Our current research includes investigations on topological insulators, topological superconductors, and Weyl phases. Besides, we focus on the development of novel spintronic devices based on topological phases. Topological insulators are materials characterized by an insulating bulk and topologically protected metallic surface states. In recent years, TIs have witnessed a surge of interest due to their surface states’ remarkable properties that host helical Dirac Fermions with the electron spin locked to the direction of momentum. Topological phases are seen as the potential candidate for new quantum phenomena and new future technological applications in spintronics, low-power electronics, and host for Majorana fermions that might lead to fault-tolerant quantum computation. Our group uses magnetotransport measurements, angle-resolved photoemission spectroscopy, Raman spectroscopy etc. to study the fundamental properties of topological matter. We grow single crystals and thin films. Using these materials, we fabricate mesoscopic devices using e-beam/optical lithography to explore the surface state physics of diverse quantum materials. Some of the exciting developments are listed below.

The discovery of strong topological insulators led to enormous activity in condensed matter physics and the discovery of new types of topological materials. Bisumth based chalcogenides are exemplary strong three dimensional topological insulators that host an odd number of mass-less Dirac fermionic states on all surfaces. A departure from this notion is the idea of a weak topological insulator, wherein only certain surface terminations host surface states characterized by an even number of Dirac cones leading to exciting new physics.

*Simulated crystal structure of (a)BiSe, which consists of a bilayer of bismuth sandwiched between two Bi*_{2}*Se*_{3}* layers. (b) top view of the system. (c) a single unit cell of BiSe (c=22.9Å.)*

Experimentally however, weak topological insulators have proven to be elusive. Here, we present the discovery of a weak topological insulator (WTI), BiSe, of the Bi-chalcogenide family with an indirect band gap of 42 meV. Its structural unit consists of bismuth bilayer (Bi_{2}), a known quantum spin hall insulator sandwiched between two units of Bi_{2}Se_{3} which are three dimensional strong topological insulators. Angle resolved photo-emission spectroscopy (ARPES) measurements on cleaved single crystal flakes along with density functional theory (DFT) calculations confirm the existence of weak topological insulating state of BiSe. Additionally, we have carried out magnetotransport measurements on single crystal flakes as well as thin films of BiSe, which exhibit clear signatures of weak anti-localization at low temperatures, consistent with the properties of topological insulators.

(a) *The ARPES spectrum along the -M direction of the surface Brillouin zone of the BiSe. (b) relativistic surface electronic structure of bismuth bilayer terminated BiSe calculated on (001) plane. SSB states (red box) Dirac-like linear dispersing are indicated. (c) and (d) show ARPES intensity plots along –*M^{0}* and – *M^{“} *directions. Diﬀerence in the energy position of crossing of SSB like bands(E*_{R}*) between (a) and (d) could* *be possibly a clear signature of band bending eﬀect because ARPES spectra was taken after half an hour from the cleaving while later case it was collected after four hour from the cleaving. (e) displays ARPES intensity plot of Bi*_{2}*Se*_{3}* along the -M direction. The bulk and surface states are clearly distinguished and Dirac point (DP) occurs around binding energy *E_{b}* = -0.28 eV.*

(https://aip.scitation.org/doi/full/10.1063/1.4981875)

We study the low temperature electrical transport in gated BiSbTe_{1:25}Se_{1:75}/hexagonal-Boron Nitride van der Waals heterostructure devices. Our experiments indicate the presence of Rashba spin-split states confined to the sample surface. While such states have been observed previously in photo-emission spectroscopy and STM experiments, it has not been possible to unambiguously detect them by electrical means and their transport properties remain mostly unknown. We show that these states support high mobility conduction with Hall eﬀect mobilities 2000 to 3000 cm^{2}/V-s that are paradoxically much larger than the mobilities of the topological surface states 300 cm^{2}/V-s. The spin-split nature of these states is confirmed by magneto-resistance measurements that reveal multi-channel weak anti-localization. Our work shows that Rashba spin split states can be electrically accessed in Topological insulators paving the way for future spintronic applications.

