The optical properties of monolayer and bilayer transition metal dichalcogenide semiconductors are governed by excitons in different spin and valley configurations, providing versatile aspects for van der Waals heterostructures and devices. We present experimental and theoretical studies of exciton energy splittings in external magnetic field in neutral and charged WSe$_2$ monolayer and bilayer crystals embedded in a field effect device for active doping control. We develop theoretical methods to calculate the exciton $g$-factors from first principles and tight-binding for all possible spin-valley configurations of excitons in monolayer and bilayer WSe$_2$ including valley-indirect exciton configurations. Our theoretical and experimental findings shed light on some of the characteristic photoluminescence peaks observed for monolayer and bilayer WSe$_2$. In more general terms, the theoretical aspects of our work provide new guidelines for the characterization of single and few-layer transition metal dichalcogenides, as well as their heterostructures, in the presence of external magnetic fields.
We report the fabrication and characterization of gate-defined hole quantum dots in monolayer and bilayer WSe$_2$. The devices were operated with gates above and below the WSe$_2$ layer to accumulate a hole gas, which for some devices was then selectively depleted to define the dot. Temperature dependence of conductance in the Coulomb blockade regime is consistent with transport through a single level, and excited state transport through the dots was observed at temperatures up to 10 K. For adjacent charge states of a bilayer WSe$_2$ dot, magnetic field dependence of excited state energies was…
Momentum resolved electron energy-loss spectroscopy was used to measure the dispersions of excitons in a free-standing monolayer of WSe2. Besides the parabolically dispersed valley excitons, a sub-gap dispersive exciton was observed at specific q values for the first time. The simultaneous STEM-ADF imaging of the local probed areas suggests that this sub-gap exciton is attributed to the prolific Se vacancies.
We report the strong dependence of resistance on uniaxial strain in monolayer WSe2 at various temperatures, where the gauge factor can reach as large as 2400. The observation of strain-dependent resistance and giant gauge factor is attributed to the emergence of nonzero Berry curvature dipole. Upon increasing strain, Berry curvature dipole can generate net orbital magnetization, which would introduce additional magnetic scattering, decreasing the mobility and thus conductivity. Our work demonstrates the strain engineering of Berry curvature and thus the transport properties, making monolayer W…
The results of magneto-optical spectroscopy investigations of excitons in a CVD grown monolayer of WSe2 encapsulated in hexagonal boron nitride are presented. The emission linewidth for the 1s state is of 4:7 meV, close to the narrowest emissions observed in monolayers exfoliated from bulk material. The 2s excitonic state is also observed at higher energies in the photoluminescence spectrum. Magneto-optical spectroscopy allows for the determination of the g-factors and of the spatial extent of the excitonic wave functions associated with these emissions. Our work establishes CVD grown monolaye…
Monolayer WSe$_2$ hosts a series of exciton Rydberg states denoted by the principal quantum number n = 1, 2, 3, etc. While most research focuses on their absorption properties, their optical emission is also important but much less studied. Here we measure the photoluminescence from the 1s - 5s exciton Rydberg states in ultraclean monolayer WSe$_2$ encapsulated by boron nitride under magnetic fields from -31 T to 31 T. The exciton Rydberg states exhibit similar Zeeman shifts but distinct diamagnetic shifts from each other. From their luminescence spectra, Zeeman and diamagnetic shifts, we dedu…
We investigate interlayer tunneling in heterostructures consisting of two tungsten diselenide (WSe2) monolayers with controlled rotational alignment, and separated by hexagonal boron nitride. In samples where the two WSe2 monolayers are rotationally aligned we observe resonant tunneling, manifested by a large conductance and negative differential resistance in the vicinity of zero interlayer bias, which stem from energy- and momentum-conserving tunneling. Because the spin-orbit coupling leads to coupled spin-valley degrees of freedom, the twist between the two WSe2 monolayers allows us to prob…
Using time-resolved Kerr rotation, we measure the spin/valley dynamics of resident electrons and holes in single charge-tunable monolayers of the archetypal transition-metal dichalcogenide (TMD) semiconductor WSe2. In the n-type regime, we observe long (70 ns) polarization relaxation of electrons that is sensitive to in-plane magnetic fields $B_y$, indicating spin relaxation. In marked contrast, extraordinarily long (2 microsecond) polarization relaxation of holes is revealed in the p-type regime, that is unaffected by $B_y$, directly confirming long-standing expectations of strong spin-valley…
