This review is written by non-expert and used for personal study only.
Quantum-well states at the surface of a heavy-fermion superconductor
- Superconducting Properties and Materials
This article presents an in-depth analysis of the observation of two-dimensional heavy fermion (2DHF) states on the U-terminated surface of the heavy-fermion superconductor URu$_2$Si$_2$, using scanning tunneling microscopy (STM). Heavy fermions are a distinct class of quantum materials known for their extraordinary properties arising from their narrow electronic-band dispersion. Prior experiments have demonstrated that lowering the dimensionality of heavy fermions leads to increased electronic correlations and enhanced superconducting coupling. The discovery of 2DHFs on a superconducting compound’s surface represents a significant milestone, as such states have not been observed before. STM images reveal well-defined 2DHFs with an effective mass 17 times greater than the free electron mass, as well as quantization due to lateral confinement and insights into the surface-bulk interaction. The article presents the tunneling conductance data obtained near the Fermi level and at a temperature of 0.1 K, well below the superconducting critical temperature.
The article also describes the observation of quantum-well states by confinement on the URu$_2$Si$_2$ heavy-fermion superconductor surface through STM. The tunneling conductance is examined along a line that displays four distinct terraces with varying sizes. The conductance is found to depend on both bias voltage and position, with each terrace exhibiting different characteristics. The lateral quantization of 2DHFs is observed as a result of partially reflected wavefunctions interfering at the steps. The Fabry–Pérot expression for an interferometer, constructed from partially reflecting mirrors, is employed to describe the quantization pattern of confined electrons. The position and energy of peaks in the tunneling conductance are governed by the phase shift and reflection coefficient, respectively. The effective mass of the 2DHF is found to be 17 times greater than the free electron mass. The energy dependence of the reflection coefficient differs significantly from typical metals, exhibiting a marked decrease within a few meV. A potential well model is used to account for this energy dependence.
Furthermore, the article explores the lifetime of quantum-well states on the URu$_2$Si$_2$ heavy-fermion superconductor surface using STM. The lifetime of these states is determined by the decay of the 2DHF into heavy-fermion bulk states. The quadratic energy term in ħ/τ establishes the bulk correlations sensed by the quantum-well states. The estimated lifetimes for the ground state and states close to the Fermi level are 11 ps and 3 ps, respectively. The mean free path is calculated to be ℓ0 = vFħ/Γ(0) ≈ 0.14 μm, which is comparable to observations in ultraclean URu$_2$Si$_2$ single crystals. Density functional theory calculations are performed on the surface band structure of a URu$_2$Si$_2$ slab to corroborate the existence of a heavy-fermion surface state. A shallow, U-derived f-electron band with a flat dispersion relation is found to align with experimental observations.
Additionally, the article examines the observation of one-dimensional edge states (1DESs) on the URu2Si2 heavy-fermion superconductor surface using STM. The 1DESs are detected at steps separating terraces, where tunneling conductance features change dramatically. A high peak is observed at E$_{1DES}$ ≈ −0.38 meV in steps, but only along one of the two equivalent in-plane axes, suggesting a spontaneous symmetry breaking of the fourfold rotational symmetry near the surface. In-plane symmetry breaking has been proposed for bulk URu$_2$Si$_2$ but has been difficult to detect. The presence of 1DES provides a sensitive probe into the fundamental electronic properties of the near-surface U lattice.
The article also reports on the observation of two-dimensional heavy-fermion states (2DHFs) within the hidden order (HO) phase of the heavy-fermion superconductor URu$_2$Si$_2$, as revealed through scanning tunneling microscopy (STM) measurements. These 2DHFs display quantum-well states with energy separations in the order of fractions of a meV when confined between steps. The researchers further identified one-dimensional edge states (1DESs) at the steps, which exhibit in-plane electronic symmetry breaking and non-equivalent electronic arrangements in subsequent uranium layers in the HO phase. STM measurements also uncovered a large zero-bias conductance at energy ranges below the superconducting gap. The researchers explained this phenomenon using a model that accounts for the coupling of the 2DHF to strongly energy-dependent resonant states.