(a) *Schematic of h-BN as the top gate dielectric. (b) AFM topography image of device (scale bar= 5 ). (c) Sheet resistance as a function of temperature at zero gate voltage for devices A and B. (D) Sheet resistance and (e) conductance as a function of top gate voltage at diﬀerent sample temperatures(device A). Inset shows the extracted electronic field eﬀect mobilities at diﬀerent temperatures.*

(https://aip.scitation.org/doi/full/10.1063/1.4971834)

We demonstrate experimentally that a macroscopic topological insulator (TI) phase can emerge in a granular conductor composed of an assembly of tunnel coupled TI nanocrystals of dimension 10nm×10nm×2 nm. These structures are fabricated by pulsed laser ablation. Electrical transport measurements on thin films of Bi_{2}Se_{3} nanocrystals reveal the presence of decoupled top and bottom topological surface states that exhibit large surface state penetration depths ( 30 nm at 2 K). By tuning the size of the nanocrystals and the couplings between them, this new class of TIs may be readily tuned from a non-topological to a topological insulator phase, that too with designer properties. Paradoxically, this seemingly ‘dirty’ system displays properties that are closer to an ideal TI than most known single crystal systems, making granular/nanocrystalline TIs an attractive platform for future TI research.

(a) *Schematic of a granular system composed of ordered TI granules. (b) shows tunnel coupled Dirac fermion states on the surfaces of TI nanocrystals. The cross and dot marks represent the spin polarizations of channels with opposite momenta. t _{1} and t_{2} are the tunnelling amplitudes between intra-grain and inter-grain surfaces respectively.*

(https://pubs.rsc.org/en/content/articlehtml/2011/nr/c7nr01355h)

Surface states consisting of helical Dirac fermions have been extensively studied in three-dimensional topological insulators. Yet, experiments to date have only investigated fully formed topological surface states (TSS) and it is not known whether preformed or partially formed surface states can exist or what properties they could potentially host. Here, by decorating thin films of Bi_{2}Se_{3} with nanosized islands of the same material, we show for the first time that not only can surface states exist in various intermediate stages of formation but they exhibit unique properties not accessible in fully formed TSS. These include tunability of the Dirac cone mass, vertical migration of the surface state wave-function and the appearance of mid-gap Rashba-like states as exemplified by our theoretical model for decorated TIs. Our experiments show that an interplay of Rashba and Dirac fermions on the surface leads to an intriguing multi-channel weak anti-localization eﬀect concomitant with an unprecedented tuning of the topological protection to transport. Our work oﬀers a new route to engineer topological surface states involving Dirac–Rashba coupling by nano-scale decoration of TI thin films, at the same time shedding light on the real-space mechanism of surface state formation in general.

*Growth of Bi2Se3 thin films with varying surface decorations AFM phase image of surfaces for different samples: a) S1 shows 100 nm wide nanoflake like features, scattered 3D nuclei and small density of nanoribbons b) S3 shows nanoribbons that grow along the step edges in the [110] direction. Lower panels show the corresponding X-ray pole figures measured at the {105} peak. The peak broadening is smaller for S3 compared with S1 showing increased coupling between adjacent quintuples. c) Constant current STM images of sample S5 show atomically smooth surfaces with large terrace widths. Inset shows the six-fold symmetric Low energy electron diffraction (LEED) pattern d) Height profile of 1-2 in c) showing quintuple layer height ∼ 1nm. e) Atomic resolution image (tunneling current IT = 3.1 nA, bias UT = 50 mV) of a flat terrace with in-plane lattice constant of 0.5 nm. f)Auger electron spectrum showing the presence of Bi NVV Auger line at 101 eV and Se MVV at 43 eV. From the relative intensities of these Auger peaks, considering their sensitivities, we obtain the ratio of Bi:Se to be about 0.7. Here N and M denote core shells and V represents valence band. g) Standard θ − 2θ XRD scan shows identical results for all samples. All {0 0 3n} peaks are visible implying a highly c-axis oriented film. h) Histogram showing particulate coverage of samples S1-S5 analysed from AFM surface topography images. Particulate coverage decreases from S1 to S5.*

*(a)Magnetoresistance of samples S1–S5 at T=2 K. (b) Fitting of low-field magnetoconductance to the WAL equation for sample S2. (c) Ingap Rashba states and topological surface states are coupled when the interband scattering rate is larger than phase breaking rate. The two channels get decoupled with rising temperature when phase breaking rate dominates over inter band scattering rate. (d) Number of channels A contributing to WAL for samples S1 to S5**.*

https://iopscience.iop.org/article/10.1088/1361-648X/aa666a/meta

For the first time, we demonstrate topological insulator (TI) thin films that achieve surface dominated conduction while simultaneously exhibiting highly enhanced quantum coherence of surface state carriers. Achieving these two seemingly antagonistic goals has proved to be one of the most enduring challenges of this field. Our solution to this problem is predicated on the hitherto unexplored, and rather non-trivial role played by *structural disorder* in TIs.