In monolayer transition-metal dichalcogenide semiconductors, many-body correlations can manifest in optical spectra when photoexcited electron-hole pairs (excitons) are introduced into a 2D Fermi sea of mobile carriers. At low carrier densities, the formation of positively and negatively charged excitons ($X^\pm$) is well documented. However, in WSe$_2$ monolayers, an additional absorption resonance, often called $X^{-\prime}$, emerges at high electron density. Its origin is not understood. Here we investigate the $X^{-\prime}$ state via polarized absorption spectroscopy of electrostatically-g…
The variety of excitonic states in tungsten-based dichalcogenide monolayers stems from unique interplay between the spin and valley degrees of freedom. One of the exciton species is the indirect exciton (momentum or valley dark), which is responsible to a series of resonances when the monolayer is charge neutral. We investigate the short-range electron-hole exchange interaction of the indirect exciton, as well as its recombination mechanism mediated by impurities. The analysis provides thorough understanding of the energy and polarization of the zero-phonon indirect exciton resonance in the em…
Two-dimensional materials and their heterostructures have opened up new possibilities for magnetism at the nanoscale. In this study, we utilize first-principles simulations to investigate the structural, electronic, and magnetic properties of $\textrm{Fe}/\textrm{WSe}_2/\textrm{Pt}$ systems containing pristine, defective, or doped $\textrm{WSe}_2$ monolayers. The proximity effects of the ferromagnetic Fe layer are studied by considering defective and vanadium-doped $\textrm{WSe}_2$ monolayers. All heterostructures are found to be ferromagnetic, and the insertion of the transition-metal dichalc…
Janus transition-metal dichalcogenide monolayers are fully artificial materials, where one plane of chalcogen atoms is replaced by chalcogen atoms of a different type. Theory predicts an in-built out-of-plane electric field, giving rise to long-lived, dipolar excitons, while preserving direct-bandgap optical transitions in a uniform potential landscape. Previous Janus studies had broad photoluminescence (>15 meV) spectra obfuscating their excitonic origin. Here, we identify the neutral, and negatively charged inter- and intravalley exciton transitions in Janus WSeS monolayer with $\sim 6$ meV …
Motivated by a recent experiment [arXiv:2205.05087], we investigate a possible mechanism that enhances superconductivity in hole-doped Bernal bilayer graphene due to a proximate WSe$_2$ monolayer. We show that the virtual tunneling between WSe$_2$ and Bernal bilayer graphene, which is known to induce Ising spin-orbit coupling, can generate an additional attraction between two holes, providing a potential explanation for enhancing superconductivity in Bernal bilayer graphene. Using microscopic interlayer tunneling, we derive the Ising spin-orbit coupling and the effective attraction as function…
We report the observation and gate manipulation of intrinsic dark trions in monolayer WSe$_2$. By using ultraclean WSe$_2$ devices encapsulated by boron nitride, we directly resolve the weak photoluminescence of dark trions. The dark trions can be tuned continuously between negative and positive charged trions with electrostatic gating. We also reveal their spin triplet configuration and distinct valley optical emission by their characteristic Zeeman splitting under magnetic field. The dark trions exhibit large binding energy (14-16 meV). Their lifetime (~1.3 ns) is two orders of magnitude lon…
Monolayers of transition metal dichalcogenides are ideal materials to control both spin and valley degrees of freedom either electrically or optically. Nevertheless, optical excitation mostly generates excitons species with inherently short lifetime and spin/valley relaxation time. Here we demonstrate a very efficient spin/valley optical pumping of resident electrons in n-doped WSe2 and WS2 monolayers. We observe that, using a continuous wave laser and appropriate doping and excitation densities, negative trion doublet lines exhibit circular polarization of opposite sign and the photoluminesce…
Exciton binding energy and excited states in monolayers of tungsten diselenide (WSe2) are investigated using the combined linear absorption and two-photon photoluminescence excitation spectroscopy. The exciton binding energy is determined to be 0.37eV, which is about an order of magnitude larger than that in III-V semiconductor quantum wells and renders the exciton excited states observable even at room temperature. The exciton excitation spectrum with both experimentally determined one- and two-photon active states is distinct from the simple two-dimensional (2D) hydrogenic model. This result…
