Theoretical Nanophysics
Theoretical nanophysics group studies the quantum and classical phenomena in small electronic systems, with a focus on superconductivity, magnetism, topological media and optomechanics. Our approach is based on phenomenological lowenergy theory of quantum systems. In each project we work in close collaboration with worldleading experimental groups.
See a video explaining research in theoretical condensed matter physics (in Finnish).
Contact person: Tero Heikkilä
Detailed research topics
Our present research focuses on three particular topics:

Figure 1. Dirac lines in AB graphite. Left: momentum space of graphite has two sets of four Dirac lines that merge at the Nexus point (exaggerated view). Right: the pseudomagnetic field describing the lowenergy physics around the Dirac lines exhibits vortices at the Dirac lines. From T. Hyart and T.T. Heikkilä, Phys. Rev. B 93, 235147 (2016). 
 Group members »
 Tero Heikkilä, Prof.
 Subrata Chakraborty, Dr.
 Faluke Aikebaier, M.Sc.
 Teemu Peltonen, M.Sc.
 Risto Ojajärvi, M.Sc.
 News »
 Quantum theory for manipulating nanomagnets (June 2017) (suomeksi tässä)
 Tero Heikkilä was invited as a member of the Finnish Academy of Science and Letters
 See the talks by Tero Heikkilä and the Nobel laureates Duncan Haldane and Michael Kosterlitz in the public event on the Nobel prizes in Physics, organised in Espoo 15.12.2016.
 Researchers beat the quantum limit of microwave measurements (March 2017) (suomeksi tässä)
 Researchers nearly reached the quantum limit with nanodrums (October 2016) (suomeksi tässä)
 When mediated by superconductivity, light pushes matter million times more (April 2015) (suomeksi tässä)
 Heat makes electrons' spin in magnetic superconductors (April 2015) (suomeksi tässä)
 See our work predicting a very large thermophase in superconducting junctions with ferromagnetic insulators (February 2015)
 See our prediction of the amplification of the radiation pressure type coupling between light and matter via the Josephson effect (May 2014)
 See our prediction of a huge thermoelectric effect taking place in superconductorferromagnet interfaces (in Finnish, here is the link to the paper) (Jan 2014)
 See Tero Heikkilä's Science Perspective Cold Atom Thermoelectrics (Nov 2013)
 Videos about our research »
 Tero Heikkilä's talk Superconductor/ferromagnet systems out of equilibrium in the SPICE Workshop "Exotic new states in superconducting devices" 23.10.2017
 See the talks by Tero Heikkilä and the Nobel laureates Duncan Haldane and Michael Kosterlitz in the public event on the Nobel prizes in Physics, organised in Espoo 15.12.2016.
 Recent research
 Spin transfer torque and stochastic magnetization dynamics in the quantum limit
P. Virtanen and T.T. Heikkilä, Phys. Rev. Lett. 118, 237701 (2017)
The state of small magnets containing a single magnetic domain can be described via their magnetisation vector. Typically the size of the magnetisation is fixed to some particular value, but its direction may vary. One way of changing the magnetisation is via the spin transfer torque that is exerted on the magnet by a spinpolarised current injected into the magnet from a nearby ferromagnetic electrode. Under proper conditions, this spin transfer torque may drive the small magnet into a stable precession. As a result, the precession drives a reciprocal effect to the spin transfer torque: spin pumping, i.e., a spin current is injected from the magnet, and converted into a real current in the ferromagnetic electrode. These phenomena have been intensively studied in the past two decades, and they form a basis in the search of new types of methods to create magnetic memories. However, the stochasticity of the spin transfer torque or spin pumping have not been thoroughly studied in the past. We have devised a means to calculate the full probability distribution of magnetisation dynamics and spin pumping, valid in the quantum limit where the precession rate (times the Planck's constant) exceeds the temperature (times Boltzmann constant). Our approach allows for example calculation of transition probabilities, current noise, and other stochastic phenomena in the magnet.  Graphite and its electronic structure »
T. Hyart and T.T. Heikkilä, Phys. Rev. B 93, 235147 (2016)
T.T. Heikkilä and G.E. Volovik Nexus and Dirac lines in topological materials, New J. Phys. 17, 093019 (2015)