Conventionally, surface-state dominated conduction has been obtained in topological insulators by compensation doping of residual bulk carriers in the Bi_{x}Sb_{(2-x)}Te_{y}Se_{(3-y)} class of materials. However, recent works including ours have shown that compensation doping also introduces significant electronic disorder, that leads to strong dephasing of surface state carriers. This is detrimental to future applications of TIs, that will inevitably rely on large quantum coherence of topological carriers. These two goals, that is, of achieving surface dominated transport, and obtaining superior carrier coherence, have therefore turned out to be antagonistic. Here, we consider a hitherto unexplored route towards achieving these two goals simultaneously. We recall that bulk conductivity *σ=enμ*, where *n *is the carrier density and *μ* is the mobility. While compensation doping tries to suppress σ by decreasing the bulk carrier density *n*, our idea is to suppress *μ* instead. To this end, we use finely tuned structural disorder in our samples. Such disorder leads to significant degradation of bulk carrier mobility while leaving the surface state mobility intact, due to its inherent topological protection against scattering.

While, our samples indeed achieve surface dominated conduction with the two topological surface states electronically decoupled from each other, we also evince a completely different mechanism of decoherence of topological surface state carriers. In conventional 2D electronic systems, including previous experiments on thin films of TIs, electronic dephasing at low temperatures is usually due to Nyquist electron-electron interactions where the dephasing length L_{Φ}~T^{-0.5 }(T being the temperature). On the other hand, in our experiments, we obtain a completely different dephasing regime with L_{Φ}~T^{-1}. It is immediately obvious that such a power-law dependence will produce much larger values of L_{Φ} at lower temperatures compared to standard e-e interactions. Indeed, we obtain L_{Φ} as large as ~650-700nm, which is the highest value reported till date for a surface-dominated TI. We argue that this new dephasing regime is dominated by direct electron-electron interaction between the top and bottom topological surface states. The carriers on opposite surfaces interact with each other and exchange energy at a rate that exactly produces L_{Φ}~T^{-1}

*(a) and (b) AFM images of samples with crystallite sizes of 150nm and 50nm respectively (c) Resistance vs temperature measurements for samples with different thicknesses (d) Sheet conductance G _{sh} vs thickness*

*(a) Parallel field magnetoconductance for different sample thicknesses at T=2K (b) Surface state coupling parameter **b** obtained by fitting of the MC data (c) **a** and **b**as a function of sample thickness at T=2K (d) s=i _{z}/i_{x} as a function of temperature obtained from *

To probe deeper into the mechanism of these striking observations, we perform comprehensive magnetotransport studies with magnetic fields aligned parallel to the sample plane and estimate the bulk currents. We show that the decoupling of surface states and enhanced coherence are both a direct result of suppression of residual bulk currents due to structural disorder. Finally, as a smoking gun proof of our hypothesis, we perform a disorder dependent study (while keeping the sample thickness fixed) and show conclusively that the localization of bulk states is indeed responsible for driving our samples into a regime with conductance dominated by surface states, and dephasing dominated by frictional coupling between the two topological surface states.

In a nutshell, our work has several unprecedented ramifications: i) it introduces the idea of using structural disorder to tune conductivity in topological insulators ii) achieves surface dominated transport in TI thin films with decoupled surface states ii) Achieves highly enhanced quantum coherence lifetimes of surface states carriers iv) Opens up a new regime of electronic dephasing in TIs dominated by Coulomb drag between opposite surface states.

https://aip.scitation.org/doi/10.1063/1.5033428

Studies of electronic dephasing in metallic and semiconducting systems are not only important for designing high coherence quantum devices, but also for gaining fundamental new insights into diverse physical properties of systems at energy scales as low as a few μeVs, that is otherwise impossible using conventional spectroscopic or transport tools. While different systems may display different types of electronic decoherence mechanisms, it is generally accepted that a single system/sample can exhibit only one characteristic decoherence mechanism. In fact, such experiments have often been treated as a unique ‘fingerprint’ to a given system.