The discovery of 2DHFs and related confined states promises to enable further studies into the interplay between quantized heavy-fermion states and unconventional superconductivity in other heavy-fermion materials. These materials often display unconventional superconductivity in their bulk forms. The findings presented in this article contribute to a deeper understanding of the complex electronic properties of heavy-fermion systems, paving the way for future exploration and potential applications of these unique quantum materials.
Required Additional Study Materials
- Fiete, G. A. & Heller, E. J. Colloquium: Theory of quantum corrals and quantum mirages. Rev. Mod. Phys. 75, 933–948 (2003).
- Hewson, A. C. The Kondo Problem to Heavy Fermions (Cambridge Univ. Press, 1993).
- Mydosh, J. A. & Oppeneer, P. M. Hidden order behaviour in URu2Si2 (a critical review of the status of hidden order in 2014). Philos. Mag. 94, 3642–3662 (2014).
Introductory material
- “Heavy-fermion systems” by G. R. Stewart
Reference
Herrera, E., Guillamón, I., Barrena, V. et al. Quantum-well states at the surface of a heavy-fermion superconductor. Nature 616, 465–469 (2023).
Ballistic two-dimensional InSe transistors
- Electronic Devices
This study delves into the potential of two-dimensional (2D) layered semiconductors for use as channel materials in transistors, aiming to mitigate the short-channel effects that can negatively impact their performance. Up until now, it hasn’t been proven that field-effect transistors (FETs) based on 2D semiconductors can outdo state-of-the-art silicon FETs when it comes to on-state current and transconductance. Transconductance, in simple terms, refers to the responsiveness of a transistor’s output current to changes in its input voltage. The researchers in this study explore the use of a three-layer material called indium selenide (InSe) to fabricate ultrashort ballistic transistors, which will help assess the ultimate capabilities of 2D semiconductors.
InSe holds several advantages over silicon, such as a higher thermal velocity (the speed at which particles move within a material when heated), reduced scale length (a measure of the size of certain features in a material), and lower valley degeneracy (a property related to the energy bands and charge carriers in a material). However, some challenges remain, including low-quality interfaces, suboptimal source and drain contacts, and other inherent limitations.
The researchers describe the fabrication of a 2D InSe transistor structure that features a 10-nanometer (nm) channel length and 2.6-nm-thick hafnium oxide (HfO$_2$) dielectrics. Dielectrics are insulating materials that don’t conduct electricity but can support an electrostatic field. The importance of ohmic contacts in building high-performance FETs is emphasized. Ohmic contacts are connections between the semiconductor material and the metal electrodes that allow for efficient current flow with minimal energy loss. A phase-transition technique is employed in the contact region, using yttrium doping to transform semiconducting InSe into semimetallic Y-InSe. Doping is a process used to introduce impurities into a material to modify its electronic properties.
Density functional theory (DFT) is a computational method used to investigate the electronic structure of materials. It is utilized in this study to identify the most likely doping lattice structure, while the experimental process for achieving yttrium doping in InSe is outlined. Several characterization methods, such as X-ray photoelectron spectroscopy (XPS), Raman spectroscopy, and electric-transfer characteristics, are employed to verify the anticipated semiconductor-to-semimetal phase transition. The resulting FET exhibits semimetallic properties with notably weak gate-field modulation, which is significantly lower than that of a pure InSe channel. Gate-field modulation is a measure of how effectively a gate voltage can control the current flow in a transistor.
The study further examines the band alignment between Y-InSe and intrinsic InSe. Band alignment refers to the energy levels of the valence and conduction bands in a semiconductor material, which can impact its electronic properties. The researchers also investigate the implementation of semimetallic Y-InSe contacts in InSe FETs. They show that the source and drain contacts are free from the Fermi-pinning effect, which can impede the performance of a transistor by limiting the achievable current. As a result, the FETs demonstrate superior on-state performance in output characteristics.