Regular graphite that can be found for example in pencils has an intriguing electronic structure. We have shown in our recent work that graphite in its pristine form is neither a regular metal, nor an insulator, but forms a semimetal structure where electronic bands cross each other. In physics such crossings are typically forbidden due to the coupling between such bands, and only allowed in the presence of some symmetry forbidding the coupling. We have shown that the crossing of the bands in graphite happens within a line of momenta, so that graphite is an example of a Dirac line semimetals. This line is "protected" by the mirror symmetries of the graphite structure. What is more, we have also shown that graphite also contains a more rich topological structure, exhibiting a transition between type I and type II Dirac lines, and a nexus point where Dirac lines merge and annihilate each other. This nexus point is an example of the structure dubbed "new fermions" in the recent physics literature, as it host a point of a triple degeneracy of electronic states.  Hightemperature superconductivity in flat band systems »
T.T. Heikkilä and G.E. Volovik, Flat bands as a route to hightemperature superconductivity in graphite, arXiv:1504.05824
V.J. Kauppila, F. Aikebaier, and T.T. Heikkilä, Flat band superconductivity in strained Dirac materials, Phys. Rev. B 93, 214505 (2016)
V. Kauppila, T. Hyart, and T.T. Heikkilä, Collective amplitude mode fluctuations in a flat band superconductor, Phys. Rev. B 93, 024505 (2016)
Traditionally, superconductivity is viewed as a lowtemperature property of materials. Within the BCS theory this is understood to result from the fact that the pairing of electrons takes place only close to the usually twodimensional Fermi surface residing at a finite chemical potential. Because of this, the critical temperature is exponentially suppressed compared to the microscopic energy scales. On the other hand, pairing electrons around a dispersionless (flat) energy band leads to very strong superconductivity, with a meanfield critical temperature linearly proportional to the microscopic coupling constant. We have studied the microscopic theory of superconductivity for different types of (approximate) flat band models, and infer the characteristics of such models, deviating from that of regular superconductors. Our studies may pave the way to construction and detailed understanding of very hightemperature superconductivity in systems exhibiting such flat bands.  Nonequilibrium and thermoelectric effects in superconductorferromagnet hybrid structures »
P. Virtanen, T.T. Heikkilä and F.S. Bergeret, Stimulated quasiparticles in spinsplit superconductors, Phys Rev. B 93, 014512 (2016)
M. Silaev, P. Virtanen, F.S. Bergeret, and T.T. Heikkilä, LongRange Spin Accumulation from Heat Injection in Mesoscopic Superconductors with Zeeman Splitting, Phys. Rev. Lett. 114, 167002 (2015)
F. Giazotto, T.T. Heikkilä, and F.S. Bergeret, Very large thermophase in ferromagnetic Josephson junctions, Phys. Rev. Lett. 114, 067001 (2015)
M. Silaev, P. Virtanen, T.T. Heikkilä, and F.S. Bergeret, Spin Hanle effect in mesoscopic superconductors, Phys. Rev. B 91, 024506 (2015)
A. Ozaeta, P. Virtanen, F.S. Bergeret, and Tero T. Heikkilä, Predicted very large thermoelectric effects in ferromagnetsuperconductor junctions in the presence of a spinsplitting field, Phys. Rev. Lett. 112, 057001 (2014)
Superconductors are characterised by extreme properties: lack of electrical resistance, perfect diamagnetism, poor electronic heat conduction, and typically at most tiny thermoelectric response. We have shown that a hybrid structure consisting of a ferromagnetic insulator and a superconducting film exhibits giant thermoelectric effects, and a very highefficiency thermoelectric device could be constructed from such a hybrid structure. Our finding also indirectly explains seemingly unrelated and previously unexplained observations, such as the longrange spin accumulation observed in such structures. Some of our predictions have been confirmed experimentally (group of D. Beckmann in the University of Karlsruhe).  Amplification close to a quantum limit in optomechanical systems »
C. F. OckeloenKorppi, T. T. Heikkilä, M. A. Sillanpää, F. Massel: Theory of noiseless phasemixing amplification in a cavity optomechanical system, arXiv:1610.07579.
C. F. OckeloenKorppi, E. Damskägg, J.M. Pirkkalainen, T. T. Heikkilä, F. Massel, M. A. Sillanpää, Noiseless quantum measurement and squeezing of microwave fields utilizing mechanical vibrations, Phys. Rev. Lett. 118, 103601 (2017).
C. F. OckeloenKorppi, E. Damskägg, J.M. Pirkkalainen, T. T. Heikkilä, F. Massel, and M. A. Sillanpää, Lownoise amplification and frequency conversion with a multiport microwave optomechanical device, Phys. Rev. X 6, 041024 (2016).
