Microwave Impedance Microscopy
How do different electronic states look in real space? What happens at the boundaries of these states, and at interfaces between different states? We aim to answer these questions with scanning Microwave Impedance Microscopy.
- Mesoscopic Percolating Resistance Network in a Strained Manganite Thin Film
- Imaging quantum Hall edge states
- Mobile metallic domain walls in an all-in-all-out magnetic insulator
- Imaging quantum spin Hall edges in monolayer WTe2
- Visualization of an axion insulating state at the transition between two chiral quantum anomalous Hall states
- Microwave impedance microscopy and its application to quantum materials
In condensed mater systems, strong correlations can lead to novel emergent phenomena, producing new phases of fundamental interest and potential usage in practical applications. Although most of the Shen group studies emergent states in momentum space using different forms of angle resolved photoemission spectroscopy, many novel phases also have interesting properties in real space. This is because boundaries or interfaces in quantum materials produce a range of exotic quantum effects. These include protected surface/edge states in topological insulators, chiral edge states in quantum anomalous Hall insulators, metallic domain walls in magnetic insulators, and Majorana bound states in superconductors. In order to study such states systematically, there is a need to develop a well-controlled technique to measure nanoscale conductivity in a non-invasive manner.
Microwave Impedance Microscopy (MIM) is a scanning probe microscopy technique that utilizes the local interaction between a microwave probe and a sample to make nano-scale images (with <100 nm spatial resolution) of the sample's electrical conductivity and permittivity. It has important applications and potential in imaging semiconductor devices, buried structures and two-dimensional electron gases (2DEG), phase separated materials, biological specimens, amongst others. MIM works by bringing a sharp metal tip, driven at microwave frequencies, in close proximity to a sample surface. The electric potential around the tip is modified by the sample, and a portion of the electrical signal sent to the tip is reflected back up the microwave line, with a dependence on the mismatch in tip-sample admittance. The reflected signal is related to the electrical conductivity and permittivity of the sample. By rastering the tip across the sample, we can map the local conductivity and permittivity of the sample with approximately 100 nm spatial resolution. The typical response curve of a conductive sample is shown above.
We use two types of tip depending on the sample and measurement conditions.
- Well shielded cantilever
- Low loss, low capacitance
- Sharp tip (~50 nm)
- Batch fabricated
Tuning-fork based tips
- Self-sensing topography feedback
- Simultaneous differential mode measurement
- Sharp tip (~50 nm)
- Multiple-frequency measurements
We have two cryogenic MIM instruments — one based on a Janis 3He cryostat, the other on a Janis 4He/VTI — and a room temperature instrument based on a Park Systems AFM.
Many complex oxides possess rich phase diagrams. Their variety of different phases arises from the competition between charge, spin, orbital, and lattice degrees of freedom, all of which which may be active in these compounds. When there is significant phase competition, two or more phases can appear to coexist on the macroscopic scale despite being spatially separated on the microscopic scale. The iconic high temperature cuprate superconductors, for example, display competing antiferromagnetic, superconducting and charge density wave ground states. Manganites are another interesting family, and show colossal magnetoresistance between competing paramagnetic, ferromagnetic and charge/orbital-order phases.
We have used MIM conductivity mapping to study Nd1/2Sr1/2MnO3 thin films grown on (110) SrTiO3 substrates. Cooling a single crystal of this manganite system produces a paramagnetic-to-ferromagnetic transition at a Curie temperature TC ~ 250 K, followed by a second phase transition into a charge/orbital-ordered state at TCOO ~ 160 K. When a magnetic field is then applied at temperatures below TCOO, a dramatic first-order phase transition — with colossal magnetoresistance — from the antiferromagnetic charge/orbital-order insulating state to the ferromagnetic metallic state, occurs. We have studied this transition with nanoscale conductivity measurements and have observed an orientation-ordered percolating network of domains through the transition. This network has a large period of ~100 nanometers. Filamentary metallic domains preferentially align along certain crystal axes of the substrate, suggesting that anisotropic elastic strain from the substrate is a key interaction in this system.
In clean two-dimensional electron systems (2DESs), an applied magnetic field produces an unusual macroscopic quantum phenomenon, the integer quantum Hall (IQH) effect. The magnetic field quantizes electronic states into Landau levels. At precise field strengths, the carriers completely fill a number of bulk Landau levels, and the Fermi level resides in the energy gap between levels. The bulk becomes highly incompressible and longitudinal resistivity vanishes. The Hall resistivity, however, does not vanish; instead, it takes on precisely quantized values (proportional to an integer, ν) dependent on the total Chern number of the occupied Landau levels. The IQH effect was first demonstrated in semiconductor-based 2DESs, but has more recently been demonstrated in graphene. We have imaged both systems.
