Ubiquitous nematic Dirac semimetal emerging from interacting quadratic band touching systems

Letter

Ubiquitous nematic Dirac semimetal emerging from interacting quadratic band touching systems

Hongyu Lu, Kai Sun, Zi Yang Meng, and Bin-Bin Chen

Phys. Rev. B 109, L081106 – Published 12 February 2024

Abstract

Quadratic band touching (QBT) points are widely observed in two- and three-dimensional (2D and 3D) materials, including bilayer graphene and Luttinger semimetals, and attract significant attention from theory to experiment. However, even in its simplest form, the 2D checkerboard lattice QBT model, the phase diagram characterized by temperature and interaction strength, still remains unknown beyond the weak-coupling regime. Intense debates persist regarding the existence of various interaction-driven insulating states in this system. To address these uncertainties, we employ thermal tensor network simulations, specifically exponential tensor renormalization group and tangent space tensor renormalization group, along with density matrix renormalization group calculations to provide a comprehensive finite-temperature phase diagram for this model and shed light on previous ambiguities. Notably, our findings reveal the emergence of a robust bond-nematic Dirac semimetal phase with distinct thermodynamic properties that set it part from the nematic insulating state and other symmetry-broken states. This previously overlooked feature is found to be ubiquitous in interacting QBT systems. We also discuss the implications of these results for experimental systems such as bilayer graphene and iridate compounds.

Received 1 June 2023
Revised 19 August 2023
Accepted 23 January 2024

DOI:https://doi.org/10.1103/PhysRevB.109.L081106

Physics Subject Headings (PhySH)

Phase diagrams

Dirac semimetal Strongly correlated systems

Density matrix renormalization group Tensor network methods

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Hongyu Lu ¹, Kai Sun^2,*, Zi Yang Meng ^1,†, and Bin-Bin Chen ^1,‡

¹Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
²Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA

^*sunkai@umich.edu
^†zymeng@hku.hk
^‡bchenhku@hku.hk

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 109, Iss. 8 — 15 February 2024

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) The checkerboard lattice with blue (red) dots denoting the A (B) sublattices. (b) The comprehensive ground-state phase diagram. The QBT is denoted by the black dot at the origin, while the red dotted lines represent the paths of simulations. (c)–(f) The real-space signature of the QAH, stripe, SNI, and BNDS phases, respectively. The QAH phase is depicted with arrows indicating the loop currents. In the stripe and SNI phases, large (small) dots represent high (low) electron density. In the BNDS phase, the thickness of the bonds corresponds to the absolute value of the hopping amplitude.
Reuse & Permissions
Figure 2
The $T − V_{2}$ phase diagrams at $V_{1} = 4$ . Plots show (a) the SNI order parameter, (b) BNDS order parameter, (c) QAH structure factor, (d) stripe structure factor, and (e) specific heat $c_{V}$ . The white dashed lines indicate the boundaries between the high-temperature thermal metallic regime and the intermediate-temperature QBT regime, identified using the red circles, which represent the crossover temperature between the high- $T$ and QBT regimes, as illustrated in Figs. 3. The red squares denote the transition temperature between the QBT regime to the low-temperature symmetry-breaking phases.
Reuse & Permissions
Figure 3
The thermodynamic characteristics along the cuts in Fig. 2 as a function of temperature $T$ . With fixed $V_{1} = 4$ , (a1) and (a2) represent SNI at $V_{2} = 1.65$ , (b1) and (b2) represent BNDS at $V_{2} = 1.85$ , (c1) and (c2) represent QAH at $V_{2} = 2.2$ , and (d1) and (d2) represent stripe at $V_{2} = 2.7$ . The first row displays the specific heat, while the second row shows the order parameters or structure factors for each phase. The separation temperature between the low-, intermediate-, and high-temperature regimes is indicated by the black solid lines. The $c_{V} \sim T^{2}$ for BNDS at low temperature is distinctively different from the $c_{V} \sim exp (- Δ / T)$ for the three other phases.
Reuse & Permissions
Figure 4
The $T − V_{2}$ phase diagram with $V_{1} = 6$ , including (a) the site-nematic order, (b) the NNN bond-nematic order, and (c) the structure factor for stripe. (d) Entanglement entropy in the BNDS phase, with a log-scale horizontal axis. (e) With twisted boundary conditions in BNDS, by inserting flux $ϕ$ , the single-particle gap and fitted central charge compared with that of no flux are shown. The corresponding shift of momenta grids is $ϕ / L_{y}$ .
Reuse & Permissions
Figure 5
(a), (b) Mean-field analysis. With increasing site-nematic order $δ$ , the opening of the energy gap is shown in (a) and expectation values of NNN hoppings along the $a_{1}$ ( $a_{2}$ ) directions for two sublattices respectively are shown in (b). (c) DMRG results of the NNN bond order of the BNDS phase throughout the phase diagram. (d) The product of signs of NNN hoppings along two directions with fixed $V_{1} = 4$ , which is $\pm 1$ if the hoppings take the same (opposite) sign(s).
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics