Enhanced Anharmonicity by Forming Low-Symmetry Off-Center Phase: The Case of Two-Dimensional Group-IB Chalcogenides

Abstract

Enhanced anharmonicity is required to achieve many interesting phenomena in thermoelectricity, superconductivity, ferroelectricity, etc. Here, we propose a novel mechanism for enhancing anharmonicity by forming the low-symmetry off-center ground state, such as the s­(II) phase, in two-dimensional A IB 2X chalcogenides (A IB = Cu, Ag and Au; X = S, Se, and Te). In this system, the in-plane rotational phonon mode introduces a much stronger anharmonicity in the distorted s­(II) phase than in the nondistorted s­(I) phase. We show that the stabilities of the s­(I) and s­(II) phases arise from the ionicity and the ionic size; for example, the low ionicity and the small ionic size favor the s­(II) phase. We further demonstrate that the anharmonicity can be tuned by controlling the strain-induced s­(II)-to-s­(I) phase transition, which explains the anomalous lattice thermal conductivity. Our work relates anharmonicity to symmetry-breaking structural distortion and widens the ways to design excellent thermoelectric materials.

Tunable Intrinsic Phonon Mode versus Anomalous Thermal Transport in Two-Dimensional Strongly Anharmonic Group IB Chalcogenides A2IBSe1/2Te1/2 (AIB = Cu, Ag, or Au)

“…This is ascribed to the high covalency and the small size of the metal atom of the group IB compounds. 15 Here, our main purpose is to elucidate how to further tune κ L and thus to improve the thermoelectric performance by controlling the anharmonicity in 2D A 2 IB Se 1/2 Te 1/2 . The T −1 relationship of κ L , based on the harmonic phonons at 0 K and lowest-order perturbative treatment, is generally applicable in high-κ L materials at high temperatures 16 and fails in describing the thermal transport in strongly anharmonic systems.…”

“…44 First, when the bondstrength difference is larger, the anharmonicity is usually stronger. To verify this point, we refer to 2D A 2 IB X systems, 15 where the bond-strength difference between adjacent bonds is To further explore the relationship between the anharmonicity and the B 2 mode, we focus on the lattice thermal conductivities κ 3+4ph , including the 3ph and 4ph scatterings at different metal-atom masses, temperatures, and strains in the s(I) and s(II) phases. κ L = Σ λ C λ ν λ 2 τ λ , where C λ is the heat capacity per mode, ν λ is the group velocity, and phonon relaxation time τ λ is the inverse of the scattering rate.…”

“…Using in-plane rotational vibration as an example, the E versus Δθ curve is described as E ( Δ θ ) = E ( θ 0 ) + 1 2 Ë ( θ − θ 0 ) 2 + 1 6 E⃛ ( θ − θ 0 ) 3 + ... where equilibrium angle θ 0 is <180° in the s(II) phase, as listed in Table S1. The first two terms are fitted harmonic energy E harm near the equilibrium position, and the higher terms reflect the perturbed anharmonic effect. − The anharmonicity of the in-plane rotational mode obeys the trend Au 2 Se 1/2 Te 1/2 < Ag 2 Se 1/2 Te 1/2 < Cu 2 Se 1/2 Te 1/2 , which is from competition between the ionicity of the chemical bond and the ionic size of the metal atom as described in the dimensionless parameter b = f i + r A / r X . Ionicity f i is comparable in three alloy systems because of the close electronegativities of the Cu, Ag, and Au atoms; therefore, the ionic size is more decisive in the anharmonicity.…”

“…43−45 The anharmonicity of the in-plane rotational mode obeys the trend Au 2 Se 1/2 Te 1/2 < Ag 2 Se 1/2 Te 1/2 < Cu 2 Se 1/2 Te 1/2 , which is from competition between the ionicity of the chemical bond and the ionic size of the metal atom as described in the dimensionless parameter b = f i + r A /r X . 15 Ionicity f i is comparable in three alloy systems because of the close electronegativities of the Cu, Ag, and Au atoms; 26 therefore, the ionic size is more decisive in the anharmonicity. The smaller ionic size of the metal atom usually favors the stronger Coulomb repulsion between adjacent bonds and thus the stronger anharmonicity.…”

“…Due to the shallow d orbital, group IB chalcogenide semiconductors have attracted a great deal of attention because of their excellent properties in terms of thermoelectricity, optoelectronics, etc. − For instance, Cu 2 S, as a promising thermoelectric material, exhibits high carrier mobility and superior oxidation resistance. , Bulk α-, β-, and γ-Cu 2 S have been synthesized at different temperatures, as have two-dimensional (2D) α-Ag 2 S, β-Cu 2 S, and γ-Cu 2 S. − Recently, the s­(I) ( P 4/ nmm ) and s­(II) ( P 4212) phases are proposed to be more energetically favorable in 2D group IB chalcogenides A 2 IB X (A IB = Cu, Ag, or Au; X = O, S, Se, or Te). , The low-symmetry off-center s­(II) phase is formed to reduce the lattice thermal conductivity (κ L ), compared with the s­(I) phase. This is ascribed to the high covalency and the small size of the metal atom of the group IB compounds . Here, our main purpose is to elucidate how to further tune κ L and thus to improve the thermoelectric performance by controlling the anharmonicity in 2D A 2 IB Se 1/2 Te 1/2 .…”