Francesco Massel, T.T. Heikkilä, J.M. Pirkkalainen, S.U. Cho, H. Saloniemi, P.J. Hakonen, and Mika A. Sillanpää, Microwave amplification with nanomechanical resonators, Nature 480, 351354 (2011)
The quality of amplifiers can be characterised by the amount of noise they add to the amplified signal. Quantum mechanics poses a lower limit to this added noise: for large gain (amplification), the added noise to the input signal is always more than half a quantum, corresponding an added energy of hf/2, where h is Planck's constant and f is the signal frequency. The question is how to reach this limit. For optical frequencies (visible light) systems with noise performance very close to the quantum limit have been constructed since the 1990's, but the task has been much harder for setups involving signals in the microwave (GHz) regime. We have shown, both theoretically and experimentally (M. Sillanpää's group in Aalto University performing the experiments) that a system comprising a microwave resonator (antenna) coupled to a highquality micro mechanical resonator can be tuned so that amplification very close to the quantum limit can be obtained. In our recent work a system consisting of two microwave resonators coupled to the same mechanical resonator allows for reaching close to quantum limited performance, and simultaneously allowing for a frequency conversion of microwave signals. This type of setup could also be used to convert quantum information between microwave and optical regimes.  Approaching singlephoton strong coupling regime in optomechanics »
J.M. Pirkkalainen, S.U. Cho, F. Massel, J. Tuorila, T.T. Heikkilä, P.J. Hakonen, and M.A. Sillanpää, Cavity optomechanics mediated by a quantum twolevel system, Nature Commun. 6, 6981 (2015)
T.T. Heikkilä, F. Massel, J. Tuorila, R. Khan, and M.A. Sillanpää, Enhancing optomechanical coupling via the Josephson effect, Phys. Rev. Lett. 112, 203603 (2014)
Optomechanics studies hybrid systems of microwave or visible light quantum optical setups together with vibrating wires. The field has been driven by the analysis of gravitational wave detection in such setups. In typical realisations the coupling between the two parts of the system has been very weak so that the electromagnetic system needs to be heavily pumped so that the physics of this nonlinear dispersive coupling can be studied. We have theoretically shown and experimentally (in M. Sillanpää's group in Aalto University) demonstrated that utilising a superconducting contact and its Josephson effect, this coupling can be greatly enhanced towards the singlephoton strong coupling regime, where a single photon in the electromagnetic cavity would lead to an observable optomechanical frequency shift, for example visible as a photon blockade effect.
 Spin transfer torque and stochastic magnetization dynamics in the quantum limit
 Recent publications, year 2016 »
 C. F. OckeloenKorppi, E. Damskägg, J.M. Pirkkalainen, T. T. Heikkilä, F. Massel, M. A. Sillanpää, Noiseless quantum measurement and squeezing of microwave fields utilizing mechanical vibrations, Phys. Rev. Lett. 118, 103601 (2017).
 S. Baieva, O. Hakamaa, G. Groenhof, T.T. Heikkilä, and J. Toppari: Effect of Stokes shift on dynamics of strongly coupled modes between surface plasmon polaritons and photoactive molecules, ACS Photonics 4, 28 (2017)
 C. F. OckeloenKorppi, E. Damskägg, J.M. Pirkkalainen, T. T. Heikkilä, F. Massel, and M. A. Sillanpää: Lownoise amplification and frequency conversion with a multiport microwave optomechanical device, Phys. Rev. X 6, 041024 (2016) [arXiv:1602.05779]
 T. Hyart and T. T. Heikkilä: Momentumspace structure of surface states in a topological semimetal with a nexus point of Dirac lines, Phys. Rev. B 93, 235147 (2016) [arXiv:1604.06357]
 V.J. Kauppila, F. Aikebaier, and T.T. Heikkilä: Flat band superconductivity in strained Dirac materials, Phys. Rev. B 93, 214505 (2016) [arXiv:1601.04505]
 P. Virtanen, T.T. Heikkilä and F.S. Bergeret: Stimulated quasiparticles in spinsplit superconductors, Phys Rev. B 93, 014512 (2016) arXiv:1511.00817
 J. Arjoranta and T.T. Heikkilä: Intrinsic spinorbit interaction in diffusive normal wire Josephson weak links: supercurrent and density of states, Phys. Rev. B 93, 024522 (2016) arXiv:1507.02320
 V. Kauppila, T. Hyart, and T.T. Heikkilä: Collective amplitude mode fluctuations in a flat band superconductor, Phys. Rev. B 93, 024505 (2016) arXiv:1505.02670
 T.T. Heikkilä and G.E. Volovik: Flat bands as a route to hightemperature superconductivity in graphite, Chapter 6 in the book "Basic Physics of functionalized Graphite" (Edited by Pablo Esquinazi, Springer 2016) [arXiv:1504.05824]
See the complete list of publications in a separate web page.
 Book on the physics of nanoelectronics
Tero Heikkilä's book "The Physics of Nanoelectronics" has been published by Oxford University Press. You can order it from Amazon.
The book has also a separate web site.