<p>We explore the transport behavior of charge carriers in gapped bilayer graphene under a perpendicular magnetic field and electrostatic barriers. Using the Hamiltonian of the four low-energy bands of bilayer graphene, we compute the transmission probability and the associated conductance via the transfer matrix method. Our investigation reveals that altering the gap parameter (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_13840_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Delta\)</EquationSource> </InlineEquation>), the energy (<i>E</i>), the number of magnetic barriers (<i>N</i>) and the magnetic field strength (<i>B</i>) changes the range of incident angles, resulting in a wave-vector filtering effect. These parameters also influence the forbidden zones of transmission and conductance in the magnetic system. A forbidden zone exists for <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_13840_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">\(E&lt;\Delta\)</EquationSource> </InlineEquation>. For a multibarrier structure with <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_13840_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">\(N&gt;2\)</EquationSource> </InlineEquation>, another forbidden zone appears for <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_13840_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">\(E&gt;\Delta\)</EquationSource> </InlineEquation>, along with resonance effects and conductance oscillations as functions of <i>N</i> and <i>E</i>. A strong wave-vector filtering effect is observed for specific values of <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_13840_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Delta\)</EquationSource> </InlineEquation> and <i>E</i>. The Klein tunneling occurs for <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_13840_Article_IEq6.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="47" /> </InlineMediaObject> <EquationSource Format="TEX">\(N=1\)</EquationSource> </InlineEquation> at low values of <i>E</i> and <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_13840_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Delta\)</EquationSource> </InlineEquation>. By focusing on the resonances in transmission and the oscillatory behavior of conductance with <i>N</i>, <i>E</i> and <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_13840_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Delta\)</EquationSource> </InlineEquation>, we can confine charge carriers within the studied magnetic bilayer graphene by efficiently adjusting these parameters. The perfect transmission is observed for appropriate values of the electrostatic barrier height and the widths of magnetic and non-magnetic regions. The conductance is suppressed when <i>N</i>, <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_13840_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Delta\)</EquationSource> </InlineEquation> or <i>B</i> exceed their critical values.</p>

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

Confinement of charge carriers in gapped bilayer graphene within magnetic and electrostatic barriers

  • Fatemeh Pakdel,
  • Mohammad Ali Maleki

摘要

We explore the transport behavior of charge carriers in gapped bilayer graphene under a perpendicular magnetic field and electrostatic barriers. Using the Hamiltonian of the four low-energy bands of bilayer graphene, we compute the transmission probability and the associated conductance via the transfer matrix method. Our investigation reveals that altering the gap parameter ( \(\Delta\) ), the energy (E), the number of magnetic barriers (N) and the magnetic field strength (B) changes the range of incident angles, resulting in a wave-vector filtering effect. These parameters also influence the forbidden zones of transmission and conductance in the magnetic system. A forbidden zone exists for \(E<\Delta\) . For a multibarrier structure with \(N>2\) , another forbidden zone appears for \(E>\Delta\) , along with resonance effects and conductance oscillations as functions of N and E. A strong wave-vector filtering effect is observed for specific values of \(\Delta\) and E. The Klein tunneling occurs for \(N=1\) at low values of E and \(\Delta\) . By focusing on the resonances in transmission and the oscillatory behavior of conductance with N, E and \(\Delta\) , we can confine charge carriers within the studied magnetic bilayer graphene by efficiently adjusting these parameters. The perfect transmission is observed for appropriate values of the electrostatic barrier height and the widths of magnetic and non-magnetic regions. The conductance is suppressed when N, \(\Delta\) or B exceed their critical values.