Microwave Impedance Microscopy
How do different electronic states look in real space? And what happens at the boundaries of these states and the interfaces between different states? With scanning Microwave Impedance Microscopy we aim to answer these questions.
· 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
In condensed mater systems strong correlations can lead to novel emergent phenomena. These novel phases are of fundamental interest but can also lead to practical applications. While most of our group focuses on studying these emergent states in momentum space using angle resolved photoemission spectroscopy, many novel phases have interesting real space properties. The presence of boundaries or interfaces in quantum materials can give rise to many exotic quantum effects: These include protected surface/edge states in a topological insulators, chiral edge states in quantum anomalous Hall insulators, metallic domain walls in magnetic insulators, and Majorana bound states in superconductors. To study such states systemically there is a need to develop a well-controlled technique to measure nanoscale conductivity non-invasively.
Schematic of the MIM setup and the typical response curve for a conductor.
Microwave Impedance Microscopy (MIM) is a scanning probe microscopy technique that utilises the local interaction between a microwave probe and a sample to make nano-scale images (<100 nm spatial resolution) of the electrical conductivity and permittivity of a sample. It has important applications and potentials in imaging semiconductor devices, buried structures and two-dimensional electron gases (2DEG), phase separated materials, biological specimens, and others. The technique works by bringing a sharp metal tip, which is being driven at microwave frequencies, into close proximity of the sample’s surface. The electric potential around the tip is disturbed by the sample and a portion of the electrical signal sent to the tip is reflected back up the microwave line depending on the mismatch with the tip-sample admittance. The reflected signal can be related to the electrical conductivity and permittivity of the sample. By rastering the tip across the sample it is possible to map the local conductivity and permittivity of the sample with ~100 nm spacial resolution. The typical response curve for a conductive sample is shown in the right hand panel.
We use two types of tip depending on the sample and measurement conditions:
Gen5 Cantilever tips.
• Cantilever probes
- Well shielded cantilever
- Low loss, low capacitance
- Sharp tip (~50 nm)
- Batch fabricated
Tuning-fork based tips.
• Tuning-fork based
- 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 one room temperature instrument based on a Park Systems AFM.
Mesoscopic percolating resistance network in a strained manganite thin film
Percolating resistance network in Nd1/2Sr1/2MnO3 thin films.
Many complex oxides possess rich phase diagrams with a variety of different phases due to the competition between charge, spin, orbital and lattice degrees of freedom which can all be active in these compounds. High temperature cuprate superconductors are one such example with competing antiferromagnetic, superconducting and charge density wave ground states. Manganites are another such family, and shows colossal magnetoresistance between competing paramagnetic, ferromagnetic and charge/orbital-order phases. When there is significant phase competition, two or more phases can appear to coexist on the macroscopic scale, but are actually spatially separated on the microscopic scale. We have used MIM conductivity mapping to study Nd1/2Sr1/2MnO3
thin films grown on (110) SrTiO3
substrates. In single crystals of this manganite, a paramagnetic to ferromagnetic transition occurs at a Curie temperature TC
~250 K, then a second phase transition into a state with charge/orbital-order occurs at TCOO
~160 K. When a magnetic field is then applied at temperatures below TCOO
, a dramatic first-order phase transition with a 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 observed an orientation-ordered percolating network of domains through the transition. The network has a large period of ~100 nanometers and the filamentary metallic domains preferentially align along certain crystal axes of the substrate, suggesting that the anisotropic elastic strain from the substrate is a key interaction in this system.
Imaging quantum Hall edge states
In clean two-dimensional electron systems (2DESs), applied magnetic field can lead to the unusual macroscopic quantum phenomena of integer quantum Hall (IQH) effect. In such systems magnetic field quantises the electronic states into Landau levels. At precise fields the carriers can completely fill a certain number of bulk Landau levels, causing the Fermi level to lie in the energy gap between levels. The bulk becomes highly incompressible and the longitudinal resistivity vanishes. The Hall resistivity, however, does not vanish and takes on precisely quantised values depending on the total Chern number of the occupied Landau levels. The IQH effect was first demonstrated in semiconductor-based 2DESs but has also more recently been demonstrated in graphene. We have imaged both systems.
Imaging of Coulomb-Driven Quantum Hall Edge States in GaAs/AlGaAs 2DEG Devices
Quantum Hall Edge States in GaAs/AlGaAs 2DEGs.