Two-dimensional (2D) semiconducting materials are promising building blocks for optoelectronic applications, many of which require efficient dissociation of excitons into free electrons and holes. However, the strongly bound excitons arising from the enhanced Coulomb interaction in these monolayers suppresses the creation of free carriers. Here, we probe and identify the main exciton dissociation mechanism through time- and spectrally-resolved photocurrent measurements in a monolayer WSe2 p-n junction. We find that under static in-plane electric field, excitons dissociate at a rate correspondi…
We report scanning tunneling microscopy (STM) and spectroscopy (STS) measurements of monolayer and bilayer WSe$_2$. We measure a band gap of 2.21 $\pm$ 0.08 eV in monolayer WSe$_2$, which is much larger than the energy of the photoluminescence peak indicating a large excitonic binding energy. We additionally observe significant electronic scattering arising from atomic-scale defects. Using Fourier transform STS (FT-STS), we map the energy versus momentum dispersion relations for monolayer and bilayer WSe$_2$. Further, by tracking allowed and forbidden scattering channels as a function of energ…
We report on nanosecond long, gate-dependent valley lifetimes of free charge carriers in monolayer WSe$_2$, unambiguously identified by the combination of time-resolved Kerr rotation and electrical transport measurements. While the valley polarization increases when tuning the Fermi level into the conduction or valence band, there is a strong decrease of the respective valley lifetime consistent with both electron-phonon and spin-orbit scattering. The longest lifetimes are seen for spin-polarized bound excitons in the band gap region. We explain our findings via two distinct, Fermi level-depen…
Moiré superlattices in van der Waals heterostructures have emerged as a powerful tool for engineering novel quantum phenomena. Here we report the observation of a correlated interlayer exciton insulator in a double-layer heterostructure composed of a WSe2 monolayer and a WS2/WSe2 moiré bilayer that are separated by an ultrathin hexagonal boron nitride (hBN). The moiré WS2/WSe2 bilayer features a Mott insulator state at hole density p/p0 = 1, where p0 corresponds to one hole per moiré lattice site. When electrons are added to the Mott insulator in the WS2/WSe2 moiré bilayer and an equal number …
We study proximity-induced spin-orbit coupling (SOC) in bilayer graphene/few-layer WSe2 heterostructure devices. Contact mode atomic force microscopy (AFM) cleaning yields ultra-clean interfaces and high-mobility devices. In a perpendicular magnetic field, we measure the quantum Hall effect to determine the Landau level structure in the presence of out-of-plane Ising and in-plane Rashba SOC. A distinct Landau level crossing pattern emerges when tuning the charge density and displacement field independently with dual gates, originating from a layer-selective SOC proximity effect. Analyzing the …
Using time-resolved optical Kerr rotation, we measure the low temperature valley dynamics of resident electrons and holes in exfoliated WSe$_2$ monolayers as a systematic function of carrier density. In an effort to reconcile the many disparate timescales of carrier valley dynamics in monolayer semiconductors reported to date, we directly compare the doping-dependent valley relaxation in two electrostatically-gated WSe$_2$ monolayers having different dielectric environments. In a fully-encapsulated structure (hBN/WSe$_2$/hBN, where hBN is hexagonal boron nitride), valley relaxation is found to…
Moire-Engineered Excitonic Landscape and Phonon-Mediated Recombination in Twisted WSe2 Bilayers
Indian Institute of Technology Mandi（印度技术学院曼迪分校）；CSIR-National Physical Laboratory（印度科学工业研究理事会国家物理实验室）；Academy of Scientific and Innovative Research (AcSIR)（科学与创新研究学院）；Indian Institute of Science（印度科学学院）；National Institute of Material Science（国家物质科学研究所）
In monolayer transition metal dichalcogenides, quantum emitters are associated with localized strain that can be deterministically applied to create designer nano-arrays of single photon sources. Despite an overwhelming empirical correlation with local strain, the nanoscale interplay between strain, excitons, defects and local crystalline structure that gives rise to these quantum emitters is poorly understood. Here, we combine room-temperature nano-optical imaging and spectroscopy of excitons in nanobubbles of localized strain in monolayer WSe2 with atomistic structural models to elucidate ho…