Imaging of Coulomb-Driven Quantum Hall Edge States in GaAs/AlGaAs 2DEG Devices
The bulk of an IQH state is highly insulating. Yet, near the edges of a real sample, Landau levels shift in energy due to the confining potential, and intersect with the Fermi energy. This results in alternating compressible (metal-like) and incompressible (insulator-like) edge strips. The widths of these strips are determined by the energy gaps of the QHE states and the electrostatic Coulomb interaction, and are typically submicron scale. It is often challenging to probe these small features locally, especially in GaAs/AlGaAs based devices where the 2DES is buried in the device. MIM is ideally suited for this task because real-space conductivity mapping can be performed without contact and without any additional d.c. electrodes. Using MIM, we have mapped the sizes, positions, and field dependence of edge strips around the sample perimeter of GaAs/AlGaAs 2DEG islands, and have showed that they agree quantitatively with the self-consistent electrostatic picture. We also obtained detailed information about the microscopic evolution of the ν = 2 QHE state as a function of magnetic field.
Unconventional Correlation between Quantum Hall Transport Quantization and Bulk State Filling in Gated Graphene Devices
Graphene is a single sheet of hexagonally coordinated carbon atoms. It possesses many unusual properties and can display the IQH effect even up to room temperature. With MIM, we again studied the correspondence between quantized transport and the incompressible bulk. This was done by simultaneously measuring quantized bulk transport and local conductivity across the interior of the sample in graphene to determine whether the behaviour in this system was the same. Our MIM measurements uncovered a correlation that was very different from the commonly assumed picture. The devices we studied had a back gate to tune carrier density, as is typically done; however, we found that each transport plateau occurred at only ~90% filling of each bulk Landau level, when the bulk of the sample was still conductive. While this discrepancy is likely the result of electrostatically induced charge accumulation near the edges of the sample when gate voltage is applied, this realization has important implications for interpreting many other IQH analyses.
Y.-T. Cui, B. Wen, E. Y. Ma, G. Diankov, Z. Han, F. Amet, T. Taniguchi, K. Watanabe, D. Goldhaber-Gordon, C. R. Dean, and Z.-X. Shen, "Unconventional Correlation between Quantum Hall Transport Quantization and Bulk State Filling in Gated Graphene Devices", Phys. Rev. Lett. 117, 186601 (2016)
In certain metals with strong electronic correlations, insulating phases can develop at low temperatures due to large electronic repulsion. Such metal-insulator transitions (MIT) are also commonly accompanied by magnetic order. This is the case for Nd2Ir2O7, which undergoes an MIT at a Néel temperature of ~32 K, developing an all-in–all-out magnetic structure at low temperatures. This type of magnetic order breaks the symmetry of the disordered state, and allows the formation of domains with two distinct order parameters. At the boundaries between adjacent domains, termed domain walls, magnetic order is disturbed. It has been postulated that electronic properties along domain walls can be different from the bulk. The study of such domain walls is inherently difficult as they are embedded in the insulating bulk. MIM is thus uniquely suited to this task as it enables local nanoscale conductivity measurements without requiring a continuous current path, and covers a large enough mesoscopic length scale to study domain formation and movement. Using MIM we were able to — for the first time — conclusively demonstrate the existence of conductive magnetic domain walls in a magnetic insulator. The domain walls showed no preferred orientation and were free from pinning by disorder. They could be easily manipulated by both heat and magnetic field. In the particular case of the iridates, proximity to an exotic Weyl semimetal phase may have given rise to mid-gap states responsible for enhanced conduction at the domain walls.
