Emergent Superfluidity of Hard-Core Excitons in Single-Layer Breathing-Kagome Nb$_3$Te$_x$Cl$_{8-x}$

TL;DR

This work develops a microscopic theory for emergent superfluidity of hard-core dark excitons on a triangular lattice by mapping a large-$U$ Bose--Hubbard model onto an effective XXZ spin-$\tfrac{1}{2}$ Hamiltonian, with $H_{\mathrm{XXZ}} = - J_{xy} \sum_{\langle ij \rangle}(S_i^{+}S_j^{-}+S_i^{-}S_j^{+}) + J_z \sum_{\langle ij \rangle} S_i^{z} S_j^{z}$, $J_{xy}= t$, $J_z= -4 t^{2}/U$, and $n=\tfrac{1}{2}(1+\cos\theta)$. The authors connect lattice-scale exciton dynamics to continuum critical behavior via a Landau--Ginzburg description and demonstrate a Berezinskii--Kosterlitz--Thouless transition governed by the microscope-derived superfluid stiffness, which scales as $\rho_s^{(0)}(n)= A t\, n(1-n)$ with $A=2\sqrt{3}$ and renormalizes to $\rho_s^{\mathrm{eff}}(T_{\mathrm{BKT}})= f(0)\rho_s^{(0)}(n)$ with $f(0)\approx 0.1$--$0.3$. The study applies this framework to single-layer Nb$_3$TeCl$_7$, showing vacancy-induced mobility of excitons on a breathing kagome lattice, predicting a BKT transition temperature in the tens of kelvin range (e.g., $T_{\mathrm{BKT}} \sim (\pi \sqrt{3}/k_B) t\, f(0)\, n(1-n)$ with $t \approx 22\,\mathrm{meV}$). The findings offer a concrete route to realizing and probing a two-dimensional exciton superfluid in a single-layer material, with potential implications for low-power spintronics and neutral transport channels.

Abstract

We develop a microscopic theory of superfluidity for hard-core dark excitons on the triangular lattice by mapping the large-$U$ Bose--Hubbard model to an effective XXZ spin-$\frac{1}{2}$ Hamiltonian including virtual hopping processes. Within this framework, we identify the superfluid phase that emerges between the two Mott-insulating endpoints at fillings 0 and 1, and derive its mean-field structure via a canted-spin solution. We then construct the corresponding continuum Landau-Ginzburg (LG) functional and analyze phase fluctuations and vortex dynamics. In two dimensions, the superfluid--normal transition is shown to be governed by a Berezinskii--Kosterlitz--Thouless (BKT) mechanism with a stiffness determined by microscopic parameters. Our results provide a unified description connecting lattice-scale exciton dynamics to continuum critical behavior in triangular geometries.

Figures (2)

• Figure 1: a) Top and side view of Nb$_3$TeCl$_7$, shaded grey (orange) region (rhombus) is the unit cell (Brillouin zone) of Nb$_3$TeCl$_7$ consisting of 3 Nb (dark green balls) 1 Te (orange balls) and 7 Cl (light green balls) atoms. The breathing kagome lattice is built from Nb atoms forming irregular hexagons enclosed by two inequivalent sets of equilateral triangles with different areas (shaded red and blue). SL Nb$_3$TeCl$_7$ has C$_{3v}$ symmetry. b) GW band structure of SL Nb$_3$TeCl$_7$, showing substantial increase in the electronic band gap E$_g^{\textrm{GW}}=$2.7 eV as compared with the PBE band gap of E$_g^{\textrm{PBE}}=$0.97 eV. Blue (red) colored lines show flat bands obtained through GW (PBE) -calculations. Black solid lines correspond to the continuum of states with dispersion.
• Figure 2: a) The absorption spectra of SL Nb$_3$TeCl$_7$, shown without (red curve) and with (blue curve) electron-hole interactions, exhibit a prominent peaks at 1.075 eV and 1.75 eV. b) The oscillator strength f$_{ij}$ as a function of energy reveals key insights into the system's excitonic properties. The first two bright exciton peaks can be seen at 1.075 eV and 1.75 eV with binding energies 1.59 eV and 0.68 eV, respectively.