The saturation output characteristics of the ballistic transistors are presented, and the total resistance and drain current are compared with previous findings, considering the same inversion charge. Inversion charge refers to the amount of charge induced in the channel of a FET, which controls the current flow. The extraction of contact resistance (RC) from the saturation output characteristics is deemed more reliable than the transmission-line method. Contact resistance is the resistance encountered at the interface between the semiconductor and the metal contacts, which can affect the overall performance of a transistor.
The researchers reveal that the 10-nm 2D InSe FETs with ohmic contacts demonstrate a consistent on-state current across a wide temperature range, indicating the successful establishment of ohmic contacts. The performance of 2D InSe FETs is compared to that of silicon-based FETs, revealing similar or superior saturation currents and transconductance values at lower voltages. Saturation current is the maximum current that can flow through a transistor when it is fully turned on.
The on-state performance parameters of InSe FETs are contrasted with other short-channel 2D FETs, with InSe FETs exhibiting higher on-state current and transconductance values, even at larger supply voltages. The ballistic ratios in the saturation region of the 2D FETs represent the highest recorded values for 2D-based transistors to date, surpassing all previously reported silicon FETs. A ballistic ratio is a measure of how efficiently a transistor can switch from the on-state to the off-state, which is an important property for high-performance electronic devices.
The authors showcase their findings on the high-performance, low-power operation of InSe-based FETs. They detail the materials and fabrication processes, including yttrium doping for source and drain contacts, a double-gate structure, and ultrathin HfO$_2$ dielectrics. These FETs exhibit high on-state currents, low off-state leakage currents, and ideal switching behavior, with scaling trends on par with or superior to state-of-the-art silicon FETs. Off-state leakage current refers to the small amount of current that still flows through a transistor when it is supposed to be turned off. Low leakage current is desirable for energy-efficient electronic devices.
Additionally, the FETs have low gate delay and energy-delay products, making them suitable for high-performance integrated circuits with minimal power dissipation. Gate delay is the time it takes for a signal to propagate through a transistor, while the energy-delay product is a measure of the energy efficiency of a transistor. The authors acknowledge the benefits of InSe FETs over silicon FETs, such as a lower ultimate voltage limit and reduced short-channel effects, while also highlighting challenges to overcome, such as InSe’s sensitivity to moisture.
Study presents the transfer characteristics of three typical ballistic InSe FETs with a 20-nm gate length (LG), demonstrating a large saturation-state current, substantial current on/off ratio, and ideal subthreshold swing (SS) with an average value of nearly 60 mV per decade across over three orders of current magnitude. Subthreshold swing is a measure of how sharply a transistor can switch between its on and off states. These FETs require a 0.5-V voltage window across the transfer characteristics, compared to the supply-voltage window of greater than 3 V for other 2D FETs. Achieving ohmic contact is essential for realizing ideal switching characteristics in the near-threshold region.
The researchers successfully fabricated high-performance InSe FETs with ohmic contact, high gate efficiency, and near-ideal ballistic ratios, operating at an ultralow voltage of 0.5 V. This study confirms, for the first time, that 2D FETs are strong contenders for silicon FETs at the Å node of the future, making them a promising avenue for further research and development in the field of electronics.
Required Additional Study Materials
- Chhowalla, M., Jena, D. & Zhang, H. Two-dimensional semiconductors for transistors. Nat. Rev. Mater. 1, 16052 (2016).
- Akinwande, D. et al. Graphene and two-dimensional materials for silicon technology. Nature 573, 507–518 (2019).
- Allain, A., Kang, J., Banerjee, K. & Kis, A. Electrical contacts to two-dimensional semiconductors. Nat. Mater. 14, 1195–1205 (2015).
Reference
Jiang, J., Xu, L., Qiu, C. et al. Ballistic two-dimensional InSe transistors. Nature 616, 470–475 (2023).
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