Calculations combining first-principles electron-phonon ($e$-ph) interactions with the Boltzmann equation enable studies of ultrafast carrier and phonon dynamics. However, in materials with weak Coulomb screening, electrons and holes form bound excitons and their scattering processes become correlated, posing additional challenges for modeling nonequilibrium physics. Here we show calculations of ultrafast exciton dynamics and related time-domain spectroscopies using $ab~initio$ exciton-phonon (ex-ph) interactions together with an excitonic Boltzmann equation. Starting from the nonequilibrium e…
The spectral and spatiotemporal dynamics of photoluminescence in monolayers of transition metal dichalcogenide WSe$_2$ obtained by mechanical exfoliation on a Si/SiO$_2$ substrate is studied over a wide range of temperatures and excitation powers. It is shown that the dynamics is nonexponential and, for times $t$ exceeding $\sim$50 ps after the excitation pulse, is described by a dependence of the form $1/(t+t_0)$. Photoluminescence decay is accelerated with a decrease in temperature, as well as with a decrease in the energy of emitting states. It is shown that the observed dynamics cannot be …
The twist degree of freedom provides a powerful new tool for engineering the electrical and optical properties of van der Waals heterostructures. Here, we show that the twist angle can be used to control the spin-valley properties of transition metal dichalcogenide bilayers by changing the momentum alignment of the valleys in the two layers. Specifically, we observe that the interlayer excitons in twisted WSe$_2$/WSe$_2$ bilayers exhibit a high (>60%) degree of circular polarization (DOCP) and long valley lifetimes (>40 ns) at zero electric and magnetic fields. The valley lifetime can be tuned…
Twisted layers of atomically thin two-dimensional materials realize a broad range of novel quantum materials with engineered optical and transport phenomena arising from spin and valley degrees of freedom and strong electron correlations in hybridized interlayer bands. Here, we report experimental and theoretical studies of WSe$_2$ homobilayers obtained in two stable configurations of 2H ($60^\circ$ twist) and 3R ($0^\circ$ twist) stackings by controlled chemical vapor synthesis of high-quality large-area crystals. Using optical absorption and photoluminescence spectroscopy at cryogenic temper…
The dielectric environment of atomically-thin monolayer (ML) of semiconducting transition metal dichalcogenides affects both the electronic band gap and the excitonic binding energy in the ML. We investigate the effect of the environment on the in-plane magnetic field brightening of neutral and charged dark exciton emissions in the WSe$_2$ ML. The monolayers placed in three dielectric environments are studied, in particular, the ML encapsulated in hexagonal BN (hBN) flakes, the ML deposited on a hBN layer, and the ML embedded between the hBN flake and SiO$_2$/Si substrate. We observe that the …
Two-dimensional (2D) materials, such as graphene1, boron nitride2, and transition metal dichalcogenides (TMDs)3-5, have sparked wide interest in both device physics and technological applications at the atomic monolayer limit. These 2D monolayers can be stacked together with precise control to form novel van der Waals heterostructures for new functionalities2,6-9. One highly coveted but yet to be realized heterostructure is that of differing monolayer TMDs with type II band alignment10-12. Their application potential hinges on the fabrication, understanding, and control of bonded monolayers, w…
We have combined spatially-resolved steady-state micro-photoluminescence ($μ$PL) with time-resolved photoluminescence (TRPL) to investigate the exciton diffusion in a WSe$_2$ monolayer encapsulated with hexagonal boron nitride (hBN). At 300 K, we extract an exciton diffusion length $L_X= 0.36\pm 0.02 \; μ$m and an exciton diffusion coefficient of $D_X=14.5 \pm 2\;\mbox{cm}^2$/s. This represents a nearly 10-fold increase in the effective mobility of excitons with respect to several previously reported values on nonencapsulated samples. At cryogenic temperatures, the high optical quality of thes…
Among the most common few-layers transition metal dichalcogenides (TMDs), WSe2 is the most challenging material from the lattice dynamics point of view. Indeed, for a long time the main two phonon modes (A1g and E12g) have been wrongly assigned. In the last few years, these two modes have been properly interpreted, and their quasi-degeneracy in the monolayer has been used for its identification. In this work, we show that this approach has a limited validity and we propose an alternative, more general approach, based on multi-phonon bands. Moreover, we show and interpret all the peaks (about 4…
Transition metal dichalcogenides (TMDs) are promising materials for efficient generation of current-induced spin-orbit torques on an adjacent ferromagnetic layer. Numerous effects, both interfacial and bulk, have been put forward to explain the different torques previously observed. Thus far, however, there is no clear consensus on the microscopic origin underlying the spin-orbit torques observed in these TMD/ferromagnet bilayers. To shine light on the microscopic mechanisms at play, here we perform thickness dependent spin-orbit torque measurements on the semiconducting WSe$_{2}$/permalloy bi…