E. Y. Ma, Y-.T. Cui, K. Ueda, S. Tang, K. Chen, N. Tamura, P. M. Wu, J. Fujioka, Y. Tokura and Z.-X. Shen, "Mobile metallic domain walls in an all-in-all-out magnetic insulator", Science 350, 538 (2015)
Topological insulators have an insulating bulk, but their surfaces remain conducting. This unusual state of matter is distinct from a normal insulator not through broken symmetry, associated with the standard classification of phase transitions. Instead, they are differentiated by the geometry inherent in the curvature of the electron wavefunction's phase. This gives them the name topological insulators. In two dimensions, a topological insulator exhibits the quantum spin Hall (QSH) effect. This is a spin-orbit coupling-driven version of the integer quantum Hall (IQH) effect which possesses two helical edge states — one dimensional states where spin is tied to the direction of motion. That is, all 'up' spins move in one direction around the sample and 'down' spins in the other. In the QSH state these edge modes are topologically protected. Back-scattering from non-magnetic impurities is consequently forbidden, and this leads to dissipationless quantized conduction. We have studied monolayer WTe2, a proposed QSH insulator, with MIM. By directly mapping local conductivity we have established, for the first time, that the conduction is indeed strongly localized to the physical edges of the sample. The edge conductivity showed no gap as a function of gate voltage when tuning the Fermi level between the bulk valence and conduction bands, and was suppressed by magnetic field as expected for a QSH state. Conducting features were observed along all boundaries of the sample, including the actual sample edge itself, and also tears in the edge from processing, internal cracks or regions of degradation from exposure to atmosphere and around contacts. The robustness of QSH conducting channels comes from their topological protection; it is crucial for optimizing devices and provides opportunities to access and manipulate helical edge channels.
Visualization of an axion insulating state at the transition between two chiral quantum anomalous Hall states
Topological identification of phases of matter is a new forefront in condensed matter physics. One novel phase is the axion insulator, which is predicted to exist in three-dimensional topological insulators, and may exhibit an unusual quantized magnetoelectric effect. The axion insulator state is expected to be stabilized in a magnetically doped topological insulator when magnetization either points inwards on all surfaces, or outwards. Such a state can be created using modulation doping of magnetic ions. We have studied a heterostructure of thin film (Bi,Sb)2Te3 with modulation-doped Cr ions near the top and bottom surfaces of the topological insulator thin film. Using MIM, we have mapped the real-space local complex conductivity profile. Magnetisation of the Cr-doped layers created a quantum anomalous Hall regime when trained with an external field, and well-defined edge excitations were observed. The heterostructure we measured had a built-in asymmetry, endowing its top and bottom magnetic layers with different coercive fields. This allowed us to produce a state where the magnetisation pointed in opposite directions on the top and bottom surfaces. We studied the evolution of conductivity across the transition into this state. Resulting images revealed an insulating state, exhibiting a distinct geometry of current flow, at the boundary between the two quantum anomalous Hall (QAH) states with opposite chirality. The results are consistent with the axion insulator state being stabilized in the small field window between the two coercive fields. The purely topological nature of the observed edge states in this system makes for an attractive platform foreseeably to visualize Majorana modes.
In this technical review we describe the fundamental working principles and practical implementations of microwave impedance microscopy, discuss its application to a wide range of quantum materials, including correlated, topological and 2D van der Waals materials, and outline future opportunities in expanding the capabilities of microwave impedance microscopy.
Bulk-averaging measurements, such as conventional transport or spectroscopy, are often insufficient to determine the true microscopic nature of quantum materials. Instead, a family of scanning probe microscopy techniques can provide spatially resolved imaging of different material properties. Microwave impedance microscopy (MIM), in particular, non-invasively probes local conductivity and permittivity by measuring the admittance between a sharp tip and the sample at microwave frequencies. By working in the near-field regime, MIM can achieve spatial resolution down to <50 nm, far below the diffraction limit.
We review some systems which MIM has revealed: (1) metallic magnetic domain walls in an antiferromagnetic insulator, (2) 'glassy' behaviour across a colossal magnetoresistance transition, (3) new correlated insulating states at fractional and integer filling factors in a van der Waals moiré superlattice, (4) a mismatch between critical carrier density measured by charge transport and capacitance spectroscopy in integer quantum Hall transitions, (5) the existence of field-insensitive trivial edge states and conductive features not accessible by transport in a host material for the quantum spin Hall effect, and (6) edge excitations in a heterostructure consistent with an axion insulator.
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- E. Y. Ma et al., Charge-order domain walls with enhanced conductivity in a layered manganite. Nat. Commun. 6, 7595 (2015)
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- W. Kundhikanjana et al., Hierarchy of Electronic Properties of Chemically Derived and Pristine Graphene Probed by Microwave Imaging. Nano Lett. 9, 3762 (2009)
- K. J. Lai et al., Nanoscale Electronic Inhomogeneity in In2Se3 Nanoribbons Revealed by Microwave Impedance Microscopy. Nano Lett. 9, 1265 (2009)
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