Fermi velocity renormalization in graphene probed by terahertz time-domain spectroscopy
Patrick R Whelan, Qian Shen, Binbin Zhou, I G Serrano, M Venkata Kamalakar, David M A Mackenzie, Jie Ji, Deping Huang, Haofei Shi, Da Luo, Meihui Wang, Rodney S Ruoff, Antti-Pekka Jauho, Peter U Jepsen, Peter Bøggild, José M Caridad
Abstract
Abstract We demonstrate terahertz time-domain spectroscopy (THz-TDS) to be an accurate, rapid and scalable method to probe the interaction-induced Fermi velocity renormalization <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mi>F</mml:mi> </mml:mrow> </mml:mrow> <mml:mrow> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> of charge carriers in graphene. This allows the quantitative extraction of all electrical parameters (DC conductivity σ DC , carrier density n , and carrier mobility µ ) of large-scale graphene films placed on arbitrary substrates via THz-TDS. Particularly relevant are substrates with low relative permittivity (< 5) such as polymeric films, where notable renormalization effects are observed even at relatively large carrier densities ( > 10 12 cm −2 , Fermi level > 0.1 eV). From an application point of view, the ability to rapidly and non-destructively quantify and map the electrical ( σ DC , n, µ ) and electronic ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mi>F</mml:mi> </mml:mrow> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mo>∗</mml:mo> </mml:mrow> </mml:mrow> </mml:msubsup> </mml:math> ) properties of large-scale graphene on generic substrates is key to utilize this material in applications such as metrology, flexible electronics as well as to monitor graphene transfers using polymers as handling layers.