The electronic topology is generally related to the Berry curvature, which can induce the anomalous Hall effect in time-reversal symmetry breaking systems. Intrinsic monolayer transition metal dichalcogenides possesses two nonequivalent K and K' valleys, having Berry curvatures with opposite signs, and thus vanishing anomalous Hall effect in this system. Here we report the experimental realization of asymmetrical distribution of Berry curvature in a single valley in monolayer WSe2 through applying uniaxial strain to break C3v symmetry. As a result, although the Berry curvature itself is still …
The bilayer heterostructures composed of an ultrathin ferromagnetic metal (FM) and a material hosting strong spin-orbit (SO) coupling are principal resource for SO torque and spin-to-charge conversion nonequilibrium effects in spintronics. We demonstrate how hybridization of wavefunctions of Co layer and a monolayer of transition metal dichalcogenides (TMDs)---such as semiconducting MoSe$_2$ and WSe$_2$ or metallic TaSe$_2$---can lead to dramatic transmutation of electronic and spin structure of Co within some distance away from its interface with TMD, when compared to the bulk of Co or its su…
Semiconducting transition metal dichalcogenide monolayers have emerged as promising candidates for future valleytronics-based quantum information technologies. Two distinct momentum-states of tightly-bound electron-hole pairs in these materials can be deterministically initialized via irradiation with circularly polarized light. Here, we investigate the ultrafast dynamics of such a valley polarization in monolayer tungsten diselenide by means of time-resolved Kerr reflectometry. The observed Kerr signal in our sample stems exclusively from charge-neutral excitons. Our findings support the pict…
The electronic states at the direct band gap of monolayer WSe2 at the $K^+$ and $K^-$ valleys are related by time reversal and may be viewed as pseudo-spins. The corresponding optical interband transitions are governed by robust excitons. In double resonant Raman spectroscopy, we uncover that the 2s exciton state energy differs from the 1s state energy by exactly the energy of the combination of several prominent phonons. Superimposed on the exciton photoluminescence (PL) we observe the double resonant Raman signal. This spectrally narrow peak shifts with the excitation laser energy as incomin…
Excitons and trions (or exciton-polarons) in transition metal dichalcogenides (TMDs) are known to decay predominantly through intravalley transitions. Electron-hole recombination across different valleys can also play a significant role in the excitonic dynamics, but intervalley transitions are rarely observed in monolayer TMDs, because they violate the conservation of momentum. Here we reveal the intervalley recombination of dark excitons and trions through more than one path in monolayer WSe$_2$. We observe the intervalley dark excitons, which can recombine by the assistance of defect scatte…
One of the main tasks in the investigation of 2-dimensional transition metal dichalcogenides is the determination of valley lifetimes. In this work, we combine time-resolved Kerr rotation with electrical transport measurements to explore the gate-dependent valley lifetimes of free conduction band electrons of monolayer WSe$_2$. When tuning the Fermi energy into the conduction band we observe a strong decrease of the respective valley lifetimes which is consistent with both spin-orbit and electron-phonon scattering. We explain the formation of a valley polarization by the scattering of opticall…
Monolayer transition metal dichalcogenides, known for exhibiting strong excitonic resonances, constitute a very interesting and versatile platform for investigation of light-matter interactions. In this work we report on a strong coupling regime between excitons in monolayer WSe2 and photons confined in an open, voltage-tunable dielectric microcavity. The tunability of our system allows us to extend the exciton-polariton state over a wide energy range and, in particular, to bring the excitonic component of the lower polariton mode into resonance with other excitonic transitions in monolayer WS…
Vertical and lateral heterostructures of van der Waals materials provide tremendous flexibility for band structure engineering. Since electronic bands are sensitively affected by defects, strain, and interlayer coupling, the edge and heterojunction of these two-dimensional (2D) systems may exhibit novel physical properties, which can be fully revealed only by spatially resolved probes. Here, we report the spatial mapping of photoconductivity in a monolayer-bilayer WSe2 lateral heterostructure under multiple excitation lasers. As the photon energy increases, the light-induced conductivity detec…
