<p>The phonon-drag effect in monolayer graphene (MLG) and double-layer MLG–MLG systems has attracted considerable attention due to its potential for high-performance thermoelectric applications. In this double-layer MLG–GaAs–MLG structure, GaAs serves as a spacer layer that not only separates the two graphene sheets but also contributes piezoelectric phonons, thereby strongly influencing the phonon-drag thermoelectric effect. In this work, we investigate the phonon-drag thermoelectric coefficient in a double-layer MLG–GaAs–MLG structure, taking into account both deformation potential (acDP) and piezoelectric (acPE) acoustic phonon scattering mechanisms, as well as interlayer Coulomb screening within the random phase approximation (RPA) on different dielectric substrates (h-BN/Al<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$_2$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>2</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>O<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$_3$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>3</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>/HfO<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$_2$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>2</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>). The results reveal that at low temperatures, <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$S_g$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mi>g</mi> </msub> </math></EquationSource> </InlineEquation> is dominated by acPE, while at higher temperatures, acDP increases superlinearly with <i>T</i> up to the Bloch–Grüneisen temperature and becomes the primary mechanism, then gradually saturates above <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$T_{\textrm{BG}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mtext>BG</mtext> </msub> </math></EquationSource> </InlineEquation>. The density dependence exhibits two regimes: at <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$T \ll T_{\textrm{BG}}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>T</mi> <mo>≪</mo> <msub> <mi>T</mi> <mtext>BG</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$S_g$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mi>g</mi> </msub> </math></EquationSource> </InlineEquation> decreases with increasing carrier density due to the Bloch–Grüneisen effect and enhanced screening; in contrast, for <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$T > T_{\textrm{BG}}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>T</mi> <mo>></mo> <msub> <mi>T</mi> <mtext>BG</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$S_g$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mi>g</mi> </msub> </math></EquationSource> </InlineEquation> increases with density owing to the enlarged scattering phase space and the dominance of acDP. With increasing interlayer spacing, <InlineEquation ID="IEq10"> <EquationSource Format="TEX">$S_g$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mi>g</mi> </msub> </math></EquationSource> </InlineEquation> increases progressively and saturates when <InlineEquation ID="IEq11"> <EquationSource Format="TEX">$qd \gtrsim 1 \; (\text {with } q \sim k_{F})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mi>d</mi> <mo>≳</mo> <mn>1</mn> <mspace width="0.277778em" /> <mo stretchy="false">(</mo> <mtext>with</mtext> <mspace width="0.333333em" /> <mi>q</mi> <mo>∼</mo> <msub> <mi>k</mi> <mi>F</mi> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> approaching the monolayer limit. Under asymmetric density conditions, <InlineEquation ID="IEq12"> <EquationSource Format="TEX">$S_g$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mi>g</mi> </msub> </math></EquationSource> </InlineEquation> shifts toward the layer with higher conductivity, while dielectric environment effects are evident in the sequence <InlineEquation ID="IEq13"> <EquationSource Format="TEX">$S_g^{\text {HfO}_2}> S_g^{\text {Al}_2\text {O}_3} > S_g^{h\text {-BN}}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>S</mi> <mi>g</mi> <msub> <mtext>HfO</mtext> <mn>2</mn> </msub> </msubsup> <mo>></mo> <msubsup> <mi>S</mi> <mi>g</mi> <mrow> <msub> <mtext>Al</mtext> <mn>2</mn> </msub> <msub> <mtext>O</mtext> <mn>3</mn> </msub> </mrow> </msubsup> <mo>></mo> <msubsup> <mi>S</mi> <mi>g</mi> <mrow> <mi>h</mi> <mtext>-BN</mtext> </mrow> </msubsup> </mrow> </math></EquationSource> </InlineEquation>, though the differences diminish as the MLG interlayer spacing increases. These findings provide a comprehensive understanding of the phonon-drag mechanism in MLG–GaAs–MLG heterostructures and suggest effective thermoelectric tuning through carrier density engineering, interlayer spacing, and dielectric design, which are promising for the development of graphene-based thermoelectric devices.</p>

Screening and Structural Control of Phonon-Drag Thermoelectricity in MLG–GaAs–MLG

期刊论文
发表日期：

2025年10月30日

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Truong Van Tuan,
Tran Trong Tai,
Nguyen Duy Vy

摘要

The phonon-drag effect in monolayer graphene (MLG) and double-layer MLG–MLG systems has attracted considerable attention due to its potential for high-performance thermoelectric applications. In this double-layer MLG–GaAs–MLG structure, GaAs serves as a spacer layer that not only separates the two graphene sheets but also contributes piezoelectric phonons, thereby strongly influencing the phonon-drag thermoelectric effect. In this work, we investigate the phonon-drag thermoelectric coefficient in a double-layer MLG–GaAs–MLG structure, taking into account both deformation potential (acDP) and piezoelectric (acPE) acoustic phonon scattering mechanisms, as well as interlayer Coulomb screening within the random phase approximation (RPA) on different dielectric substrates (h-BN/Al $_2$ $_{2}$ O $_3$ $_{3}$ /HfO $_2$ $_{2}$ ). The results reveal that at low temperatures, $S_g$ $S_{g}$ is dominated by acPE, while at higher temperatures, acDP increases superlinearly with T up to the Bloch–Grüneisen temperature and becomes the primary mechanism, then gradually saturates above $T_{\textrm{BG}}$ $T_{BG}$ . The density dependence exhibits two regimes: at $T \ll T_{\textrm{BG}}$ $T ≪ T_{BG}$ , $S_g$ $S_{g}$ decreases with increasing carrier density due to the Bloch–Grüneisen effect and enhanced screening; in contrast, for $T > T_{\textrm{BG}}$ $T > T_{BG}$ , $S_g$ $S_{g}$ increases with density owing to the enlarged scattering phase space and the dominance of acDP. With increasing interlayer spacing, $S_g$ $S_{g}$ increases progressively and saturates when $qd \gtrsim 1 \; (\text {with } q \sim k_{F})$ $q d ≳ 1 (with q \sim k_{F})$ approaching the monolayer limit. Under asymmetric density conditions, $S_g$ $S_{g}$ shifts toward the layer with higher conductivity, while dielectric environment effects are evident in the sequence $S_g^{\text {HfO}_2}> S_g^{\text {Al}_2\text {O}_3} > S_g^{h\text {-BN}}$ $S_{g}^{{HfO}_{2}} > S_{g}^{{Al}_{2} O_{3}} > S_{g}^{h -BN}$ , though the differences diminish as the MLG interlayer spacing increases. These findings provide a comprehensive understanding of the phonon-drag mechanism in MLG–GaAs–MLG heterostructures and suggest effective thermoelectric tuning through carrier density engineering, interlayer spacing, and dielectric design, which are promising for the development of graphene-based thermoelectric devices.