In this work, we challenge this idea and demonstrate the existence of two distinct dephasing mechanisms governing electron dynamics in the same physical system. We perform exhaustive dephasing measurements on BiSbTe_{1.25}Se_{1.75 }belonging to the most important 3D topological insulator (TI) class discovered so far and reveal the presence of different dephasing mechanisms governing different regions of the topological surface state wave-function. To rule out the possibility of any extrinsic effects, our devices are fully prepared inside an Argon glove box (<0.1 ppm of O_{2}) and capped with insulating hexagonal-Boron Nitride. This is a tremendous advantage compared to previous experiments where devices are often exposed to the ambient, and the capping material is not chemically inert. The key idea of our experiment is a comparison between surface-contacted and edge-contacted TI devices. Owing to the layered nature of this material, the surface contacted device topology probes only the top-most quintuple layers of the sample. On the other hand, an edge-contact topology provides uniform electrical contact to all quintuple layers and measures the sample uniformly. Our innovation lies is using this idea to perform a layer resolved dephasing study of our devices.

*(a) Optical image of a surface contacted device. (b) Schematic of surface-contacted measurement configuration and the corresponding resistance network model. R _{ch,i}, indicates the resistance of the i^{th} layer from the top, which is exacted to vary according to the distribution of the topological surface state wave-function ψ(z). (c) R_{xx} as a function of V_{TG} and V_{BG} for a surface contacted device(SC-1). (d) Optical image of an edge contacted device (e) Schematic of edge- contacted measurement configuration and resistance model. Note that the edge-contact electrode directly connects with each layer through a resistance R_{E}. (f) R_{xx} as a function of V_{BG} for an edge contacted device(EC-1)* On the sample surface, we obtain electronic dephasing governed by variable range hopping (VRH) type transport of charge carriers. On the other hand, a few quintuple layers away from the top surface, the dephasing mechanism dramatically changes to exhibit conventional Nyquist type electron-electron interaction as the primary source of decoherence. Three unique signatures are used to distinguish the two mechanisms: i) Different power laws governing the temperature dependence of the phase coherence length L

*(a) Magnetoconductance as a function of temperature for surface contacted sample SC-1. The low-field fits to the HLN formula are shown in solid black lines. (b) Lφ and (c) α as a function of temperature for devices surface contacted devices. (d) Magnetoconductance and HLN fitting for edge contacted sample EC-1 (e) Lφ and (f) α as a function of temperature for edge contacted devices*

We explain this behavior as a peculiar interplay between the response of the topological surface state (TSS) wave-function to the local disorder environment and screening of the disorder potential by the TSS wave-function itself. The net effect is a weakly screened disorder potential at the top-most layers of the sample leading to strong scattering of the VRH type, and significantly enhanced screening by the part of the wave-function residing in the bulk, resulting in much milder dephasing due to electron-electron interactions. The role of disorder in compensated TIs has been the subject of much recent debate, and our results provide a striking advance in this direction. In fact, our experiments contradict existing models of charge transport in compensated Tis and indicate a need for substantial revision of the latter.

To the best of our knowledge, such spatial variation of the electronic dephasing mechanism has never been observed in any electronic system. In the context of TIs, our observation of the VRH-type dephasing mechanism, its variation with chemical potential and its spatial decay with distance from the top surface offers a fundamentally different way of thinking about electronic dephasing in compensated topological insulators of the Bi_{x}Sb_{(2-x)}Te_{y}Se_{(3-y)} class. It is noteworthy that several recent breakthroughs in condensed matter physics were directly based on this material system. Our work answers several important questions surrounding topological charge transport and the role of disorder in these materials, that has bothered the community for several years now.

We also believe that similar anisotropic dephasing may exist in a wide class of two-dimensional materials (like MoS_{2}, WSe_{2}, etc.) that have recently come under intense investigation. Our edge-vs-surface method of performing spatially varying dephasing experiments may provide crucial impetus to quantum coherence studies in such systems.