While the bulk of an IQH state is highly insulating, near the edges of a real sample the Landau levels shift in energy due to the confining potential and intersect with the Fermi energy, resulting in alternating compressible (metal-like) and incompressible (insulator-like) strips. The widths of the strips are determined by the energy gaps of the QHE states and the electrostatic Coulomb interaction, and are typically submicron scale. Local probing of these small features is challenging however, especially in GaAs/AlGaAs based devices where the 2DES is buried in the device. MIM is ideally suited for this task as real-space conductivity mapping can be performed in non-contact and without any additional dc electrodes. Using MIM we mapped the sizes, positions, and field dependence of the edge strips around the sample perimeter of GaAs/AlGaAs 2DEG islands and showed that they agree quantitatively with the self-consistent electrostatic picture. We additionally could provide detailed information on 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
Comparison of quantum transport and local conductivity in gated graphene.
Graphene is a single sheet of hexagonally coordinated carbon atoms. It possesses many unusual properties and can show the IQH effect even up to room temperature. With MIM we again studied the correspondence between quantised transport and incompressible bulk by measuring simultaneously the quantized bulk transport and the local conductivity across the interior of the sample in graphene to see if the behaviour in this system is the same. Our MIM measurements uncovered a correlation that is very different from the commonly assumed picture. The devices we studied had a back gate to tune the carrier density, as is typically used in the field, however we found that each transport plateau occurred at only ~90% filling of each bulk Landau level, when the bulk of the sample is still conductive. This discrepancy is likely the result of electrostatically induced charge accumulation near the edges of the sample when the gate voltage is applied, but this realisation 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)
Mobile metallic domain walls in an all-in-all-out magnetic insulator
Conductive domain walls in Nd2Ir2O7 revealed by MIM.
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 Nd2
which undergoes a 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 the domain walls, the magnetic order is disturbed and it has been postulated that the electronic properties along the domain walls can be different from the bulk. The study of such domain walls though, is inherently difficult as they are embedded in the insulating bulk. MIM, however, is uniquely suited to this task enabling local nanoscale conductivity measurements without requiring a continuous current path and covering a large enough mesoscopic length scale to study the domain formation and movement. Using MIM we were able to, for the first time, conclusively show 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 iridates, the proximity to an exotic Weyl semimetal phase may be giving rise to the mid-gap states that are responsible for the 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)
Imaging quantum spin Hall edges in monolayer WTe2
Imaging edge conductivity in monolayer WTe2.
Topological insulators have an insulating bulk, but the surfaces remain conducting. This unusual state of matter is distinct from a normal insulator not through a broken symmetry as associated with the standard classification of phase transitions, but rather a different geometry in the curvature of the phase of the electronic wavefunctions giving 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 effect which possesses two helical edge states. These are one dimensional states where the spin is tied to the direction of motion. 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, there can be no back-scattering from non-magnetic impurities and this leads to dissipationless quantised conduction. We have studied monolayer WTe2
, a proposed QSH insulator, with MIM and by directly mapping the 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 the QSH state. Conducting features were observed along all boundaries of the sample, whether these were the actual sample edge or tears in the edge from processing, internal cracks or regions of degradation from exposure to atmosphere and around contacts. This robustness of the QSH conducing channels comes from their topologically protection and provides crucial insights for optimizing devices and opportunities to access and manipulate the helical edge channels.
Y. Shi, J. Kahn, B. Niu, Z. Fei, B. Sun, X. Cai, B. A. Francisco, D. Wu, Z.-X. Shen, X. Xu, D. H. Cobden, and Y.-T. Cui,
"Imaging quantum spin Hall edges in monolayer WTe2", Sci. Adv. 5, eaat8799 (2019)
Visualization of an axion insulating state at the transition between two chiral quantum anomalous Hall states
Imaging edge states in a magnetic topological insulator.
The topological identification of phases of matter has been a new forefront in condensed matter physics. One such 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 stabilised in a magnetically doped topological insulator when the 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)2
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. The magnetisation of the Cr doped layers creates a quantum anomalous Hall regime when trained with external field and well-defined edge excitations were observed. The heterostructure we measured had a built in asymmetry giving the top and bottom magnetic layers different coercive fields allowing us to enter a state where the magnetisation points in opposite directions on the top and bottom surfaces. We studied the evolution of the conductivity across this transition and the resulting images revealed an insulating state, which exhibits 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 stabilised 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 to hopefully visualize Majorana modes in the future.
M. Allen, Y.-T. Cui, E. Y. Ma, M. Mogi, M. Kawamura, I. C. Fulga, D. Goldhaber-Gordon, Y. Tokura, and Z.-X. Shen,
"Visualization of an axion insulating state at the transition between 2 chiral quantum anomalous Hall states", Proc. Natl. Acad. Sci. 116, 14511-14515 (2019)
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