial Structures and Quantum Control, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China

* Presenter:Chia-Min Chung, email:chiaminchung@gmail.com

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 (Tc) superconductivity.

Keywords: high-Tc superconductor, Hubbard model, Tensor network, Quantum Monte Carlo