(https://journals.aps.org/prb/abstract/10.1103/PhysRevB.98.155423)

In 2008, Fu and Kane’s landmark work envisaged inducing superconductivity into the surface states of a three-dimensional topological insulator (3D-TI) by the superconducting proximity effect. Proximitized topological surface states can host the exotic two-dimensional p-wave superconducting phase. Such superconductors are topologically non-trivial and support gapless Majorana modes circulating at the edges of the sample. Decoherence free Majorana modes hold the promise of future quantum computing technologies, apart from providing grounds for unprecedented fundamental physics investigations. Yet, despite a decade of intense effort, experimental evidence of topological superconductivity on the surface of a 3D-TI remains elusive. Three major roadblocks have prevented progress: i) Most investigations of proximity effects have been performed on bulk conducting TIs like Bi_{2}Se_{3}. The large bulk conductivity of such materials prevents signatures of surface topological superconductivity to manifest. ii) Previously, only 3D superconductors like Nb and Sn have been used for proximity effect studies. There is an intrinsic Fermi surface mismatch between a 3D superconductor and 2D topological surface states. This prevents a strong overlap of wave-functions and dilutes the proximity coupling. iii) Lack of chemically homogenous interfaces. Unless the chemical identities of materials on the superconductor (SC) and TI side are similar, it is natural that proximity effect will be weak.

In this work, we address all these problems. We chose the bulk insulating topological insulator BiSbTe_{1.25}Se_{1.75} for our experiments and fabricate atomically sharp heterostructures with thin layers of NbSe_{2} in which two-dimensional superconductivity has been recently discovered. The atomically pristine nature of the SC-TI interface and the similar chemical identities (Selenium termination on the exposed surfaces) of the materials allows a strong proximity effect to manifest. Furthermore, bulk conductivity in our samples becomes undetectable below 100K. The superconducting proximity effect therefore arises purely out of the topological surface states.

Using differential conductance measurements, we provide three distinct signatures of topological superconductivity in our samples: i) Dual gap differential conductance spectrum. The smaller gap arises from the proximitized topological surface state, while the larger gap corresponds to NbSe_{2}. ii) Asymmetric differential conductance arising out of the linear density of states of the topological surface states. With sample temperature or in-plane magnetic field tuned just enough to kill the proximity effect, but not the superconductivity in NbSe_{2}, we observe that the asymmetry vanishes. iii) Differential conductance ripples appearing at biases significantly larger than the superconducting gap. The ripples disappear when bulk superconductivity is killed, indicating their superconducting origin.

*(a) 2D color plot of differential conductance as a function of temperature and source- drain DC voltage bias VSD (b) Normalized differential conductance G(2K)/G(10K) showing a two- gap structure. The black and red dots track the evolution of coherence-like peak A1(A2) and B1(B2) respectively (c) Differential conductance ripples ∆ _{1} and ∆_{2} that exist at biases larger than the superconducting gap. Black dots trace their evolution with increasing temperature. (d) Evolution of the width and intensity of peak A1 with increasing temperature (e) Evolution of position of the conductance dip at ∆_{1} with increasing temperature.*

We focus specifically on the third aspect and its rather anomalous nature. After ruling out other trivial possibilities, we show that such signatures naturally arise out of two-dimensional topological superconductivity in 3D TIs. Using extensive calculations based on a simple tight-binding model and a more sophisticated Green’s function method, we show that topological surface states under the action of a superconducting proximity effect manifest several mini-gaps appearing, rather anomalously, at biases much larger than the superconducting gap. This arises as a peculiar level repulsion effect at high energies that is needed to create a zero energy Majorana bound state and is a smoking gun signature of topological superconductivity. In fact, we prove that such a signature cannot arise if the system does not host Majorana zero modes.

The remarkable match between our experiments and theoretical calculations suggest that topological superconductivity is indeed evinced in our devices. Combined with the two other signatures of superconducting proximity effect, our experiments demonstrate robust superconductivity of topological surface states in a bulk insulating topological insulator for the first time. Our work solves a decade-old problem and brings Fu and Kane’s original idea closer to reality.

(https://pubs.acs.org/doi/abs/10.1021/acsnano.8b07550)

Our work constitutes the first experimental demonstration of the electrical transport in n-p-n junctions of a three-dimensional topological insulator in the quantum Hall regime.