Heterostructures formed between two different van der Waals materials enable interactions and functionalities absent in each component. In this work we show that vicinity to an atomically thin WSe$_2$ sheet dramatically impacts the energies of the symmetry-broken low Landau levels of bilayer graphene, possibly due to screening. We present a systematic study of the magnetic field and electrical displacement field dependences of the Landau level gaps at filling factor $ν$ = 1, 2, 3, and compare to BN encapsulated pristine bilayer graphene. The exchange-dominated energy splitting between the N = …
We report an efficient method to observe single photon emissions in monolayer WSe2 by applying hydrostatic pressure. The photoluminescence peaks of typical two-dimensional (2D) excitons show a nearly identical pressure-induced blue-shift, whereas the energy of pressure-induced discrete emission lines (quantum emitters) demonstrates a pressure insensitive behavior. The decay time of these discrete line emissions is approximately 10 ns, which is at least one order longer than the lifetime of the broad localized (L) excitons. These characteristics lead to a conclusion that the excitons bound to d…
The newly developed two-dimensional layered materials provide perfect platform for valley-spintronics exploration. To determine the prospect of utilizing the valley degree of freedom, it is of great importance to directly detect and understand the valley dynamics in these materials. Here, the exciton valley dynamics in monolayer WSe$_2$ is investigated by the two-color pump-probe magneto-optical Kerr technique. By tuning the probe photon energy in resonance with the free excitons and trions, the valley relaxation time of different excitonic states in monolayer WSe$_2$ is determined. Valley rel…
We study the magnetotransport properties of high mobility holes in monolayer and bilayer WSe$_2$, which display well defined Shubnikov-de Haas (SdH) oscillations, and quantum Hall states (QHSs) in high magnetic fields. In both mono and bilayer WSe$_2$, the SdH oscillations and the QHSs occur predominantly at even filling factors, evincing a two-fold Landau level degeneracy. The Fourier transform analysis of the SdH oscillations in bilayer WSe$_2$ reveal the presence of two subbands localized in the top or the bottom layer, as well as negative compressibility. From the temperature dependence of…
We demonstrate a deterministic Purcell-enhanced single-photon source realized by integrating an atomically thin WSe$_{2}$ layer with a circular Bragg grating cavity. The cavity significantly enhances the photoluminescence from the atomically thin layer, and supports single-photon generation with $g^{(2)}(0)<0.25$. We observe a consistent increase of the spontaneous emission rate for WSe$_{2}$ emitters located in the center of the Bragg grating cavity. These WSe$_{2}$ emitters are self-aligned and deterministically coupled to such a broadband cavity, configuring a new generation of deterministi…
Proximity orbital and spin-orbit effects of bilayer graphene on monolayer WSe$_2$ are investigated from first-principles. We find that the built-in electric field induces an orbital band gap of about 10 meV in bilayer graphene. Remarkably, the proximity spin-orbit splitting for holes is two orders of magnitude---the spin-orbit splitting of the valence band at K is about 2 meV---more than for electrons. Effectively, holes experience spin-valley locking due to the strong proximity of the lower graphene layer to WSe$_2$. However, applying an external transverse electric field of some 1 V/nm, coun…
We have systematically examined the circular polarization of monolayer WSe2 at different temperature, excitation energy and exciton density. The valley depolarization in WSe2 is experimentally confirmed to be governed by the intervalley electron-hole exchange interaction. More importantly, a non-monotonic dependence of valley circular polarization on the excitation power density has been observed, providing the experimental evidence for the non-monotonic dependence of exciton intervalley scattering rate on the excited exciton density. The physical origination of our experimental observations h…
Suspended monolayer transition metal-dichalcogenides (TMD) are membranes that combine ultra-low mass and exceptional optical properties, making them intriguing materials for opto-mechanical applications. However, the low measured quality factor of TMD resonators has been a roadblock so far. Here, we report an ultrasensitive optical readout of monolayer TMD resonators that allows us to reveal their mechanical properties at cryogenic temperatures. We find that the quality factor of monolayer WSe2 resonators greatly increases below room temperature, reaching values as high as 1.6E^4 at liquid nit…