The quantum Hall effect in topological insulators arises as a combination of quantization of Dirac fermions belonging to the top and bottom topological surface states and has been observed recently in experiments conducted on bulk insulating topological insulators. While quantum Hall effect in graphene arises from the quantization of four species of Dirac fermions (accounting for the spin and valley degeneracies), the surface of a topological insulator hosts only one species of Dirac fermions, making it behave as “a quarter of graphene”. This not only leads to the exotic half-integer quantum Hall effect, but also results in the formation of quantum Hall edge states that are automatically spin-polarized due to spin-momentum locking. More fundamentally, the conventional picture of quantum Hall edge states that is applicable for two-dimensional systems, is replaced by more general topological criterion for edge state formation in a 3D topological insulator. This happens because surface states in a 3D TI live on a closed surface enclosing a 3D bulk, with no real boundaries.

While the differences between quantum Hall effect in a topological insulator and graphene (or other two-dimensional electron gas systems) are startling, the simple experimental geometries used to probe quantum Hall effects in 3D-TIs till date have been unable to probe these differences. On the other hand, quantum Hall effect experiments on p-n junction structures of topological insulators can clearly elucidate these differences and manifest the *topological* aspects of quantum Hall effects in TIs. Apart from providing grounds for fundamental new insights, p-n junction structures of 3D-TIs have also been theoretically shown to be of enormous technological importance. The quantum Hall edge states in TIs are spin-momentum locked and can be used to design perfect spin-filters and Datta-Das type spin-field effect transistor devices where gate voltages can be used to tune the chirality and hence spin-polarization of edge states, leading to perfect resistance manipulation from 0 to 1(units of h/e^{2}).

In this work, we fabricate bulk insulating topological insulator (BiSbTe_{1.75}Se_{2.25}) devices where the top and bottom surfaces of the sample are exposed to dissimilar electrostatic environments created by a combination of local and global gating. This not only breaks the vertical structural inversion symmetry of the system, but also generates n-p-n type double junctions on both the top and bottom surfaces of the sample. When quantizing magnetic fields are applied, we obtain enhanced or suppressed electrical conductance depending upon the chirality of 1D edge states appearing centrally gated and back gated regions, manifesting as a sequence of resistance peaks and plateaus. To model these junctions, we use a combination of electrostatic charging analysis and the Landauer-Buttiker formalism for one-dimensional edge state propagation. We show that the electrostatics of the system gives rise to four distinct filling factors, corresponding to 6 quantum Hall edge modes that propagate along the side walls and p-n junction boundaries on the top and bottom surfaces of the sample. Mode mixing between these channels in the unipolar and bipolar regimes gives rise to the observed resistance peak-plateau structure. Additionally, the exact values of resistance plateaus indicate a lack of spin-degeneracy, as expected for a TI but not experimentally proven before. Such lifting of spin-degeneracy is possible only in ultra-clean graphene samples and in large magnetic fields. Its observation in TIs at rather low magnetic fields opens up the route to using spin-momentum locked edge states for a panoply of spintronic device applications.

*(a) Schematic of a topological insulator n-p-n structure formed by a combination of local top gating and global back gating. Schematic showing electron and hole densities in different regions of the device in (b) p-n-p (c) n-p-n (d) p-p-p and (e) n-n-n configurations. The voltages on the top and bottom gates required for the different charge configurations are chosen to correspond to a particular device*

In a nutshell, the demonstration of electrically abrupt n-p-n junctions and quantization of transport across these devices are landmark achievements in topological insulator research and will constitute testing grounds for several theoretical proposals based on such structures, apart from providing fundamental insights into quantum Hall effects in topological insulator systems.

*(a) Schematic of the measurement configuration of a topological insulator n-p-n structure formed by a combination of local top gating and global back gating. In the quantum Hall regime, electrical current is carried by quantum Hall edge modes with chiralities that depend on the type of the charge carrier. (b) Optical micrograph of device A. Red and blue dotted lines represent the outlines of the BSTS and h-BN flakes respectively. (c) Rxx (left) and Rxy (right) as a function of VTG at a fixed VBG=-10.8V. Rxx measured at zero magnetic field, Rxy measured at B=7T. (d) 2D color map of Hall resistance Rxy (B=7T) and (e) Rxx (B=0T) as a function of VTG and VBG . The ‘vertical’ and ‘horizontal’ dotted lines indicate the charge neutrality points of the bottom and top topological surface states respectively.*

* (a) 2D color map of Rxx as a function of VBG of top gate voltage at VBG=3V, -3V and -10.2V. The peak-plateau structure is clearly visible. The dashed lines indicate the plateau regions. (c) Rxx as a function of back-gate voltage at fixed top gate voltage VTG=0.15V. A distinct plateau appears at Rxx =1.5 h/e2.(d) Rxx vs VTG as a function of magnetic field measured at VBG=-1.5V (e) Landau fan plot obtained by plotting the first difference dRxx vs VTG as a function of magnetic field (f) Trajectories of the peak at Rxx = 1.5 h/e2(upper panel) and Rxx = 1.33 h/e2(lower panel) plateaus as a function of magnetic field.* (https://pubs.rsc.org/en/content/articlehtml/2019/nr/c8nr10306b)

Our work proves for the first time that the anomalous Bose metal state observed in disordered superconductors is truly a “quantum” metal and is borne out of purely quantum mechanical effects. Cooper pairs, being Bosons, can exist in one of two states: a localized insulating state, or a superfluid state with zero resistance. However, in two dimensions, experiments over the last two decades have shown surprising evidence for a metallic state of Cooper pairs. It is not clear why such a state occurs. Various theoretical models have approached the subject from different directions, however a clear consensus is far from reached.

*Electrical transport measurements in low-dissipation configuration, Config-1 with Zs = 1014Ω (a) Resistance (R) versus temperature (T) measurements at different magnetic fields (b) 2D color plot of sample resistance as a function of magnetic field (H) and Temperature(T) (b) Arhenius plots showing log(R) vs. 1/T at different magnetic fields. Solid black lines indicate linear fits, indicating thermal fluctuation induced motion of vortices. The saturation of resistance at lower temperatures indicates the onset of the Bose metal phase (d) Energy barrier U(K) to vortex motion as a function of magnetic field (H). The solid line indicates a linear fit to the depicted empirical form.*

While it is understood that quantum fluctuations that become strong in reduced dimensions may lead to this state, the lack of a direct proof that the Bose metal phase is of quantum mechanical origin is at the heart of the controversy surrounding this field. In this work, we lay this controversy to rest by unambiguously demonstrating that the Bose metal phase is entirely driven by quantum phase fluctuations, and that killing the quantum phase fluctuations also leads to a complete suppression of the Bose metal phase and restores a fully superconducting state.

(a) Electrical transport measurements in high-dissipation configuration, Config-2 with Zs = 106Ω (a) Resistance (R) versus temperature (T) measurements at different magnetic fields (b) 2D color plot of sample resistance as a function of magnetic field (H) and Temperature(T) (c) Arhenius plot showing log(R) vs. 1/T at different magnetic fields. Solid black line indicates linear fits. Beyond the linear regime, the sample immediately obtains a zero resistance state (d) Energy barrier U(K) to vortex motion as a function of magnetic field (H). The solid line indicates a linear fit to the depicted empirical form. Our experiments are performed on clean 2D layers of NbSe_{2} where the Bose metal phase has been recently observed. To prove that the Bose metal phase originates from quantum phase fluctuations, we use a simple but ingenious method to suppress quantum fluctuations of the order parameter. This is achieved by coupling the device to an environment with very low impedance. Quantum phase fluctuations lead to fluctuations of the voltage across the sample in the microwave regime. A low impedance environment acts as a sink for these voltage fluctuations, thereby suppressing the quantum phase fluctuations.

*(a) R vs H for the two measurement configurations. Bose metal resistance RBM is obtained by subtracting the high impedance resistance from low impedance resistance (b) Color plot showing RBM as a function of T and H (c) Magnetoresistance of the Bose metal phase at different temperatures (d) Full H-T phase diagram of the device.*

When quantum phase fluctuations are left untouched (high impedance environment), clear signatures of the Bose metal phase are observed with the sample resistivity saturating to a non-zero value in the zero-temperature limit. However, when the same device is coupled to a low impedance environment, quantum phase fluctuations are strongly damped, and the Bose metal phase is fully quenched restoring a perfectly superconducting state. This is a striking, and direct signature of the fact that the Bose metal is a true “quantum” metal.

Our experiment, for the first time, proves without any doubt the quantum mechanical origin of the Bose metal phase and paints a crystal-clear picture of this phase in NbSe_{2}. Using this technique, we perform a thorough characterization of the Bose metal resistance, obtaining a new phase diagram, and power law turn on exponents that are in complete agreement with the recent theory treating Bose metals as a phase glass, while providing new insights that are not captured by any known model yet.

A versatile van der Waals epitaxy of BiTe, a newly discovered dual TI and a predicted higher order topological insulator (HOTI) thin film on muscovite mica is demonstrated using pulsed laser deposition. Topographic, structural and XPS analyses confirm the chemical homogeneity and high crystalline quality with large-area coverage with atomically smooth surface. The magneto transport data reveals weak anti-localization and electron-electron interaction driven insulating ground state with n-type character. An elaborate thickness, temperature and magnetic field dependence of transport data indicates a transition from coupled, partially coupled and fully decoupled surface states wherein 3D electron-electron and electron-phonon scatterings play significant role in dephasing mechanism, unlike 2D electron-electron dephasing in most TIs. Also from the fitting of the resistivity upturn we found that the coulomb screening factor (F) in thicker samples turns out to be negative which indicates the presence of the electron phonon coupling in those samples.

*(a) XRD scan of BiTe film on mica(001) and of bare mica, (b) Pole figure (log plot) of BiTe (1 0 9), (c) AFM image of the surface (10 μm × 10 μm area) topography of the BiTe film on Mica (Inset is 1 μm × 1 μm area scan), (d) Schematic illustration of BiTe/mica heterostructure via the van der Waals heteroepitaxy*.

*(a) Normalized magneto-resistance curve for different thicknesses at T = 2 K, (b)Low-field magneto-conductance data (symbols) along with HLN fit (solid red lines) for 30 nm BiTe thin film at various temperatures. Temperature dependence of extracted (c) α, the prefactor and (d) the phase coherence length (l) versus Temperatrure for different thickness. Lower inset shows β for different thickness. Solid straight lines indicate the fitting.*

In this work, we have studied the transport properties of two different single crystals, Sb2Te2Se and Sn-doped Sb2Te2Se. By analyzing the Shubnikov–de Haas oscillations for the devices made from both the crystals, we have extracted the Berry phase. The non-trivial value of the Berry phase for both the samples unambiguously indicates the robustness of the topological surface states against the impurity doping. The parent compound is n-type due to excess Te vacancies, and we could show from the sign of the intercept in the Landau level fan diagram and from the Hall effect measurements that doping with Sn makes it p-type. This demonstrates the tuning of the Fermi level in a topological insulator upon Sn doping.

*Sn-doped Sb2Te2Se: (a) AFM image of the device. The longitudinal (V _{xx}) and transverse (Hall,V_{xy}) geometries are also shown. (b)The perpendicular and parallel MR of the same sample. The parallel MR hardly shows any oscillation, whereas the perpendicular MR has clear SdH oscillations. (c) SdH oscillations in the reciprocal magnetic field at different temperatures. (d) Temperature dependence of the SdH oscillation amplitudes at a particular magnetic field. Fitting with temperature dependence part of the Liftshitz-Kosevich formula yields the effective mass of the electron. The inset shows the fast Fourier Transform corresponding to the oscillation at 2 K.*

*The undoped sample (Sb2Te2Se): (a) Lifshitz–Kosevich fit to the SdH oscillation at 2 K. (b) Landau fan diagram. (c) Linear Hall data indicating electrons as the carrier. (d) Schematics for Fermi level tuning by Sn doping.*

https://aip.scitation.org/doi/10.1063/5.0040697

- Ambili KK
- Gagan Rastogi
- Abinab Mohapatra
- Devyani
- Sunetra Srutakirti Khatua
- Pranay Ghosh

- Dr. R. Ganesan (IISc, Bangalore)
- Prof. Biju Sekhar (IOP Bhubaneswar)
- Prof. Umesh Waghmare (JNCASR, Bangalore)
- Prof. Diptiman Sen (IISc Bangalore)
- Prof. Sudipta Roy Barman (CSR Indore)

- Dr. Abhishek Banerjee
- Dr. Kunjalatha Majhi
- Dr. Anil Yadav
- Dr. Nagaiah Kambhala
- Dr. Debarghya Mallick
- Dr. Shoubhik Mandal
- Dr. Minna Theres James